Question

A. Find the Expected Return for a 0 coupon bond that pays $100 in one year with probability of 0.8 or defaults with probability 0.2. It currently trades for $90

B. What is the volatility of the same bond

Answer 1

(A)

In the case of default, the payment is $0.

Hence, the expected payoff can be calculated as (in $): -

The expected return is -11.11%: -

(B)

The volatility can be calculated as the standard deviation.

In case the bond pays $100, the return is 11.11%: -

In case the bond pays $0, the return is -100%: -

Hence, the variance: -

Hence, the standard deviation is 45.811%. The volatility is 45.811%.