3433-vol. 6 issue 2-3.pmd - iarfc

Volume 6, Issue 2 & 3 115
Hypothesis Testing:
(1) Average Returns Wilcoxon signed rank test = 4.62 (p-value = 0.00)
are equal. van der Waerden test = 4.34 (p-value = 0.00)
(2) Standard Deviations Wilcoxon signed rank test = 4.22 (p-value = 0.00)
are equal. van der Waerden test = 4.03 (p-value = 0.00)
Data and Methodology
The data were collected from the Dow Jones Call Option database for
January 1990 through December 2003, which was provided by Quantitative
Analytics, Inc., a Chicago-based company. Because of missing data, the
sample consisted of 28 companies.
There are many approaches to establishing a bull call spread. In this
paper a simple approach is adopted, with the assumption that, on the third
Friday of each month, investors buy one contract of the call option that has
the strike price right below the stock price, and sell one contract of the call
option that has the strike price right above the stock price. Both calls should
have the same term to expiration, 3 months in this analysis. If no calls with 3
months to expiration were available, options with 4 months to expiration were
used. In the case that 4 month calls were not available, 2 month calls were
used. Then the investors liquidate the position approximately one month
later. This is repeated month after month. Therefore, the long position of the
spread has intrinsic value and time value, but the short position has only time
value. As indicated earlier, buying a call is done at the ask price, and selling a
call is done at the bid price. A simple investment strategy is assumed, without
considering any type of follow-up. Therefore, this investment strategy can be
used by anyone even if she or he has no sophisticated skills in options
trading. It should be remembered that the goal is to determine whether or not
a so-called “simple” strategy, such as bull call spread, works for ordinary
investors.
To measure the performance of the strategy, Sharpe ratios (Sharpe
(1966, 1994)) are used. The Sharpe ratio is a measure of risk-adjusted performance
that uses a benchmark based on the ex post capital market line. It
measures returns relative to the total risk of the portfolio where total risk is the
standard deviation of portfolio returns. Other measures widely used in
measuring performances include the Treynor index and Jensen’s alpha. Given
the controversial validity of the beta coefficient (e.g., Fama and French (1992,
1993, 1996)), however, the Treynor index and Jensen’s alpha are not appropriate
for the purpose of this study. The Sharpe measure of the bull call spread
is then compared to that of outright stock investment.
Research & Theory