Chapter 26: Buying Options and Treasury Bills 417 
the 30-day period. However, for purposes of computing annualized risk easily, the 
assumption that will be made is that the risk during any holding period is 100%, 
regardless of the length of time remaining in the life of the option. Thus, a 30-day 
option purchase represents an annualized risk of 1,200% (100% risk every 30 days 
times twelve 30-day periods in one year). Ninety-day purchases have 400% annual­
ized risk, and 180-day purchases have 200% annualized risk. There is a multitude 
of ways to combine purchases in these three holding periods so that the overall risk 
is 10% annualized. 
Example: An investor could put 2½% of his total money into 90-day purchases four 
times a year. That is, 2½% of his total assets are being subjected to a 400% annual­
ized risk; 400% times 2½% equals 10% annualized risk on the total assets. Of course, 
the remainder of the assets would be placed in risk-free, income-bearing securities. 
Another of the many combinations might be to place 1 % of the total assets in 90-day 
purchases and also place 3% of the total assets in 180-day purchases. Thus, 1 % of 
one's total money would be subjected to a 400% annual risk and 3% would be sub­
jected to a 200% annual risk (.01 times 400 plus .03 times 200 equals 10% annualized 
risk on the entire assets). If one prefers a formula, annualized risk can be computed 
as: 
A al. d • k • r 1. Percent of total 360 nnu 1ze ns on entire portro 10 = d x assets investe Holding period 
If one is able to diversify into several holding periods, the annualized risk is merely 
the sum of the risks for each holding period. 
With this information in mind, the strategist can utilize option purchases of 1 
month, 3 months, and 6 months, preferably each generated by a separate computer 
analysis similar to the one described earlier. He will know how much of his total 
assets he can place into purchases of each holding period, because he will know his 
annualized risk. 
Example: Suppose that a very large investor, or pool of investors, has $1 million com­
mitted to this T-bill/option strategy. Further, suppose ½ of 1 % of the money is to be 
committed to 30-day option purchases with the idea of reinvesting every 30 days. 
Similarly, ½ of 1 % is to be placed in 90-day purchases and 1 % in 180-day purchases. 
The annualized risk is 10%: 
Total annualized risk = ½% x 360 + ½% x 360 + 1 % x 360 
30 90 180 
= .06 + .02 + .02 = 10%