The Belly of Capitalism

Much Less Low Volatility Stocks This Week

2007-01-28T15:21:00.000-05:00

Categories: stock options, volatility, delta neutral
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New Batch of Low Volatility Stocks

2007-01-15T09:36:00.000-05:00

Click on the snapshots below to see the rest of the list.

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Happy New Year!

2007-01-03T09:52:00.000-05:00

Click on the snapshots below to see the rest of the list.

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More Low Volatility Stocks

2006-12-18T09:17:00.000-05:00

Click on the snapshots below to see the rest of the list.

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This Week Low Volatility Stocks

2006-12-11T08:56:00.000-05:00

The list of stocks at their lowest volatility reading for the year is getting shorter:

Click on the snapshots below to see the rest of the list.

Categories: stock options, volatility, delta neutral
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Low Volatility Stocks

2006-12-03T10:00:00.000-05:00

This week scan is still loaded:

Click on the snapshots below to see the rest of the list.

The following charts show that the implied volatility index is at his lowest values since quite a while:

Categories: stock options, volatility, delta neutral
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A Lot of Low Volatility Stocks This Week!

2006-11-27T10:00:00.000-05:00

I don't rememember to have seen so many stocks with relative low implied volatility as this week and so many of them hitting the lowest value of the year. It wasn't so long ago that I was remarking how few opportunities were out there.

Click on the snapshots below to see the rest of the list.

Categories: stock options, volatility, delta neutral
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This Week Scan for Low Volatility Stocks

2006-11-20T07:48:00.000-05:00

Here we go again:

Categories: stock options, volatility, delta neutral
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Another Low Volatility Scan

2006-11-12T13:47:00.000-05:00

Stocks with relatively low implied volatility but with large open interest and sufficiently high price, as of the end of last week:

Categories: stock options, volatility, delta neutral
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Effects of the Change of Delta

2006-11-11T11:57:00.000-05:00

The following charts show the minute by minute price during the last ten trading days of the underyling security and of the call and put contracts composing my last delta neutral portfolio. The call and put charts have the corresponding delta values at the end of each trading day.

The following spreadsheet shows the price and the greeks of each option contract as they change as the undelrlying asset price and volatility change. The column named "theoretical" reports the theoretical contract price to be compared with the actual end of day price of the contract. The column named "effective" reports the effective delta resulting from the actual market price changes of both contracts and underlying stock to be compared with the theoretical delta.

Notice the considerable difference between the theoretical delta values and the effective ones at the end of 10/31/2006. The spreadsheet below show the position performance if I had used the effective delta values to build it. It would have been a gain of 44% instead of nothing. The following spreadsheet shows what actually happened.

This spreadsheet reports prices and greeks for AMGN. The agreement between actual values and theoretical values is good. The position lost money because AMGN was threading water.

The prices and greek values for UNH are in the spreadsheet below. Here again I can see a discrepancy between the theoretical and effective values of the delta.

If I had used the effective values the gain in this position would have been of 23% instead of 14%:

Categories: stock options, volatility, delta neutral
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Analysis of Each Position

2006-11-05T13:26:00.000-05:00

I broke even on my DNA position. However, that is disappointing because it did move quite sharply.

The AMGN position lost 6.19%. Here again there was a move though not as clean cut as DNA. These positions might have been incorrectly built.

The UNH position yielded 13.93% though the move was quite churning.

Categories: stock options, volatility, delta neutral
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Closed Portfolio at Break Even

2006-11-05T13:16:00.000-05:00

I closed all positions on Friday essentially breaking even on the initial capital invested. I could never open a position in either PAYX, NCC and CBH because of lack of liquidity in the contracts. The following spreadsheet shows the sale transactions closing each position:

The values of the greeks are as at the close of the previous day.

The following spreadsheets show the mark to market value of each position at the end of trading for all the days of the week (including the last day after I closed the portfolio):

The greeks in these spreadsheets are all calculated at the close of the trading day.

Categories: stock options, volatility, delta neutral
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New Portfolio Open for Business

2006-10-31T09:50:00.000-05:00

The following spreadsheet shows the trades that opened the positions of this week delta neutral portfolio:

I made a few changes to the spreadsheet. The columns are commission paid per contract, date of the transaction, security ticker, strike price of the contract, theoretical price of the contract per share of the underlying security, actual price (of the transaction or marked to market), implied volatility of the underlying security, delta of the contract, gamma of the contract, vega of the contract, number of contracts, action (1 means buy, -1 means sell or mark to market), cost of the transaction (a negative value represents the proceeding of a sale or the mark to market value of the position), total delta of the position, total gamma of the position, total vega of the position.

The following spreadsheet shows the portfolio marked to market at the end of yesterday trading:

Categories: stock options, volatility, delta neutral
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Low Volatility Scan

2006-10-29T18:14:00.000-05:00

Here is the list of stocks with low implied volatility at the end of last week:

Categories: stock options, volatility, delta neutral
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In-Depth Review of each Position

2006-10-29T17:04:00.000-05:00

I lost 9.84% with GILD. It was just churning. Excellent opportunities with GILD did exist at the beginning and at the end of September and again at the beginning of October. Note the extended period of low volatility in September and October.

The AXP position lost 11.82%. It was consolidating with decreasing volatility. The move was not large enough.

The CBH position lost 24%. Again, just churning resulting in decreasing volatility.

With JNJ I lost 7.72%. It consolidated after a big move.

The OEX position was slightly profitable with a 5.66% gain. Notice the stairway pattern of a sharp move after a long consolidation. However, the jump is never sufficiently large to produce a big gain.

UNH was a break even. It was in a consolidation pattern.

Overall, a week of poor opportunities.

Categories: stock options, volatility, delta neutral
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What If?

2006-10-29T09:33:00.001-05:00

This spreadsheet shows again the trades opening all the positions:

The following spreadsheets show the mark to market value (as a negative cost) and the performance of each position and of the entire portfolio at the end of each trading day of the week if I had done nothing:

I also show the theoretical value, the delta and the vega for each contract.

Clearly, the only way to make money from this portfolio was to close it intraday on Monday. The loss at the end of the week is larger than the one that I actually had.

Categories: stock options, volatility, delta neutral
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Closed the Portfolio with a Small Loss

2006-10-27T11:49:00.000-04:00

I had problems blogging this week. Things seems to be back on track now.

These trades opened the positions of the delta neutral portfolio of this week:

I added a few columns to the trade spreadsheet. After the security ticker I have the strike price of the contract and the theoretical value of the contract per share calculated using the IVolatility basic calculator. After the price of the transaction I have the delta and the vega calculated using the basic calculator.

These trades closed all positions:

After the delta column I have the performance of each position.

Categories: stock options, volatility, delta neutral
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Scan for Next Week Opportunities

2006-10-22T09:36:00.001-04:00

As of the end of trading last week the scan for low implied volatility stocks provides the following result:

Not that many opportunities. In fact, they are even less if we filter out mergers and buy-outs. FSL agreed on September 15 to to sell itself to a private-equity consortium led by the Blackstone Group for $17.6 billion, or $40 per share. UNV is being purchased by a group of private equity firms and media mogul Haim Saban for $12.3 billion, or $36.25 in cash per share. HCA is about to go private in a $21 billion management-led leveraged buyout. CVC received an offer by the Dolan family to buy all the shares they do not already own for $27 a share.

The following charts show the price and standard deviation of the remaining stocks over the past year of trading:

The following charts focus on the past two months:

Categories: stock options, volatility, delta neutral
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Performance of Each Trade

2006-10-08T10:53:00.000-04:00

I will be traveling in the next two week and I will not trade. It's a good time to post the performance of all the delta neutral trades (mostly straddles) that I have executed so far:

For each underlying security I print the date of the trade, the cash used to make the trade, including commissions (cash in), the cash released by liquidating the position, minus the cost of commissions (cash out), the performance of each trade and the total performance for that underlying security.

Categories: stock options, volatility, delta neutral
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Analysis

2006-10-07T11:17:00.000-04:00

I made a 50% gain with CELG. This was a good trade. A bit of churning followed by a sharp and large move.

I lost 6.35% on JNJ. Though it did make a decent move it backtracked it immediately.

I broke even on MT. It did move in the end but the initial churning was to strong.

PG was a loss of 13.6%. It did make a clean move but the call did not follow through that well. Looks like it could have been mispriced.

Categories: stock options, volatility, delta neutral
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Closed All Positions with 20% Gain

2006-10-05T17:22:00.000-04:00

The title says it all:

Categories: stock options, volatility, delta neutral
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In the Green

2006-10-04T14:00:00.000-04:00

My portfolio not so long ago:

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Option Relative Performance

2006-10-04T08:42:00.000-04:00

Yesterday evening my portfolio looked like this:

The following charts show the relative performance of each option pair and the underlying stock:

Categories: stock options, volatility, delta neutral
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Started a New Portfolio

2006-10-02T19:11:00.000-04:00

I refilled the delta neutral portfolio today with these trades:

I added a new column to the trade sheet with the theoretical value of the contract generated by the calculator corresponding to the given delta. As a side note, LQHJV and LQHVV were purchased at different times during the day and the calculated values of price and delta correspond to the purchase time.

At the end of today's trading my portfolio looked like this:

Categories: stock options, volatility, delta neutral
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Scanning Again

2006-10-01T08:54:00.000-04:00

This is the result of this week scan for low implied volatility:

The following charts show the price and standard deviation of the first 10 of the list over the past year of trading, after removing the companies that are being acquired:

The following charts focus on the past two months:

Categories: stock options, volatility, delta neutral
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Out with an 18% Profit

2006-09-30T11:18:00.000-04:00

With these trades I sold all the securities in the delta neutral portfolio on Thursday:

I am going to review each security in the portfolio.

