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

116
Journal of Personal Finance
The Sharpe ratios are calculated as follows:
___
___
R j
- R f
S j
= —————— (2)
ó j
where,
S j
= Sharpe ratio for an investment strategy j,
___
R j
= mean return on a investment strategy j,
___
R f
= mean return on U.S. Treasury bills, and
ó j
= standard deviation of return on strategy j.
For the Sharpe ratio calculation, the average of the three month T-Bill
was used as the risk free rate.
The Sharpe ratio of the bull call spreads for the whole sample period
of 1990-2003 was calculated. Two sub-periods: the more bullish period and
the less bullish period were also considered. 6 The more bullish period covers
the period of January 1993 through December 1999. The rest of the sample
period is called the less bullish period: from January 1990 to December 1992
and from January 2000 to December 2003.
Empirical Results
Table 2 presents the performance results for the bull call spread and
the outright stock investment for the sample period of January 1990 –
December 2003. For each sample firm, the table lists the average returns,
standard deviations, and the Sharpe ratios of the two strategies. It should be
noted that all of these results are based on monthly returns. For example, the
average monthly return on the Alcoa spread is -23.96% (approximately -96.3%
on an annual basis) while the average monthly return on the Alcoa stock is
1.23% (approximately 15.8% on an annual basis). Compared to outright stock
investment, the bull call spread is hideous. If anyone had used the spread for
an entire year, his or her money would have evaporated. Furthermore, the
standard deviations are 22.08% and 8.61%, respectively. Therefore, the bull
call spread generated terrible returns along with higher risk. Given these
average returns and standard deviations, the Sharpe ratios turn out to be -1.10
and 0.10 for the spread and stock investment, respectively. This indicates
that, for the Alcoa stock, the bull call strategy did not work at all during the
sample period. A bull call spread strategy using the Alcoa call options, as
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