Trading Options

COF Update

The most notable development was a notable decline in liquidity. The typical bid-ask spread observed during the day has widened from 1 cent to about 2 cents. However, the jumpiness of price moves has risen by more than this. The sharp price moves just after the open at 9:30 AM show the decline in liquidity most spectacularly.

For example, a stop order set at, e.g., 77.50 and trigered shortly after the open, could be executed as far as 20 cents away from the trigger level. The points to note are that,

• Stop orders are not normally executed outside of NYSE hours, as the stock price is not really well-defined (the bid-ask spread is very large). It is only in case of exceptional circumstances (an earnings release, for example), that the underlying risk that led to stop orders is sometimes hedged manually.
• The observation that the order was triggered after the open means that just before the open or around the opening time, the prices have not yet moved enough to trigger the stop. In other words, it is not the case that the execution of the order is delayed by the decision to not hedge prior to the open.

So, it is really the widened bid-ask spread or a very jumpy price behavior,
that lead to this exceptionally large slippage.

Throughout the past week, COF continued to trade in a range, and no exceptional price moves have taken place. The model-based estimate of the current realized volatility has remained at about 25-25.5%.

The past week has been relatively quiet. COF has been range-bound, trading between 75.75 and 78.74. At Friday’s close it was about 1% down from its level when the current strategy was initiated. Its intraday volatility was largely as expected. I would have benefited from setting wider intervals for delta hedging (at the expense of a larger tracking error if any big move did take place).

No new ideas have come up, as the market scanner’s analysis of volatility measures continues rejecting all supported strategies. I would like to spend some time working on new model development; this is the best way to generate ideas.

In other markets, I have noticed a significant decline of EUR and JPY against the dollar on Friday.

For several weeks, my market scanning program was returning exactly zero new trade ideas. In other words, all strategies of several types the program supports were being rejected. I am pleased to report that a new strategy has appeared and has been put in action. The idea: shorting the volatility of COF (Capital One Financial Corp.), using the options expiring in March 2007. Let’s talk about some basic features of this stock and its options.

COF is a fairly expensive stock that traded around 77.50 recently. It is fairly liquid. While I was watching the market and putting positions in place, the bid-ask spread in the stock price was 1 cent most of the time, only occasionally widening to 2 cents. However, the prices often moved with a sort of a jump, i.e., from 77.45-46 bid-ask, to 77.47-48 (as opposed to moving to, e.g., 77.46-47), so the true average sum of slippage and spread is probably a bit over 1 cent. This jumpiness is bad when trading the hedge position.

The March 2007 options on COF displayed varying liquidity over time. I am typically interested in options that are somewhat out-of-the-money. For options priced at around 1.50-2.00, the bid-ask varied from very occasional 5 cents to all the way wide at 15 cents, while I was monitoring them. This corresponds to a widening of bid-ask spread in implied vol from about 0.3% to about 1%. The spread of 10 cents, or about 0.6% in terms of implied vol, was most typical. So, it was important to trade carefully.

The main option being shorted had the implied volatility of about 28.5% when the pre-trade analysis was done. I saw the current (realized) volatility at about 23%. An analysis of recent history suggests that, in the longer term in the past, the typical volatility was about 22%.

COF last released its earnings on October 18, 2006. The next quarterly release will probably come around January 18, 2007 and the following one, around April 18, 2007, will occur after the March 2007 options expire. So there is one earnings release between now and the expiration date.

Needless to say (this is beyond the scope of this post), the options traded also pass other criteria - particularly the criteria, comparing the model-based prices to prices seen in the market.

Disclaimer: I hold positions in securities discussed in this posting. This posting is not an investment advice.

Today I will analyze the correlation of contemporaneous returns on my portfolio with those of S&P 500 index. Just as I would have hoped, the correlation between returns of the stock-and-option portfolio and those of the index has been close to zero since when I started using my current set of models.

The input data are prepared as follows.

A series of dates is considered. This series covers all business days since late 2003 and until now. Prior to this, these were some missing data. The returns for the whole portfolio, the portfolio excluding the impact of trades in futures, and the S&P 500 index are computed for consecutive pairs of dates. I then compute rolling correlations. For a given date, I take a window of the series of returns that includes the preceding 6 months, take the series of index returns and returns for either the full portfolio, or the portfolio ex-futures, and compute the sample correlation.

The result is an estimate of correlation between daily returns, on the same day, of the index and of my portfolio (or the portfolio ex-futures). The estimates are available from early 2004 (the dates of the first 6 months are lost because to estimate the correlation for a given date, I need to have data for all of the preceding 6 months) until present. The results are shown in the following chart.

Reviewing the above chart, I cannot explain the strongly negative correlations seen at the end of 2004 and the start of 2005. To understand this, I would need to review the positions at that time - for example, whether they were balanced between puts and calls or whether one option kind was traded in preference to the other. I think this negative correlation was due to an outright short position (not short volatility - this would not be unusual at all, but actually short one or more stocks). This position or rather, some trading that preceded me taking this position, were in violation of the rules that I impose on the type of positions that I allow myself to take.

Since then, I have been much more diligent in avoiding directional positions in stocks. As the chart shows, the correlation (for the stock-and-option portfolio) was quite small since the middle of 2005. It has been positive, which is not very good. However, this reflects the basic fact that a portfolio short in volatility tends to decline in value, as the volatility rises when the market experiences a decline. This positive correlation is hard to avoid.

To explain the positive and not-so-small (around 20% during the recent months) correlation between the returns of the whole portfolio and the index, I would need to research the correlation between the major foreign currencies and S&P 500. This is not a very interesting subject in the context of my typical positions. For example, if the Euro happened to be somewhat correlated with S&P 500, this would not mean much as I do not trade any pure correlation products. If I were aggressive in utilizing margin or the Value-at-Risk allotment for the entire portfolio, then the co-dependency between futures and stocks would be of importance. However, the risks being taken are quite moderate (I wish there were more good trade ideas!) In the long run this correlation simply does not matter.

Summary

I have observed that the correlation between my trading in stocks and options has been small and positive over the latest year. Its small magnitude is reasonable, as most of the time the positions are delta-neutral. The small positive value might be due to mis-hedging - meaning that I need to hold small short-the-stocks positions in addition to whatever hedges my models tell me to hold. Alternatively, it might be the evidence of me not buying insurance against a sudden drop in the market. Time will tell.