I lost 11.73% with JNJ and I should not have considering that it did make a move. I suspect that it was mispriced when I opened the position. The delta of the call was 0.3 and the delta of the put was -0.7. During the time that JNJ moved from $64.25 to $65, the call moved from $0.5 to $0.75 and the put from $1.5 to $0.8, giving effective deltas of 0.33 and -0.93. That is the delta of the put was substantially underestimated.

I made 22.03% on KFT. It was a well timed sharp move.

The gain on NFI was just 4.94%. Just churning.

RAI gave me a 27.71% gain. Nice move between the Bollinger Band and the moving average, even if it is a bit late in the volatility expansion for this stock.

I lost 2.84% with USG. This one was churning.

I made a 36.51% gain on TYC. This was a momentum trade in volatility since the expansion started in the middle of September.

Categories: stock options, volatility, delta neutral
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Third Day

2006-09-27T18:22:00.000-04:00

At the end of trading today my portfolio looked like this:

Categories: stock options, volatility, delta neutral
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Two Days After

2006-09-27T08:41:00.000-04:00

This is the portfolio that I started on Monday at the end of trading yesterday:

The following charts show the relative performance of each option contract and of the underlying security:

Categories: stock options, volatility, delta neutral
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New Portfolio Started With Six Positions

2006-09-25T18:09:00.000-04:00

This morning I opened delta neutral positions in JNJ, KFT, NFI, RAI, USG and TYC with the following trades:

This time I calculated the deltas using a free calculator offered by trader-soft.com. I still use ivolatility.com to get the parameters to fill the calculator. Clicking the thumbnails will show a snapshot of the calculator for each security in the portfolio.

JNJJM
JNJVM
NFIJF
NFIVF
RAIJM
RAIVL
USGJW
USGVW
TYCJY
TYCVY

Categories: stock options, volatility, delta neutral
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Scanning for New Opportunities

2006-09-24T08:17:00.000-04:00

This is the result of my usual scan for low implied volatility:

The following charts show the price and standard deviation of the first 20 of the list over the past year of trading:

Many of them are not interesting. Besides the buy outs and acquisitions of last week, SBL is being acquired by Motorola.

The following charts focus on the past two months of the most attractive opportunities:

Categories: stock options, volatility, delta neutral
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Analysis of Each Position

2006-09-23T11:45:00.000-04:00

The GE positions returned a 9.65% profit. It was just churning.

RAI gave me an excellent 114.51%.

With PG I lost 2.5%. Another one that was just churning.

With T I got a 42.41% gain.

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A Long Term View of My Positions

2006-09-23T08:51:00.000-04:00

The following charts show a six month perspective on the price and volatility action of the securities forming the portfolio that I liquidated yesterday:

The best straddle opportunity with GE was before the middle of August.

The best opportunity with PG was at the end of July. Right now it's still churning in a channel.

A very good straddle with RAI would have played in the middle of June. A new similar opportunity might have been this past week. The 63 day moving average has contained it for now.

The best straddle with T was in the second half of July. It may be playing it again now.

Categories: stock options, volatility
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Cashing the Portfolio with a 47% Profit

2006-09-22T16:43:00.000-04:00

By end of trading today all my positions have been liquidated. These are the sales transactions, resulting in a profit of 47.23%:

Categories: stock options, volatility
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Checking the Deltas

2006-09-20T10:15:00.000-04:00

I created the following chart by pasting two charts on top of a third one. I'm trying to check how accurate are the deltas that I get from ivolatility.com and it would be nice to have a charting tool that would allow to do that.

As of the end of last week the delta of GEJG was 0.45 and the delta of GEVG was -0.58. Therefore I bought 58 GEJG contracts and 45 GEVG contracts. Now the chart above shows that when GE price dropped from $34.96 to $34.6 between Monday and Tuesday, GEJG dropped from $0.41 to $0.30, which is a delta of (0.3-0.41)/(34.6-34.96) = 0.30, and GEVG increased from $0.60 to $0.80, which is a delta of (0.8-0.6)/(34.6-34.96) = -0.56.

The following charts show the relative performance of the securities in the portfolio:

Categories: stock options, volatility
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Hard to Find Good Positions This Week

2006-09-18T19:52:00.000-04:00

This morning I could use only a fraction of the portfolio cash to open new positions, the other securities being too illiquid to even try:

These are the greeks used to open my positions:

Categories: stock options, volatility
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Scanning for Opportunities

2006-09-17T11:15:00.000-04:00

As of the end of last week, these are the stocks with the lowest implied volatility relative to a year of trading and with sufficiently high stock price and open interest:

The following charts show the price and standard deviation of the first 20 of the list over the past year of trading:

The following charts focus on the past two months:

UVN has been on the block for a while, with litigations on top of that.

KMI is the objective of a leveraged buyout at $107.5 per share which explains the large jump in late May and the strange price action afterward.

ADRX is being acquired by Watson Pharma for $25 per share, which explains the low volatility since March.

N has been the target of an acquisition first by Phelps Dodge and later by Compania Vale do Rio Doce for $76.60 a share.

HCA is going to be taken private with a leveraged buyout at $51 a share.

Excluding the companies just mentioned, the securities that look interesting at first sight are AXP, USG, GE, PG, RAI and T.

Categories: stock options, volatility
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One Big Winner and One Loser

2006-09-16T12:11:00.000-04:00

The title says it all.

The Google positions originated a gain of 41.39%. Volatility started to increase just after I opened the positions. The timing was very good.

USG produced a good 24.5% gain after a couple of days of churning.

The RAI postions lost 14.07%. Instead of the October contracts like with GOOG and USG, here I used November contracts. They are obviously not liquid and their price did not act as it should have.

These charts show the October contracts at the same strike price. They are much more liquid.

Categories: stock options, volatility
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Closed All Positions for a 26% Profit

2006-09-16T09:34:00.000-04:00

Yesterday morning I liquidated the portfolio by executing the following sales:

The result is an almost 26% gain on the cash used to purchase the contracts.

The following charts show a six month perspective on the price and volatility action of the securities forming the portfolio:

Categories: stock options, volatility
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The Portfolio Three Days After

2006-09-14T09:39:00.000-04:00

The securities composing my delta-portfolio have started to move:

This is a snapshot of the portfolio as of yesterday at end of trading:

Categories: stock options, volatility
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New Delta-neutral Portfolio

2006-09-11T16:17:00.000-04:00

This morning I built my new delta-neutral portfolio by calculating the delta of these securities:

However, I opened positions in only three of them because the price of Google options is so high:

This is a snapshot of the portfolio at the end of the trading day:

Categories: stock options, volatility
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Scanning for Low Volatility Again

2006-09-10T16:53:00.000-04:00

I'm going to open new positions in the delta neutral portfolio next week. Scanning for securities with the lowest implied volatility relative to a year and with sufficiently large stock price and open interest, I get:

These are the first ten stocks in the list with a year of price and volatility history (measured by the standard deviation of price):

And these charts show the price action of the same stocks over two months with the most interesting strike prices:

The best candidates for opening delta-neutral positions seem to be RAI at $65, NRG at $50, GOOG at $380, MON at $47.5, GFI at $20.

Categories: stock options, volatility
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Lessons Learned

2006-09-10T08:00:00.000-04:00

The USG positions generated a 28.42% profit. I would have made even more if I had not rebalanced twice to keep the delta low. Volatility increased during the time I hold the positions. It is leveling off now.

ECA positions generated a 21.38% profit. In this case rebalancing once increased my gain. Volatility increased and it still increasing now.

I basically broke even with DNA. The first rebalancing avoided actuallu losing money on these positions. The second rebalancing prevented me from making a bigger profit. Volatility started growing late in the trade and it is already leveling off now.

I lost 30.65% on OSTK positions. I would have lost less if I had not rebalanced. I would have essentially broken even if I had closed these positions earlier. Again, volatility started to grow late into the trade.

Categories: stock options, volatility
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Cashed Out

2006-09-09T09:59:00.000-04:00

These are the trades that closed all positions in the portfolio. At the end, I made a 7.95% profit on the cash used to buy the original contracts.

The following spreadsheets show the day by day performance of the pair of contracts for each security in the portfolio:

Categories: stock options, volatility
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Closing Some Positions

2006-09-05T19:58:00.000-04:00

This morning I closed all my positions but USG. This is a snapshot of the portfolio after the close of trading today:

Categories: stock options, volatility
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Planning for Next Week

2006-09-03T07:58:00.000-04:00

The following charts of the securities underlying my option portfolio and of the corresponding options show what has happened in the past few days. The only component that has seen a real increase in volatility is USG. OSTK is starting to experience that as well. DNA and ECA, on the other hand, are just churning, with no definite breakout. If they keep doing this I will be losing money on these positions.

It is quite likely that I will liquidate this portfolio next week.

Categories: stock options, volatility
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End of Week Situation

2006-09-02T07:53:00.000-04:00

This snapshot from MarketWatch shows the situation of my portfolio at the end of trading yesterday:

Categories: stock options, volatility
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Lowering the Delta and Taking Profits

2006-09-01T07:50:00.000-04:00

Yesterday I took some profits and brought the total portfolio delta from an original value of 29 back close to zero:

This is a snapshot of my portfolio at the end of trading yesterday (taken from MarketWatch):

Categories: stock options, volatility
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No Delta-neutral Trading This Week

2006-08-31T08:47:00.000-04:00

This is a snapshot of my portfolio from MarketWatch taken after the end of trading yesterday:

I have left the portfolio delta fluctuate this week. The thumbnails below link to snapshots of IVolatility basic calculator showing the greeks of my portfolio components the morning of the 28 and yesterday's morning:

The total delta of the portfolio has been bouncing between a negative and a positive value, averaging out to about zero over time. However, the total vega is decreasing and the total theta is increasing. That means that the portfolio is becoming less sensitive to a change in volatility and time decay is getting stronger. I may want to take profits at some point.

