Question: Consider n = 100 defaultable corporate bonds, where the probability of a default over the next year is identical for all bonds and is equal

Consider n = 100 defaultable corporate bonds, where the probability of a default over the next year is identical for all bonds and is equal to 2%. You can assume that bond defaults are independent events. The current price of each bond is 100 and if there is no default, a bond will pay 105 one year from now. If the bond defaults then there is no repayment. Do the following: (i) Compute the 95% VaR for a fully concentrated portfolio consisting of 100 units of bond 1. (ii) Compute the 95% VaR for a completely diversified portfolio consisting of 1 unit of each of the 100 bonds. (You may want to use the fact that if M ∼ Bin(100, 0.02) then P (M ≤ 5) ≈ .984 and P (M ≤ 4) ≈ .949, where P (A) denotes the probability of event A.

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