Chapter 40: Advanced Concepts 867 
TABLE 40·8. 
General risk exposure of common strategies. 
Strategy Delta Gamma Theta Vega RHo 
Buy stock + 0 0 0 0 
Sell stock short 0 0 0 0 
Call buy + + + + 
Put buy + + 
Straddle buy 0 + + + 
Covered write + + 
Naked call sale + 
Naked put sale + + + 
Ratio write 
(straddle sale) 0 + 
Calendar spread 0 + + 
Bull spread + + 
Bear spread + 
Ratio call spread 0 + 
Ratio put spread 0 + + 
As might be expected, spread strategies involving both long and short options are 
less easily quantified than outright buys or sells. The calendar spread strategy is one 
in which the spreader does not want a lot of stock movement - he would prefer the 
underlying security to remain near the striking price, for that is the area of maximum 
profit potential. This is reflected by the fact that gamma is negative. Also, for calendar 
spreads, the passage of time is good, a fact that is reflected by the fact that theta is pos­
itive. Finally, since an increase in implied volatilities or interest rates would boost 
prices and widen the spread (creating a profit), vega is positive and rho is negative. 
A bull spread has positive delta, reflecting the bullish nature of the spread, but 
it has negative gamma. The reason gamma is negative is that the position becomes 
less bullish as the underlying security rises, since the profit potential, and hence the 
bullishness of the position, is limited. For similar reasons, a bear spread has negative 
delta (reflecting bearishness) and negative gamma (reflecting limited bearishness). 
Both the bull spread and the bear spread are the same with respect to the other risk 
measurements: Theta is negative, reflecting the fact that time decay can hurt the 
spread. Less obvious is the fact that these spreads are hurt by an increase in per­
ceived volatility; a negative vega tells us this is true, however. 
These risk measurement tools are important in that they can quite graphically 
depict the risk and reward characteristics of an option position or option portfolio.