Categories: stock options, volatility
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My Delta-neutral Portfolio at the End of the First Week

2006-08-26T10:50:00.000-04:00

At the end of trading yesterday my portfolio was as captured in this snapshot from MarketWatch:

Categories: stock options, volatility
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Position Delta-neutral Trading

2006-08-25T11:45:00.000-04:00

At the end of trading yesterday my portfolio was as captured in this snapshot from MarketWatch:

This morning I checked the delta for each contract in my portfolio, using IVolatility basic calculator:

Since the deltas have changed considerably I needed to perform a few trades to keep the total portfolio delta as close as possible to zero:

Categories: stock options, volatility
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Building a Delta-Neutral Portfolio

2006-08-24T10:32:00.000-04:00

I'm going to use a spreadsheet to keep track of trades. The following snapshot shows the trades resulting from my previous post analysis:

The following snapshots from Shaeffer's Research show the greeks for the option contracts involved, as of yesterday:

Categories: stock options, volatility, delta neutral
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A Closer View

2006-08-23T12:00:00.000-04:00

The following charts from StockCharts and IVolatility offer a closer view of the recent action in the stocks identified in the previous post.

USG Corp.

Genentech, Inc.

EnCana Corp.

Overstock.com Inc.

Categories: stock options, volatility
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Scanning for Low Volatility

2006-08-22T13:21:00.000-04:00

A tool needed to plan trades such as the one mentioned in my last posts is a scanner for low volatility. Schaeffer's Investment Research offers such a tool for free.

If I try to get all stocks with the lowest implied volatility readings and I filter the results by stock price higher than $10 and option open interest highter than 50,000, today I get the following list:

Using the CandleGlance tool from StockCharts.com I can get a bird view of the first few stocks in the list:

It looks like good candidates would be Univision, Genentech, USG Corp., EnCana and Overstock.

However, Univision has low volatility simply because it accepted a takeover offer at the end of June.

The very low volatility of UGS may be related to the offer to their stockholders to buy one share at $40 for every share owned.

Categories: stock options, volatility, delta neutral
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The Case of a Smooth Trend

2006-08-15T14:14:00.000-04:00

The previous post considered several strategies to buy volatility low and sell it high when the underlying security experienced a sharp price change.

I want to look now at the case of a trending price in the underlying stock. The following chart shows the price of eBay (EBAY) in the past three months:

Not only the price decline is well defined and quite smooth from June onward but the historical volatility as measured by the price standard deviation is pretty much constant.

This chart shows EBAY historical volatility and implied volatility over the same period of time:

It is interesting that historical volatility had been decreasing since the big jump in May but implied volatility had been steadily on the rise. The opposite has been happening since the first half of July.

Let's consider again options that were at the money in the middle of June, that is when EBAY was selling for about $30.5.

The following chart shows the price of XBAHF, the August call with strike at $30:

This chart shows the price of XBATF, the August put with strike at $30:

Now let's look at the following fantasy trades:

Buy 50 shares of EBAY at $30.5 and one XBATF contract at 100 times $2, then sell EBAY at $33.5 and XBATF at 100 times $6.75. The net profit, excluding commissions, would be $125, that is 7%.

Sell short 50 shares of EBAY at $30.5 and buy one XBAHF contract at 100 times $2.375, then cover EBAY at $23.5 and let XBAHF expire worthless. The net profit would now be $112.5.

Buy one XBAHF contract at 100 times $2.375 and one XBATF contract at 100 times $2, then sell XBATF at 100 times $6.75 and let XBAHF expire worthless. The resulting profit would be $237.5, that is 54%.

I want to check what happens if instead of using options expiring in August I use options expiring in January 2007.

This is the chart of XBAAF, January call with strike at $30:

And this is the chart of XBAMF, January put with strike at $30:

Buy 50 shares of EBAY at $30.5 and one XBAMF contract at 100 times $3.25, then sell EBAY at $33.5 and XBAMF at 100 times $7.25. The net profit, excluding commissions, would be $50, that is 3%.

Sell short 50 shares of EBAY at $30.5 and buy one XBAAF contract at 100 times $4.25, then cover EBAY at $23.5 and sell XBAAF at 100 times $1.25. The net profit would again be $50.

Buy one XBAAF contract at 100 times $4.25 and one XBAMF contract at 100 times $3.25, then sell XBAMF at 100 times $7.25 and XBAAF at 100 times $1.25. The resulting profit would be $100, that is 13%.

Categories: stock options, volatility, delta neutral
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The Case of an Unexpected Event

2006-08-12T12:44:00.000-04:00

I'm going to take a closer look at a specific case, starting with an unexpected event that translates into a sudden price change. This happened recently to Yahoo! stock. The following chart from iVolatility shows

the historical volatility and the implied volatility of Yahoo! over the past three months. Note how for a while the implied volatility was substantially higher than the historical volatility. Then a large overnight change of the stock price brought the historical volatility suddenly to extremely high levels. On the other hand, implied volatility actually decreased from there.

The following chart from BigCharts shows Yahoo! stock price over the past three months:

Here I use the Bollinger bands to see how the historical volatility (as measured here by the price standard deviation) suddenly increased as an effect of the overnight price drop after a long period of almost no change.

Let's try different trading strategies where one tries to buy volatility low and sell it high.

Let's consider first Yahoo! options expiring this month. Before the sudden drop the stock price of Yahoo! was gently fluctuating between $30.5 and $33. I want to consider options that were at the money during this period.

This is a chart of YHQHF, August call with $30 strike:

And this is a chart of YHQTF, August put with $30 strike:

One strategy would be to buy 50 YHOO shares and one YHQTF contract (I will explain later the reason of the 50:1 ratio). We are buying YHOO at $30.5 a share and YHQTF at 100 times $1.5. That means a total cost of $1,675, disregarding commissions. Now, if I sell the 50 YHOO shares just after the drop at $25.5 and the YHQTF contract at 100 times $5, I get $1,775. That is I make a profit of $100, a 6% gain. With a round trip commission of $0.01/share and of $2.00/contract the profit would be $97.5.

On the other hand if the price drop did not happen, I would close the position by selling the 50 YHOO shares at, say, $31.5, and the YHQTF contract at 100 times $0.75, for a loss of $25, that is a 1% loss.

Another strategy would be to sell short 50 YHOO shares and buy one YHQHF contract. Now we are selling YHOO at $30.5 a share and buying YHQHF at 100 times $2.25. That means that we earn $1,300. If we then buy 50 shares of YHOO to cover at $25.5 and sell the YHQHF contract at 100 times $0.1 our earning is $35.

Again, if the price drop did not happen, I would close the position by covering YHOO at $31.5 and selling YHQHF at 100 times $2.75, breaking even.

Note that if YHOO price were to go up instead of down I would not need to cover my short position at a loss because the call contract allows me to cover at a price slightly lower than the price I sold YHOO short.

This is the chart of YHQHZ, August call with $32.5 strike:

This is the chart of YHQTZ, August put with $32.5 strike:

Now I am going to buy 50 YHOO shares at $33 and one YHQTZ contract at 100 times $1.25 for a total cost of $1,775. If I then sell the YHOO shares just after the drop at $25.5 and the YHQTZ contract at 100 times $7.25 I am going to make a profit of $225, a 13% gain.

If the price drop had not happened I could have sold YHOO at $31.5 at YHQTZ at $1.75 for a loss of $25, a 1% loss.

Another strategy would be to sell short 50 YHOO shares at $33 and buy one YHQHZ contract at 100 times $2.25 which generates $1,425. If I buy 50 YHOO shares after the drop to close my short position at $25.5 and sell YHQHZ at 100 times $0.05 I have a profit of $155.

In the case the price drop had not happend I could have covered YHOO at $31.5 at sold YHQHZ at $1.25 for a loss of $25.

What about trading just options? Again, here I am considering only at-the-money options.

I could buy 4 YHQHF contracts at 4 times 100 times $2.25 and 4 YHQTF contracts at 4 times 100 times $1.5 for a total cost of $1,500. This type of strategy is called a long straddle. Just after the drop I would sell each YHQHF contract at 100 times $0.1 and each YHQTF contract at 100 times $5 for a total of $2,040 and therefore for a profit of $540, a 36% gain.

In this case, in the event the price drop had not happened I could have sold YHQTF at 100 times $0.75 and YHQHF at 100 times $2.75 for a loss of $100, a 7% loss.

I could as well buy 4 YHQHZ at 100 times $2.25 each and 4 YHQTZ at 100 times $1.25 each for a total cost of $1,400. After the drop I would sell each YHQHZ at 100 times $0.05 and each YHQTZ at 100 times $7.25 for a total of $2,920 and a profit of $1,520, a whopping 109% gain.

If the price drop had not happened, I could have sold YHQTZ at 100 times $1.75 and YHQHZ at 100 times $1.25 for a loss of $200, a 14% loss.

Categories: stock options, volatility, delta neutral
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Trading Volatility Not Price

2006-08-10T14:21:00.000-04:00

If would appear from the results of the previous post that volatility should be more predictable than price. If there is a way to buy and sell the volatility of a security as opposed to the security itself, it should be much easier to make profitable short term trades.

