Trading Options

2006 was a fairly good year. The whole portfolio earned about 29%, while the stock-and-option trading earned 23%. In comparison, a holder of the S&P 500 index would have earned 15.7% (this figure includes the dividend yield, assumed to be 1.79% p.a. as estimated by Prof. Aswath Damodaran of NYU).

I have previously presented the summary statistics for the series of (logarithmic, or continuously compounded) daily returns on the whole portfolio, and the portfolio ex-futures. An update to those figures is now in order.

The “Average” row shows the average daily return. The row labeled “St.Dev.” gives the sample standard deviation of the series of about 250 (the number of trading days in one year) daily returns. The last row, “Sharpe Ratio” gives the ratio of average to standard deviation. These statistics are computed for three investment strategies. The “Full” column shows statistics for the entire portfolio, including trades in stocks, stock options and futures. As trading in futures is not particularly meaningful, and is done for the peace of mind only, its contribution to P&L of the whole portfolio can be isolated, leaving just the stock and option trades. Statistical measures for the resulting series of returns are shown in column “Ex-Futures”. The last column shows statistics for the S&P 500 index (each daily return has been incremented by a daily share of the assumed 1.79% per year dividend yield).

The conclusion is that the higher return, 0.083% daily, of my stock and option trading, as compared to 0.058% for the index, has come at the expense of a higher daily noise of 0.79% as compared to 0.63% for the index. However, when the ratio of the average daily return to its standard deviation is taken as the Sharpe Ratio measure of performance, it is seen that I have managed to outperform the index (the value of this ratio being 0.104 for the stock-and-option portfolio versus the value of 0.092 for the index).

The value of one dollar, invested as of January 1, 2006, in (dark blue) my actual portfolio, (purple) my portfolio with the exception of all futures trades and (yellow) the S&P 500 index:

Imagine that one dollar was invested on January 1, 2006. The value of the resulting portfolio during the year is shown by the dark blue line in the above chart. This line is built without any assumptions; it is merely a rescaled chart of the actual dollar value of the account. Positions were marked at mid-market to arrive at this value.

As the trading of futures is not done according to any model, it makes sense to isolate its effect and consider the portfolio value net of the contribution of trades in futures. The value of the one dollar under this assumption is shown by the purple line. The series, plotted by this line, is a series of mark-to-market values of a portfolio that includes trades in stocks, stock options, interest amounts, stock splits and dividend payments. The mark-to-market calculation is done using the daily closing prices I maintain in a database.

Lastly, the yellow line represents the value of one dollar invested in the S&P 500 index. As this index is not adjusted for dividends, I make an assumption about the annual dividend yield. Prof. Aswath Damodaran of NYU gives an estimate of 1.79% annual yield. Accordingly, each daily return of the series of index returns, used to build the yellow line, is incremented by 1.79%/250, assuming 250 business days per year.

The following table shows the same statistics for the entire trading history, up to the end of the year 2006.

The following chart is similar to the chart for 2006 above, except it covers the entire trading history. It shows the value of one dollar, invested as of the date the trading commenced, in (dark blue) my actual portfolio, (purple) my portfolio with the exception of all futures trades and (yellow) the S&P 500 index.