Exercise Solution 1.10

1. Measured in USD 1000s, the portfolio’s value has a binomial distribution with parameters n = 20 and p= 0.9. The general formula for the probability function of a binomial distribution is:

   [s1]

   

   Applying this to our portfolio, we obtain:

   [s2]

   

   This is graphed in Exhibit s1.

   

   Exhibit s1: The market value (measured in USD 1000s) of the bond portfolio has a binomial distribution with parameters 20 and 0.9.
2. The formula for the standard deviation of a binomial random variable X with parameters n and p is:

   [s3]

   

   Measured in USD 1000s, our portfolio’s market value is binomially distributed with parameters 20 and 0.9. Accordingly:

   [s4]