What one needs to understand now is how to translate the apparent predictability of volatility into actual trading strategies.

The following chart shows the VIX, the implied volatility index of the US stock market calculated from the components of the SP500 index, over a period of a few years. The VIX is plotted in red with the SP500 in black in the background for a comparison.

Just below I have added the value of the VIX as a percentage of the VIX range over the past 252 days (a trading year) and over the past 63 days (a trading quarter). One can see that the VIX spends most of the time in the 20-80% region of the range. It spends less time in the lowest 20 percentiles of the range, depending on the time frame considered to calculate the range, and even less time in the highest 20 percentiles of the range.

If one takes a look at the following chart of the VIX,

will see at the bottom the standard deviation of the VIX calculated over a period of 252 days and over 63 days. The chart of the VIX shows superimposed the Bollinger bands for the corresponding time periods. Here one can see that when the VIX is in the low percentiles of her range it almost never breaks below the lower Bollinger band, regardless of the time frame. On the other hand, when the VIX is in the high percentiles of her range, the upper Bollinger band is unable to contain it and the VIX spikes above it briefly.

Categories: stock options, volatility, delta neutral
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Autocorrelations of Stock Price and Volatility

2006-05-16T13:45:00.000-04:00

Continuing the line of thought into a possible time-dependence of stock market volatility, it is worthwile to use a statistical tool known as autocorrelation. In fact, the autocorrelation of a data series can tell how long it will take to a signal to disappear from the data. In other words, one can measure the duration of the memory effect in the data.

First of all, I take the following log-normal computer generated price series with the same mean and standard deviation of GE stock prices:

Superficially, the computer generated series does not look that different from the "real thing":

The following picture shows the autocorrelation of the historical volatility (red curve) and of the price (black curve):

Both autocorrelations fall down very quickly to zero, signifying that there is no memory effect whatsoever in both price and volatility, as it should be.

This picture shows the historical volatility calculated from the GE prices:

The autocorrelation of GE historical volatility (thick red curve) does not fall off right away. In fact, it is well approximated by an exponential decay with life-time of about 175 trading days (thin red curve). On the other hand GE price autocorrelation (black curve) shows no memory effect just like the random walk:

Categories: stock options, volatility
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Is Volatility Time Dependent? - Part II

2006-05-08T15:57:00.000-04:00

In the previous post we have seen how increasing the time horizon of the stock returns has the effect of making the volatility statistics closer to the one that one would expect for a log-normal random walk. This leads me to suspect that there could be a memory effect that fades away when waiting longer for a return.

Another way of looking at this is to fix the time horizon of the returns to one day and calculate the historical volatility and the other statistical moments using longer time windows than 21 days.

I have already seen side by side the daily plots of GE mean, historical volatility, skewness and kurtosis and the corresponding quantities of a log-normal random walk, calculated using a windows of 21 consecutive trading days sliding over the available data:

Here I do the same with a window of 63 consecutive trading days:

Here I use 252 consecutive trading days:

And here I use 1260 consecutive trading days:

The sharp jumps visible in the skewness and kurtosis of GE once the window grows longer than a quarter are due to the effect of the 1987 stock market crash to the distribution of log-returns.

If we compare the theoretical distributions with the histograms of the mean and historical volatility obtained from the random walk as the duration of the window grows from 21 days

to 63 days

to 252 days

and then to 1260 days,

the observation that one can make is that the size of the fluctuations grow as the number of samples contained in the histograms decreases because the length of the window is increased keeping the total number of data constant.

However, if I make this comparison using the GE data I see, not so much from the mean histograms,

but especially from the historical volatility histograms,

that, as the time window gets larger, the fluctuations become much larger than what they are in the case of the random walk prices.

Categories: stock options, volatility
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Is Volatility Time Dependent?

2006-04-19T15:34:00.000-04:00

In the previous posts "Weekly Volatility", "Monthly Volatility", "Quarterly Volatility" and "Yearly Volatility", I have calculated the historical volatility of GE stock price using returns over an increasing time period from weekly returns to yearly returns and compared them with the corresponding quantities for a random walk. It may be worthwile to show all these results together to better see the effect of time on the calculation of volatility.

These are the histograms of the 21 day mean of GE annualized log returns going from daily returns to yearly returns, compared with the corresponding normal distributions:

And these are the histograms of the 21 day volatility for the same time periods, compared with the corresponding random walk distributions:

It seems clear that the discrepancy between the stock price statistics and the random walk statistics is concentrated at the shortest time horizons. The longer the period used to calculate the returns, the less the discrepancy. That could mean that there is a "memory effect" that fades away with time, being the strongest considering daily returns and being almost gone when we reach the yearly returns.

Categories: stock options, volatility
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Yearly Volatility

2006-04-17T14:47:00.000-04:00

This post considers yearly volatility. This is the histogram of the yearly log-returns of GE stock price, compared with the normal distribution with the same mean and standard deviation:

Since the standard deviation of GE daily log returns is 3.848, I should expect a standard deviation of the GE monthly log returns to be close to 3.848 times the square root of 1/256, that is 0.242. In fact, the mean is 0.090, the standard deviation is 0.219, the skewness is -0.450 and the kurtosis is 3.490.

I generate 21 day mean, historical volatility, skewness and kurtosis as usual by calculating these quantities for a sample of 21 consecutive days and sliding this sample over the entire range of available data.

I calculate the same quantities for a log-normal random walk with the same standard deviation and mean as the GE data.

The mean and historical volatility histograms of the random walk are, of course, in good agreement with the theoretical distributions (the "chi distribution" is in fact the histogram of the historical volatility of a log-normal random walk 10 times larger):

The histograms of the GE data are pretty much in agreement as well:

Categories: stock options, volatility
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Quarterly Volatility

2006-04-17T12:41:00.000-04:00

This post considers quarterly volatility. This is the histogram of the quarterly log-returns of GE stock price, compared with the normal distribution with the same mean and standard deviation:

Since the standard deviation of GE daily log returns is 3.848, I should expect a standard deviation of the GE monthly log returns to be close to 3.848 times the square root of 4/256, that is 0.485. In fact, the mean is 0.086, the standard deviation is 0.434, the skewness is -0.375 and the kurtosis is 3.988.

I generate 21 day mean, historical volatility, skewness and kurtosis as usual by calculating these quantities for a sample of 21 consecutive days and sliding this sample over the entire range of available data.

I calculate the same quantities for a log-normal random walk with the same standard deviation and mean as the GE data.

The mean and historical volatility histograms of the random walk are, of course, in good agreement with the theoretical distributions (the "chi distribution" is actually the histogram of the historical volatility of a log-normal random walk 10 times larger):

The histograms of the GE data are not but only so slightly:

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Monthly Volatility

2006-04-14T12:42:00.000-04:00

Today I am going to look at the monthly volatility. The histogram of GE monthly log returns is presented here compared with the normal distribution with the same standard deviation:

Since the standard deviation of GE daily log returns is 3.848, I should expect a standard deviation of the GE monthly log returns to be close to 3.848 times the square root of 12/256, that is 0.840. In fact, the mean is 0.086, the standard deviation is 0.780, the skewness is -0.226 and the kurtosis is 4.615.

I generate 21 day mean, historical volatility, skewness and kurtosis as usual by calculating these quantities for a sample of 21 consecutive days and sliding this sample over the entire range of available data.

I calculate the same quantities for a log-normal random walk with the same standard deviation and mean as the GE data.

The mean and historical volatility histograms of the random walk are, of course, in good agreement with the theoretical distributions (the "Chi distribution" is actually the histogram obtained from a random walk 10 times larger):

The histograms of the GE data are less in disagreement than in case of the weekly returns:

Categories: stock options, volatility
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Weekly Volatility

2006-04-13T10:01:00.000-04:00

In "Calculation of Historical Volatility of Daily Returns" I have calculated the historical volatility of the stock price of General Electric. This calculation has been the basis for a comparison with the volatility of a computer generated series with normally distributed log returns.

In a few more posts I am going to extend this comparison to returns over an increasing period of time. I will start today with considering the weekly returns that were calculated in my post "Understanding Market Volatility".

The following picture shows the distribution of the annualized weekly log returns of GE stock price, compared with the normal distribution with the same standard deviation and mean.

In the case of a computer generated price series with normally distributed log returns, increasing the period over which the returns are calculated by a factor of T, simply decreases the historical volatility by a factor of the square root of T. This is a consequence of the fact that such price series is what statisticians call a Wiener process or a Gaussian random walk.

Since this concept is quite important I will expand on it briefly here. If I use the following definitions of annualized log daily returns and of daily returns, with Y indicating the number of trading days in a year,

and if I construct the annualized log daily returns to be a normally distributed random variable with given mean mu and standard deviation sigma,

and I define the annualized log returns over m days and the returns over m days like this

I can derive

where I use the summation properties of normally distributed independent random variables.

Eq. (8) seems to imply that the stock price at day i could be derived from the stock price at day i-m following the law

In fact, this is incorrect. There is only one random walk, characterized by a given mu and sigma, which is the one generating the random daily price sequence. The random m-day returns must be derived from this random walk and should not be calculated by generating a new random walk with a sigma divided by the square root of m. I'm going to explain how to do it now.

First of all, I recall the definitions of mean and variance over a sample of k consecutive days and I apply them to the case of the m-day log returns:

Of course, the square root of (10) is the m-day historical volatility calculated using a k day sample. But I will derive the k day mean first. I expect the k day mean of the m-day log returns to be a normally distributed random variable like this

and I will solve for the factors a and b. First of all, I re-write (7) like this

where I associate a subscript to the random variable N to indicate the particular random number generated on that specific day.

