936 Part VI: Measuring and Trading Volatility 
MATHEMATICAL RANKING 
The discussion above demonstrates that it is not possible to ultimately define the best 
strategy when one considers the background, both financial and psychological, of the 
individual investor. However, the reader may be interested in knowing which strate­
gies have the best mathematical chances of success, regardless of the investor's per­
sonal feelings. Not unexpectedly, strategies that take in large amounts of time value 
premium have high mathematical expectations. These include ratio writing, ratio 
spreading, straddle writing, and naked call writing (but only if the "rolling for cred­
its" follow-up strategy is adhered to). The ratio strategies would have to be operated 
according to a delta-neutral ratio in order to be mathematically optimum. Unfor­
tunately, these strategies are not for everyone. All involve naked options, and also 
require that the investor have a substantial amount of money ( or collateral) available 
to make the strategies work properly. Moreover, naked option writing in any form is 
not suitable for some investors, regardless of their protests to the contrary. 
Another group of strategies that rank high on an expected profit basis are those 
that have limited risk with the potential of occasionally attaining large profits. The T­
hill/option strategy is a prime example of this type of strategy. The strategies in which 
one attempts to reduce the cost of longer-term options through the sale of near-term 
options fit in this broad category also, although one should limit his dollar commit­
ment to 15 to 20% of his portfolio. Calendar spreads such as the combinations 
described in Chapter 23 (calendar combination, calendar straddle, and diagonal but­
terfly spread) or bullish call calendar spreads or bearish put calendar spreads are all 
examples of such strategies. These strategies may have a rather frequent probability 
of losing a small amount of money, coupled with a low probability of earning large 
profits. Still, a few large profits may be able to more than overcome the frequent, but 
small, losses. Ranking behind these strategies are the ones that offer limited profits 
with a reasonable probability of attaining that profit. Covered call writing, large debit 
bull or bear spreads (purchased option well in-the-money and possible written option 
as well), neutral calendar spreads, and butterfuly spreads fit into this category. 
Unfortunately, all these strategies involve relatively large commission costs. 
Even though these are not strategies that normally require a large investment, the 
investor who wants to reduce the percentage effect of commissions must take larger 
positions and will therefore be advancing a sizable amount of money. 
Speculative buying and spreading strategies rank the lowest on a mathematical 
basis. The T-bill/option strategy is not a speculative buying strategy. In-the-money 
purchases, including the in-the-money combination, generally outrank out-of-the­
money purchases. This is because one has the possibility of making a large percent­
age profit but has decreased the chance of losing all his investment, since he starts