(Risky Business) Suppose we are considering investing in a Venezuelan bond. The Venezuelans have just cast off Chavismo, but 17 years of rule by Ch´avez has left the country in tatters: inflation and crime are high and debt owed is more than the reserves held. Furthermore, the country’s main wealth (oil) has fallen greatly in value. Because of this, Venezuelan government bonds are trading at very high yields. If Venezuela is able to pay their debts, a bond will pay off $1000 in one year; if not, creditors will only get a partial recovery: a bond will pay off, say, $500.
a) If the bond is a zero-coupon bond and the probability of a default is 1/2 — and a “riskfree” zero-coupon bond is yielding 10% — what is the present value of the Venezuelan bond?
b) What is the yield of the Venezuelan bond?
c) Now suppose we can invest in a risky perpetuity. Each year we flip a coin. If the coin comes up heads, we get $15; otherwise, we get $30. What is the value of this perpetuity if we can invest in risk-free zero-coupon bonds yielding 10% annualized?