Using (12) in the definition (9) I get

Expanding (13) leads to different expressions depending on the relative magnitude of k and m:

Now, using the summation property of normally distributed indipendent random variables, I find that the factor a is always equal to 1,

and that the factor b is given by different formulas depending on the relative size of k and m:

Deriving the distribution for (10) is too complicated. It is not a Chi distribution as in the case of the 1-day returns. To make a comparison I will just use a random walk that is 10 times larger than the GE price series and use the histogram of the historical volatility for this random walk as an approximation of the true probability distribution of the historical volatility.

The standard deviation of the annualized GE daily log returns that we are using is 3.848. This is what has been used to generate the random walk price series. We should espect the standard deviation of the annualized GE weekly log returns to be close to that value divided by the square root of 256/52, that is 1.748.

In fact, the mean is 0.088, the standard deviation is 1.746, the skewnesss is -0.146 and the kurtosis is 7.134.

This is the random price history with normally distributed log returns that will be used in my comparisons:

The following graphs show the mean, historical volatility, skewness and kurtosis calculated by taking 21 consecutive days of annualized GE weekly log returns and sliding this window over the whole period of time available (time goes from right to left):

These graphs show the same quantities calculated for the random walk prices:

The histograms of the mean and of the historical volatility of the random walk agree very well with the theoretical probability distributions (the normal distribution and the histogram obtained from the a random walk 10 times larger):

That is definitely not the case when I consider the histograms obtained from the GE weekly returns:

Categories: stock options, volatility
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Where to get my calculations

2006-03-21T15:30:00.000-05:00

All the actual calculations done in the recent posts about market volatility have been made with Mathematica 5.2.

All the Mathematica files needed to reproduce these calculations have been posted on the Google discussion group associated to this blog:

Categories: stock options, volatility
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Are market returns log normal? A quantitative answer.

2006-03-20T12:31:00.000-05:00

In "Comparison of Historical Volatilities of Market Returns and of Normal Returns" I have compared the statistics of GE daily log returns with the statistics of computer generated data that are normally distributed with the same mean and standard deviation of the GE market data. However, the comparison was purely qualitative, that is, I just calculated the histograms of quantities such as mean, standard deviation, skewness and kurtosis for samples obtained by sliding a 21 day window over the entire data set available and compare them with the same quantities for the normally distributed data.

Now I would like to make a quantitative comparison, using the Kolmogorov-Smirnov test.

First, I calculate the empirical CDF's (Cumulative Distribution Functions) from both the GE market data (red) and the normally generated data (blue):

How to get the empirical CDF from the data is explained, for example, at the College of Saint Benedict and Saint John's University web site and at the National Institute of Standards and Technology web site.

Second, I calculate the absolute value of the difference between the two CDF's, for each statistics:

The quantity that I need is the maximum of this difference, multiplied by the square root of the total sample size. This is a measure of the "distance" between the empirical distributions that I am comparing.

Now I need to know what is the probability that two empirical distributions come from the same distribution, or that they are just two different statistical realizations of the same distribution, given the value of their Kolmogorov-Smirnov distance. In other words, I want to know what is the chance that the GE market data and the computer generated data, have the same probability distribution. Since I already know that the computer generated data are normally distributed, this is the same chance that the GE daily log returns are normally distributed as well.

This probability is given by the Kolmogorov-Smirnov distribution:

It is clear that once the distance gets larger than, say, 1.5, the chance of the two distributions being the same is basically negligible.

Now, this is what I get.

In the case of the 21 day mean, the maximum of the difference between CDF's is 0.042, which, multiplied by the square root of the number of data points, becomes 4.42.

The maximum difference between the CDF's of the 21 day historical volatility is 0.349, which becomes 36.76.

In the case of the 21 day skewness I get 0.085 and 8.95, and in the case of the 21 day kurtosis, 0.139 and 14.64.

With such large values of the distance between the CDF's, the probability of them being the same, as given by the Kolmogorov-Smirnov distribution, is practically zero.

Categories: stock options, volatility
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Yield Curve Update 2006/03/10

2006-03-11T08:41:00.000-05:00

The yield curve full inversion did not last that long.

Categories: bond market, interest rates, yield curve
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Comparison of Historical Volatilities of Market Returns and of Normal Returns

2006-03-10T14:45:00.000-05:00

In "Calculation of Historical Volatility of Daily Returns" I have calculated the historical volatility of GE returns as the standard deviation of 21 consecutive trading days of daily log returns and presented the statistics of the data using histograms of the mean, volatility, skewness and kurtosis of all the 21 day samples obtained by sliding this 21 day window over the entire period of time covered by the data.

In "Is the Distribution of Log Returns Normal?" I have generated a sample of returns that are normally distributed.

Now I can use these normally distributed data to generate rolling 21 day samples in the same way I did with the GE daily log returns and calculate the mean, standard deviation, skewness and kurtosis of all of these samples.

These plots show the result of the calculation:

It is worthwile to look at the plots obtained from GE daily log returns and at the plots from the normally distributed data side-by-side:

The quantity that shows the most striking difference between the real market data and the normally distributed data is, in fact, historical volatility. Moreover, the real market data have a few outliers, that is a few samples with a mean way off the range, which are missing in the normally distributed data.

In the case of the normally distributed data, one knows which probability distribution best describes the statistics of the mean and of the volatility.

Any course of statistics 101 will say that the histogram of the mean of 21 day samples should follow the normal distribution with mean equal to the mean of the original data from which the samples have been taken and with standard deviation equal to the standard deviation of the original data divided by the square root of the sample size, that is 21.

Getting the distribution of the volatility is a bit trickier. Since historical volatility is the standard deviation of the sample, and the standard deviation is the square root of the sample variance, we need the distribution of the square root of the sum of the squares of statistically independent variables. This distribution is known as the Chi distribution.

The following two plots show, respectively, the histogram of the mean of the 21 day samples of the normally distributed data compared with the corresponding normal distribution, and the histogram of the volatility of the same 21 day samples compared with the appropriate chi distribution:

At this point, we have enough information to compare the histograms of mean, volatility, skewness and kurtosis of the 21 day samples derived from the GE daily log returns with the corresponding distributions or histograms derived from the normally distributed data:

These plots confirm that not only the distribution of the 21 day sample means of the market data is not normal but that the distribution of the historical volatilities is considerably different than the one derived from normally distributed data.

Categories: stock options, volatility
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Calculation of Historical Volatility of Daily Returns

2006-03-08T13:19:00.000-05:00

In "Understanding Market Volatility" I have calculated the distribution of daily log returns for the GE stock price series downloaded from Yahoo!

In "Is the Distribution of Log Returns Normal?" I compared this distribution with the one from a series of random numbers with the same mean and standard deviation and noted how they are quite different.

Historical volatility is defined as the standard deviation of log returns over a certain period of time. Let's take this period of time to be 21 days, that is about one trading month, and calculate mean, standard deviation, skewness and kurtosis of GE daily log returns for 21 consecutive trading days. As I slide this window of 21 days from January 2, 1962 to today I get the following charts:

The second chart from the top is the historical volatility, the quantity normally used to estimate option's implied volatility, as it changed from the beginning of the historical period considered up to today.

Now I can create the histograms of the 21-day mean, standard deviation, skewness and kurtosis of GE daily log returns:

Categories: stock options, volatility
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Is The Distribution of Log Returns Normal?

2006-03-07T09:55:00.000-05:00

The standard assumption made when evaluating option prices is that returns are log-normally distributed, that is that the logarithm of the returns follow a normal distribution. This is not the case, however.

I can easily generate a sequence of data of the same size as the GE sample that I have collected from Yahoo! and that are normally distributed. If you need to know what the normal distribution of events is, check Wikipedia.

To do that I need the mean and the standard deviation sigma of the GE sample:

mean = 0.085
sigma = 3.848

Using these values I generate normally distributed random numbers.

This chart shows the frequency histogram of the normally distributed sample:

The black curve is the normal distribution with the same mean and standard deviation used to generate the sample.

The agreement between the histogram and the theoretical distribution is very good as it should be.

Let's compare instead the histogram of the GE daily log returns with the normal distribution with the same mean and standard deviation:

The agreement is not so good. The discrepancy can be measured quantitatively by using two parameters: skewness and kurtosis.

Skewness is a measure of symmetry, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point. Since the normal distribution is symmetric, the skewness of a normnal distribution is zero.

Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. The kurtosis of a normal distribution is exactly 3.

The skewness and kurtosis of the normally distributed sample agree with the normal values:

normal sample skewness = -0.031
normal sample kurtosis = 3.044

However, the skewness and kurtosis of the GE daily log returns are quite different, about three times larger:

GE log return skewness = -0.09
GE log return kurtosis = 8.695

Categories: stock options, volatility
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Understanding Market Volatility

2006-03-06T13:05:00.000-05:00

In "How to Price American-Style Options" and "The Binomial Tree Formula" I made clear that a good estimate of market volatility is essential when pricing a derivative contract such as a stock option. I'm going to devote a few posts to a deeper study of volatility.

For the sake of concretness I am going to use General Electric stock price. Yahoo! Financial provides the daily price history from January 2, 1962. All what one has to do is to download a file and start working with the data.

The file contains 11118 records. First thing to do is to calculate stock returns over different periods.

The following charts to the left shows daily, weekly, monthly, quarterly and yearly returns. You must click on the thumbnail to see the full size chart, which is quite large.

Time on these charts goes right to left. That is, the most recent data are the left-most in the chart.

