This study spans just over nine years of data, a time in which the annualized returns for the equity indexes were lower than their respective long-term historical averages. According to Ibbotson (2006), large-cap stocks posted an annualized return of 10.4% from 1926 through 2005 and small-cap stocks returned 12.6% over that same period.

Over the period of this study, the DJIA advanced 7.7% and the Russell 2000 Index returned 8.1%. International stocks (MSCI EAFE Index) advanced 11.2% annualized since 1969 but returned 8.3% during this study period.

During this period of positive but lower-than-average stock market returns, the BXD posted advances comparable to those of other equity indexes (Exhibit 4). Bond returns were more in line with long-term averages during the period of this study.

Long-term government bonds advanced 5.5% and Treasury bills advanced 3.7% annualized since 1926, which is similar to the 6.1% return for the Lehman Brothers Aggregate Bond Index (comprised of intermediate and long-term bonds) and the 3.4% return for 3-Month T-Bills over the course of this study. During a somewhat normal performance period for cash and bonds, the BXD outperformed.

Summary of Risk

The BXD posted returns similar to several equity indexes but exhibited significantly less volatility over the course of this study. The BXD's annual standard deviation was approximately 75% of that experienced by the DJIA and was only slightly more than half that of the Russell 2000.

The period of study was modestly less volatile compared with the long term. According to Ibbotson (2006), the annual standard deviation of large-cap stocks from 1926 through 2005 was 20.2%, and the small-cap stock standard deviation was 32.9% over that same time period.

Since 1969, the volatility of international stocks (MSCI EAFE Index) was 22.1%. Volatility is not the only relevant measure of risk.

Downside deviation illustrates the magnitude of the largest decline during the period of study. Even though the BXD performance data show a negative skew (Exhibit 8), the BXD's downside deviation (8.2%) was smaller than that of all three equity indexes, and as expected, larger than bonds (Lehman Brothers Aggregate Bond Index) and cash (3-month T-Bills).

Exhibit 6: The graph above plots several indexes according to their respective risk and reward. Over the course of the study, the BXD posted annualized returns similar to equity indexes but experienced less volatility. The BXD's performance was superior to fixed income and cash, but exhibited greater volatility.

Exhibit 7: The Sharpe ratio is a measure of risk-adjusted returns. It is calculated by dividing the average return in excess of the risk-free rate by standard deviation. Over the course of this study, the BXD's Sharpe ratio was lower than bonds and international stocks but above large-cap and small-cap U.S. stocks.

Despite only modest outperformance above the risk-free rate (3-month T-bills, 3.4% over the course of the study), the Lehman Brothers Aggregate Bond Index enjoyed the highest Sharpe ratio because its standard deviation was far lower than the other indexes.

Although the BXD's performance showed measurable levels of skew and kurtosis, previous BuyWrite index studies indicated that similarly constructed indexes were not materially affected by skew and kurtosis, making the Sharpe ratio a relevant measure of risk-adjusted returns.

Bonds exhibited a higher Sharpe ratio than stocks due to the lower-than-average returns for stocks over the course of this study. According to Ibbotson, the Sharpe ratio for stocks from 1926 through 2005 was 0.42 and the Sharpe ratio for long-term government bonds was 0.22 over the same period.

Exhibit 8: Autocorrelation illustrates the correlation of a series to the same series only shifted by one period (DeFusco 2001, p. 500). High numbers indicate greater consistency of performance from one period to the next. Skewness indicates the magnitude and direction of data distribution relative to the mean (DeFusco 2001, p. 138), and kurtosis is the degree of "peakedness" of a distribution (DeFusco 2001, p. 142). A high kurtosis distribution has a sharper "peak" and fatter "tails," while a low kurtosis distribution has a more rounded peak with wider "shoulders."

The Annualized Compound Return is a geometric annualized mean of monthly returns (DeFusco 2001, p. 125).

The S&P 500 annualized return over this period was 6.47%. Standard deviation is a measure of dispersion of monthly returns that illustrates portfolio volatility (DeFusco 2001, p. 131). Downside deviation is a measure of the variability of negative monthly returns.

Sharpe ratio does not consider skew or kurtosis in its calculation, but previous studies suggest that the performance of similarly calculated BuyWrite indexes is not materially affected by the negative skew and excess kurtosis (Callan 2006).

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