Using a spreadsheet, extend Leavens’ analysis to a bond portfolio that holds 20 bonds.

1. Graph the resulting probability function for ¹ P.
2. Based upon Leavens’ “spread between probable losses and gains” VaR metric, what is the VaR of the portfolio?

1. Measured in USD 1000s, the portfolio’s value ¹P 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 below.

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 1P is binomially distributed with parameters 20 and 0.9. Accordingly:

[s4]