To have a better view at the way returns change going from the daily all the way to the yearly returns, I made these charts that show only the most recent one thousand days of data:

Now that we have the returns, we need to calculate the log returns, which are used in the definition of historical volatility. They must be annualized. This means that the daily log returns are the logarithm of the daily returns multiplied by 252, the number of trading days in one year. Similarly, the weekly log returns are the logarithm of the weekly returns multiplied by 52, etc.

Now that I have the daily log return, I can examine their statistics. For example, I can make a histogram, showing the frequency of a given log return over the entire period considered in the data:

If it is not clear what a histogram represents, check it out at Wikipedia.

Categories: stock options, volatility
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New Update on Buying Options for Protection

2006-02-19T15:30:00.000-05:00

Time to revisit Susan and John strategies. Susan wanted to lock a $30 purchase price for GE, expecting GE to be higher, possibly much higher, by the 3rd week of February.

GE lost ground instead and is now just $3.5 higher than the strike price.

The call with $30 strike expired yesterday at the intrinsic value of $3.5:

The call with $35 strike, that was at-the-money in early January, expired worthless since it went out-of-the-money in late January:

Overall, this strategy didn't pay off for Susan. However, she only lost the premium paid for the call options and did not have to actually buy GE shares at $35 and see them lose value afterward. In practice, she had an effective stop loss trade in force.

John, instead, was buying puts to lock a gain already made with GE. This strategy worked because GE did lose value in late January.

GE-OS, the put with strike at $37.5, is still very much in-the-money.

GE-OG, with strike at $35, sky-rocketed in late January as GE stock tumbled:

Even more so for GE-OZ, with strike at $32.5:

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Interest Rates Update 2006/02/17

2006-02-19T08:47:00.000-05:00

In the last update on interest rates, I pointed out that the uptrend support line of the 10 year note rate (black line) had turned into a resistance line for the 30 year bond rate. The 30 year rate effectively turned south at the beginning of November after hitting this line from below. The recent downward acceleration confirms this event.

This shorter term picture shows in more details the yield inversion: the 30 year rate below the 10 year rate and the 10 year rate lower than the 5 year rate. I gave the yield inversion as a very likely event in my Christmas post.

Categories: interest rates, bond market, yield curve
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To brrreeeport or not to brrreeeport?

2006-02-16T17:28:00.000-05:00

Just checking if I can bump this blog up a bit with the word brrreeeport, as suggested by Robert Scoble.

Edit 2006/02/19: It appears to have worked. The original post showed up on technorati search list after about a couple of days:

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The yield curve is finally fully inverted

2006-02-10T17:20:00.000-05:00

Categories: bond market, interest rates, yield curve
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The 30 year bond rate collapses!

2006-02-10T11:29:00.000-05:00

Categories: bond market, interest rates
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The Binomial Tree Formula

2006-02-04T15:37:00.000-05:00

The previous post presented an example binomial tree calculation of the price of an american-style option. The lesson drawn from thta example was that the accurate estimate of volatility is key to price options correctly.

I will look here more closely to the standard formula used in the binomial model, to see how volatility enters into the picture. The up and down price movements in the option underlying asset used to build the binomial tree are calculated as follows:

The up movement U is equal to the exponential of the product of the volatility V and the square root of the time step DT. Since the volatility is annualized, the time step is expressed in years. The down movement is simply the inverse of the up movement.

U = EXP(V*SQRT(DT))

D = 1/U

The actual option price P at the last step is known and it is the intrinsic value. The option price at an intermediate step is calculated as either the binomial value B or the exercise price E, whichever is the largest.

P = MAX(B,E)

The binomial value is

B = (X*U + (1-X)*D)*EXP(-R*DT)

where R is the risk-free interest rate, typically the deposit rate, and

X = (EXP((R-Y)*DT) - D)/(U - D)

where Y is the underlying security yield (the dividend yield if it's a stock) corresponding to the life of the option.

If V is estimated using historical volatility, the formula is

V = STANDARDDEVIATION(LOG(S[n]/S[n-1]))

where S[n] is a series of underlying asset prices over a given period of time (the historical sample).

The standard deviation is, of course the square root of the sample variance:

V = SQR(SUM((L[n]-A)*(L[n]-A))/T)

where L[n] is the logarithm of the return

L[n] = LOG(S[n]/S[n-1]),

A is the sample average

A = SUM(L[n])/T,

and T is the sample size (the total period over which prices are sampled).

Categories: stock options
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How to Price American-Style Options

2006-02-02T08:15:00.000-05:00

The options that we have considered so far are know as American-style options. This simply means that the option contract can be exercised at any time before expiration. European-style options are contracts that can be exercised only at expiration. American-style and European-style are also known as vanilla options. There are many other types of option contracts structured in arbitrarily complex ways. Bermuda-style options, for example, can be exercised only at pre-determined dates, usually monthly.

We have seen that the price of an option can change dramatically as the underlying asset price changes and as the expiration date gets closer. It is therefore very important to understand what determines such changes. The best way to estimate the price of an American-style option is to use an approximation known as the binomial model. I am going to show how it works with an example.

First of all, the time to expiration is broken down into a number of steps. Walking forward from the present time at each step the underlying security price is moved up or down by a given amount. This amount is calculated using the estimated volatility of the stock and all possible price moves are calculated.

Volatility plays the leading role in understanding and pricing options because options are insurance contracts and volatility is the risk one is insuring against. Volatility is essentially a measure of the expected range of changes in a security returns, or, to be more accurate, the deviation of returns from their mean. So, if, for example, the mean return of an asset is 0, a 10% volatility means that returns are likely to fluctuate between a -10% loss and +10% gain, annualized. The key here is the qualification "likely". If returns were perfectly random, that "likely" could be quantified as a probability of 68.3%. What one is insuring against with an option is really the event of returns being outside the volatility of 10%. In this case, the probability of such an event is 1-0.683=31.7%. Under the same assumption of perfect random returns, a volatility of 10% means that the likelihood of returns staying within -20% and 20% annualized increases to 95.4% and therefore the probability of a larger than 20% gain or loss goes down to 4.6%.

So, if at each step the underlying asset price can move either up or down by a certain amount, the number of calculated prices is going to grow geometrically as one steps away from the present and closer to expiration. If, at step 0 we have just one price, the present price, at step 1 we have the current price plus the calculated change and the current price minus the calculated change, at step 2 we have each of step 1 two prices moved up and down, giving four prices, at step 3 we have eight prices, and so on and so forth...

The result looks like a tree with branches that keep bi-furcating at each step in time. That's why this model is called the bi-nomial (tree) pricing model.

At expiration, the last step of the binomial tree, option prices must be equal to their intrinsic value. In order to determine the price of the option at the present time, that is at step 0 of the binomial tree, the option price at each step must be calculated walking back from the last step toward the first step, each time using the known option prices of the previously calculated step.

The main problem with this approach is that volatility, being a measure of risk, is only an estimate. One way to estimate it is by considering the past price history. This is what is called historical volatility. In practice, though, the volatility implied by option prices, that is the risk perceived by the option market, is usually quite different than the historical volatility.

A good place to compare the two volatility measures is IVolatility. This chart shows the historical volatility of GE (blue curve) in the past six months, calculated using 30 trailing days of historical data, together with the implied volatility (yellow curve), that is the volatility that best fits the prices of GE options expiring in one of the following three months (front options). Clearly, during the first half of January, historical volatility was much lower than implied volatility.

The following picture from Hoadley.net shows a 10 step binomial tree calculation estimating the price of GE-BG on January 6, using the appropriate values for dividend yield and risk-free interest rate and using historical volatility as the estimate for volatility:

The resulting option price is $0.73 which is quite lower than $1.05, the closing price of GE-BG on that day.

Of course, if instead of the historical volatility, I use the implied volatility I am going to get the much better estimate of $1.02:

However, that's the result of a circular argument since the implied volatility is precisely that value of volatility that best fits the option prices for the front months on the day that I am considering.

If I increase the number of steps I do not get a significantly different estimate:

Clearly, since volatility is the only calculation parameter that is not known with certainty, a good volatility estimate is paramount when pricing an option contract.

Historical volatility is not the only measure of volatility available. The following chart shows several measures of volatility based on price data for GE in the past six months:

Categories: stock options
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The US Stock Market, The Euro and Gold

2006-01-24T07:52:00.000-05:00

It's time to revisit the correlation between the US stock market and the Euro or Gold.

This chart shows the SP500 index (black) and the same index priced in Euros (red), or, to be more precise, priced in Euro future contracts. The first phase of the global carry trade, causing a strong positive correlation of the SP500 and the Euro, and therefore causing the SP500 in Euros moving in a very tight range, took about two years , from the Spring of 2003 to the Spring of 2005. A rebalancing of this trade occurred afterward, as the US Dollar bounced back from the two-year fall with respect to other currencies, causing the SP500 in Euros to move relatively quickly to a new, higher, range. A new rebalancing followed in the Fall of 2006. It appears that a new tight range is forming at a still higher level:

On the other hand, if I consider gold as the "currency" to price the US stock market, I can see very well that after a period of strong positive correlation, paralleling the one with the Euro, we have entered a phase of negative correlation. Right now, the SP500 priced in gold is almost back to where it was at the beginning of 2003, at the lowest point of the bear market:

Categories: stock market, currencies, euro, gold, correlations
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Update on Buying Options for Protection

2006-01-21T12:00:00.000-05:00

My original posts defining calls and puts used some examples to show that options are essentially insurance contracts. I want to revisit these examples.

The examples were based on General Electric, whose recent stock price action hasn't been very good:

Susan was going to buy calls expiring in February instead of buying the stock directly. This is what happened to GE-BF, call striking at $30, deep in the money:

Her rationale for buying GE-BF was to lock a $30 buying price with the expectation that GE would be substantially higher than that before the 3rd Friday of February.

This is what has happened to GE-BG, at-the-money call with strike at $35:

This contract is now deep out-of-the-money and has lost 90% of its value, pretty much like a penny stock would typically do. Again, by buying GE-BG, she wished to lock a buying price of $35, which would not make sense any longer now.

John, on the other hand, was going to buy puts to lock a gain already made.

GE-OS, with strike at $37.5, was an in-the-money put and it is even more so after yesterday decline in GE stock price, with a 75% increase in premium:

GE-OG, put striking at $35, was at-the-money and it is now in-the-money, experiencing a 166% premium increase:

And GE-OZ, put striking at $32.5, which has remained out-of-the-money, has now gained 233%:

I will revisit these positions later next month.

Categories: stockoptions
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Expiration Week

2006-01-21T08:24:00.000-05:00

Now that option expiration week is over, I would like to see what has happened to some of the contracts that I have examined in the past few posts. They have all expired at the close of trading yesterday. This is Microsoft stock price in the past two weeks. It closed at $26.41:

MSQ-AR was the in-the-money call with strike at $24.5. It expired in the money at $1.91 = $26.41-$24.5, that is the intrinsic value of the contract:

MSQ-AJ was the in-the-money call with strike at $25. The intrinsic value is $26.41-$25=$1.41 and the final price of this contract at expiration was $1.4:

MSQ-AY was an out-of-the-money call with strike at $27.5. It had no intrinsic value and it expired at $0.05:

And what about put contracts? Microsoft went down on expiration day.
MSQ-MY was the in-the-money put with strike at $27.5. It's intrinsic value was $1.09 and it expired at $0.95:

MSQ-MS was the in-the-money put striking at $27. With intrinsic value at $0.59 it expired at $0.65:

Finally, MSQ-MJ was the out-of-the-money put striking at $25. With no intrinsic value it expired at $0.05:

One could take note that an option can still move a lot on expiration day. MSQ-MS had a 700% gain within Friday.

Categories: stock options
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The Price of Puts

2006-01-18T09:09:00.000-05:00

Today I want to consider the case of put options. This is the price of the underlying security over the past six months:

I will start with a put that stays in-the-money over the whole period, MSQ-MX, with strike price $30. If I were to short MSFT at the beginning of September and cover in October, I would make a gain of (27.25-24.5)/24.5 = 11.22%, where I am neglecting the effect of the interest charged on my stock loan. A similar trade done using MSQ-MX would be done by buying the put and selling it for a profit later on. No actual shorting of MSFT stock would be needed. The yield would be in this case (5.5-2.8)/2.8 = 96.42%.

With MSQ-MT, strike price $29.5, I would get (5-2.5)/2.5 = 100%:

Using MSQ-MY, strike price $27.5, gives (3.25-1.1)/1.1 = 195%. The chart shows the price action during the periods this put goes in-the-money:

MSQ-MS, strike price $27, gives (2.8-0.8)/0.8 = 250%:

MSQ-MJ, strike price $25, with only a short period at-the-money, yields (1.3-0.3)/0.3 = 333%:

MSQ-MR, strike price $24,5, is almost always out-of-the-money, and yields (1.05-0.25)/0.25 = 320%:

MSQ-MX, strike price $22,5, is always out-of-the money and gives (0.375-0.1)/0.1 = 275%:

I see again in the case of puts that the best gain on a trade of this kind is obtained by picking a put that goes from out-of-the-money most to at-the-money.

The depreciation of puts follows a similar pattern to the one noted in the case of calls. It gets more pronounced to deeper out-of-the-money they are. Out-of-the-money puts behave quite like penny stocks as well.

Categories: stock options
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The Price of Out-of-the-money Options

2006-01-17T10:18:00.000-05:00

I'm going to consider now the case of call options expiring this week that have been going in and out of the money during the past few months. Again, this is the price of the underlying security (Microsoft stock) during the past six months:

The call at strike $27, MSQ-AS, was in-the-money the first half of August and for most of November through the first half of December. The same trade examined in my previous post would yield now (1.6-0.3)/0.3 = 433%.

Moving further out-of-the money, the call at strike $27.5, MSQ-AY, who was at-the-money the second half of November, would yield, doing the same trade, (1.3-0.25)/0.25 = 420%.

And, if I consider a call that was always out-of-the-money, MSQ-AT, with strike at $29.5, I get with the same trade (0.4-0.1)/0.1 = 300%.

If I compare the price of out-of-the-money calls with the in-the-money calls seen in the previous post it jumps out that it is not just much cheaper but it follows the underlying security only qualitatively, the more so the deeper out-of-the-money it is. More to the point, it clearly depreciates as the expiration date comes closer, no matter what the underlying security is doing, and the depreciation becomes more pronounced the more out-of-the-money it is.

Therefore, it appears that the best yield on a trade of this nature is not necessarily obtained by picking the cheapest contract. In fact, a contract that it is only moderately out-of-the-money and that is more likely to get in-the-money for certain periods of time, is the best pick.

Moreover, the general price behavior of calls out-of-the-money becomes increasingly similar to a penny stock the more out-of-the-money they are. Just compare the graphs above with the ones posted in the companion blog "penny stock scams".

Categories: stock options
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The Price of In-the-money Options

2006-01-16T16:48:00.000-05:00

My posts of January 7 have defined what calls and puts are. I would like to get a closer look now on how the price of these contracts is affected by the underlying security price has this moves relative to the contract strike price. The transactions considered in my previous posts where between someone writing call or put contracts that did not exist before to someone else that is buying them for protection. Now I am going to look at someone buying and then selling the same contracts in the secondary market for options. In the previous case the writer of the contract has to honour the contract if the underlying stock is assigned to her. That is she has to sell the stock to the call buyer at the strike price or she has to buy the stock from the put buyer at the strike price. In the case considered here there are no obligations.

Let's take the example of Microsoft options. I will consider options expiring at the end of next week as this will show better the effect of time decay to the option price.

The following chart shows Microsoft stock price in the past six months:

Note how MSFT oscillates pretty much between $24 and $29.5 during this period.
Below we see the price of MSQ-AX, the call with strike at $22.5 expiring in January. It has always been in the money during the past six months. The main difference between MSFT and MSQ-AX appears to be the fact that it is on average 15% the price of MSFT, this factor oscillating between 10% and 20% over this period of time. The price of both securities appear to be moving about the same way. The consequence of this is that buying MSQ-AX instead of MSFT is giving me a considerable leverage. Let's see why. If I buy MSFT at $24.5 in October and I sell it at $28 in November, I gain 14.28%. On the other hand, if I buy MSQ-AX at $2.5 in October and I sell it at $5.5 in November, I gain 120%. That's the leverage.

If we now look at MSQ-AR, the call with strike at $24.5, we see a higher leverage, since the same trade would have gained by (3.5-1.25)/1.25 = 180%. This contract was actually at the money for a few days in October, when we are assuming to have started the trade.

And if we look at MSQ-AJ, with strike at $25, we see an even higher leverage, where the same trade would yield (3.25-1)/1 = 225%. This contract was slightly out of the money in October.

Categories: stock options
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Yield Curve Update 2006/01/13

2006-01-14T07:46:00.000-05:00

The yield curve as of yesterday (green curve) appears to have come much closer to real inversion than it was last month:

The long term view on treasury yields seems to confirm that the uptrend support line of the 10 year note has indeed turned into resistance and has stopped and reversed the rise of interest rates on the long side of the yield curve.

Categories: bond market, interest rates
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The Stock Market is for suckers…. - Blog Maverick

2006-01-10T10:45:00.000-05:00

Just read "The Stock Market is for suckers...", by Marc Cuban. Great insight, as usual.

Put Options

2006-01-07T16:25:00.000-05:00

We have seen in the previous post that a call option is basically an insurance contract protecting against a loss of capital by effectively stopping the loss to a determined amount, the premium paid to purchase the contract.

Now what about locking gains? Is there a way to pay a premium in exchange for the insurance that current gains will not be lost in the future? Such contract exists and it is called a put option.

Let's continue with the same example and say that John already owns 300 shares of GE and he has a gain at the current market price of $35.47. He likes the dividends that he is getting and he wants to hold on the stock. However, he wants to make sure that he is not going to lose his current gain if the stock were to go down in the future.

He is looking at an expiration date of the 3rd Friday of March. There are several put contracts available:

GE-OF with $30 strike price and a cost of $0.05 a share as of Friday at the close.
GE-OZ with $32.5 strike price and a cost of $0.15 a share.
GE-OG with $35 strike price and a cost of $0.7 a share.
GE-OS with $37.5 strike price and a cost of $2.4 a share.
GE-OH with $40 strike price and a cost of $4.8 a share.
GE-OV with $42.5 strike price and a cost of $7.2 a share.

Buying any of this contracts gives the right to sell to the contract writer 100 shares of GE at the given strike price before or on the third Friday of March.

Let's say that John has a gain of $7.47 a share because he purchased his 300 shares at a price of $28. Locking a gain of $7 a share by buying 3 GE-OG contracts will cost him $0.7 a share, with a certain gain of $6.3 a share. Locking a gain of $9 a share by buying 3 GE-OS contracts will cost him $2.4 a share, with a certain gain of $6.6 a share. Locking a gain of $4.5 a share by buying 3 GE-OZ contracts will cost him only $0.15 a share with a certain gain of $4.35 a share.

Of course, he will find convenient to exercise the option only if the actual gain on his GE investment will fall below the gain locked by buying the options before or on the expiration date. Otherwise, the premium paid to buy the options will be a loss, albeit small, effectively reducing is gain on the GE investment.

Here again we have the distinction between in the money options like GE-OS, GE-OH and GE-OV, at the money options like GE-OG, and out of the money options like GE-OF and GE-OZ.

Don't forget to check out my other blog exposing penny stock scams.

Categories: stockoptions
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Call Options

2006-01-07T09:33:00.000-05:00

I have been posting about penny stock scams quite a bit. Probably the main reason why people fall for such scams is because the low price of these stocks is combined with high volatility, generating the illusion of quick and large gains from a small initial investment. Penny stocks are not the only security available that share these characteristic. Just like penny stocks options can be cheap to buy and can change their value quite drastically in a short time. That makes options another financial instrument that can be promoted to naive investors or traders.

This post is just an introduction to the topic of options, which I find in many respects fascinating.

First of all, it is important to understand what options really are. Options are for all intent and purpose insurance contracts. It is better to use an example to understand this concept.

Let's say that Susan wishes to buy 300 shares of General Electric. Yesterday GE closed at $35.47 a share. Susan is bullish and believe that GE will get much higher in price next month. Of course, she could just buy and hold until her target is reached and then sell for a profit. But, what if GE price doesn't go up? She would be stuck with a $300*35.47 = $10,641 investment that is not generating the desired gain or, worst, is losing money. Of course, she will be entitled to dividends (at $1 per share, a 2.8% yield) if she keeps the shares until the 25th of January. However, if GE goes down by more than $1 she will lose money on this investment.

Susan decides to buy 3 call options for GE that expire the 3rd Friday of February. Each option contract entitles her to buy from the contract writer 100 shares of GE at a specified price (the strike price) before or on the date of expiration of the contract. There are four such contracts available right now:

GE-BF, with a $30 strike price, that was priced $5.6 as of yesterday at the close.
GE-BZ, with a $32.5 strike price, that was priced $3.2.
GE-BG, with a $35 strike price, that was priced $1.05.
GE-BS, with a $37.5 strike price, that was priced $0.15.

In fact, the price of each contract must be multiplied by 100 because it corresponds to 100 shares of GE stock. That means that acquiring the right of buying 100 shares of GE before the 3th Friday of February at $30 costs $560.

Let's say that Susan purchases 3 such contracts. She spends 3*$560 = $1,680. If she were to take advantage of her acquired right immediately, she would spend 300*$30 = $9,000 to purchase the stock. Her total cost would therefore be $10,680, slightly higher than if she were to buy the stock at the closing price (I am disregarding commissions for the moment).
However, if she holds on the options and GE stock price goes, say, to $40 a share before the expiration of the options, she can exercises her right to buy at $30, sell at market and cash a gain of $3,000 - $1,680 = $1,320. On the other hand, if GE stock tanks below $30, she will do nothing and by the time the option expires her loss will be limited to $1,680.

Summarizing, if GE stock goes below $30, by buying the options instead of the stock, Susan is effectively insuring herself of stopping her loss at the option cost of $1,680. If she had purchased the stock directly at $35.47, her loss would be equal or larger than $1,641. On the other hand, in order to make any money she needs to see GE stock price go higher than $35.6 before the expiration. A call option with strike price lower than the market price of the underlying security is called "in the money". Such call options are the most expensive for a given expiration date.

The same consideration could be made for the other contracts available. Buying 3 calls at $35, with a price of $1.05 per share will stop the loss at 300*$1.05 = $315, but will generate a gain only if GE price goes higher than $36.05. This call option has strike price close to the market and it is called "at the money".

The cheapest call options are the ones with strike price above the market. They are "out of the money". Buying 3 calls at $37.5 limits the loss at just 300*$0.15 = $45, but will produce a gain only if GE goes above $37.65 before expiration.

Note how buying a call option in the money is pretty much equivalent to buy the shares of the underlying security and set a stop loss order at the strike price, the difference in the option case being that the capital outlay to purchase the shares occurs only if the trade is actually profitable.

At the other end of the range, buying a call option deep out of the money is more like buying a lottery ticket. The ticket is cheap but the chance of actually making money is slim.

Categories: stockoptions
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Has the yield curve inverted already?

2005-12-30T11:18:00.000-05:00

In my previous post I said that the yield curve is likely to invert next year if the Fed keeps rising the rate. Since Tuesday, a lot of fuss has been made in the press about the fact that the 2-year note yield has gone higher than the 10-year note yield, as shown by the yield curve as it appears at the time of writing this:

However, in my opinion this is not yet an inverted yield curve. When yields from the 6 month bill to the 10 year note are confined within 10 basis points any fluctuation can cause a little inversion within that duration range. I would wait for the 3 month bill to yield more than the 10 year note to call it an inverted yield curve.

Categories: bondmarket, interestrates
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yield curve keeps flattening

2005-12-25T07:59:00.000-05:00

Looks like the support line of the 10-yr note yield has become resistance, at least as far as the 30-yr bond yield is concerned. The yield curve is still flattening and any further rise of the fed rate could well cause an inversion next year.

The charts below show the price history of the 5yr-10yr note spread and of the 2yr-10yr note spread which can be used to trade either the steepening or the flattening of the yield curve. Details on how to construct these spreads can be found at the CBOT sites: The TUT Spread, Yield Curve Shift Trading Opportunities, Treasury Duration Adjustments.

Categories: interest rates, bond market

New penny stock blog

2005-12-04T10:49:00.000-05:00

I just started a new blog focused on penny stock scams. The current blog will be dedicated to the study of financial markets only.

The stock market and gold

2005-12-03T07:39:00.000-05:00

I have been following the development of the global carry trade by watching the correlation of the US stock market and the euro currency. The recent surge of the price of gold makes me wonder if there is somethimng going on there as well.

The two charts below show the US stock market priced in euros compared with the US stock market in US dollars and the US stock market priced in gold, again compared with the price in US dollar. It appears that a correlation between gold and the US stock market has been going on in a similar fashion than the one between the euro and the US stock market. The gold correlation seems to have been even more stable than the euro correlation and it has broken down for the first time in three years only recently. However, the direction of the breaking is the opposite of the one taken by the euro correlation.

For the sake of comparison with another traditional conservative investment, the following chart shows the US stock market priced in US treasury bonds compared with the price in US dollars. Here the correlation is still unbroken.

These charts provide a long term perspective for all the three cases that I am watching.

Categories: stock market, currencies, correlations

Yield curve update 2005/11/20

2005-11-20T17:10:00.000-05:00

The following chart shows the yields of the 30-year US treasury bond (blue), 10-year US treasury note (black), 5-year US treasury note (red) and 13-week US treasury bill (green) during the past few years.

The interest rate rising policy of the Fed has broken the recently established downtrend in the 30-year yield. The 10-year downtrend is being tested but it is not quite broken yet.

The next step is to observe if the 30-year yield downtrend line will become a resistance line, stopping the rise, at least for a while.

Categories: interestrates, bondmarket

The dollar carry trade may be unfolding again

2005-11-15T12:58:00.000-05:00

In a previous post I commented on the US stock market getting strongly correlated again with the euro, as a sign that the global carry trade was back in vogue. The recent steep drop in the euro (see graph below) may have something to do with a change in the trade.

The graph above shows how the volatility of the ratio SPX/XEU, after a brief respite, is growing again. The ratio is rapidly expanding against its upper Bollinger band.

On the other hand, if one takes a longer term perspective, such as the one illustrated in the graph above, the effect of this global trade in affecting the value of the US stock market has been unparalleled. Even during the bubble years the performance discrepancy between SPX in US dollars and SPX in euros was not so pronounced as in the past three years.

A similar decline has been undergoing in the Japanese Yen as well:

Similar SPX/XJY graphs are presented here for the sake of comparison with the euro.

Categories: stockmarket, currencies, correlation

USATODAY.com - Pink Sheets scams may give investors nightmares

2005-11-13T11:19:00.000-05:00

Looks like the junk promoters are attracting the attention of the authorities.

USATODAY.com - Pink Sheets scams may give investors nightmares

They must have gotten too overconfident and gone a bit too far.

Categories: pennystocks

Yield curve update

2005-10-22T08:51:00.000-04:00

Categories: interestrates, bondmarket

between hurricanes and the Fed

2005-09-26T07:45:00.000-04:00

The downtrend resistance line is still holding.

Categories: interestrates, bondmarket

yield curve at resistance

2005-09-17T08:02:00.000-04:00

The 30-yr bond yield has hit the downtrend resistance line. The yield curve is steepening as well since the short term rate has stayed close to the uptrend support.

Categories: bondmarket, interestrates

yield curve close to support

2005-08-31T19:42:00.000-04:00

The first real test of the long term yield downtrend happened in the first half of August with the confirmation of the downtrend resistance line determined by the 30yr bond yield. We are getting close to the next and most important test. The uptrend support line determined by the 5yr note yield is still valid. However, we are getting very close to it and it may break. Notice how the breaking of the support lines determined by the 30yr bond yield and by the 15yr note yield took several months to complete.

Categories: bond market, interest rates

The unwinding of the dollar carry trade may be done

2005-08-30T17:56:00.000-04:00

It's a while that I have not posted about the global carry trade. It appears like the unwinding of the trade that started in late May is over and the volatility is back to the normal value typical of the past couple of years:

Looking at the SP and EC contracts, it is quite possible that the trade is starting again on a new level but it is probably to early to tell:

Categories: stock market, currencies, correlations

new yield curve update

2005-08-21T10:10:00.000-04:00

Long term yields have been rejected by the respective downward trendlines.

Categories: bond market, interest rates