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You are considering an investment in a CAT bond. The CAT bond will mature in one year and will pay the face value of $100 with probability of 98% (which reflects the probability of no major hurricane) and nothing with probability of 2% (which reflects the probability of a major hurricane). The beta of the CAT bond is zero. The market price of the bond is $90. The expected return on the market portfolio is 15%, and risk free rate is 2%.
a) What is the alpha of the CAT bond?
b) Perhaps, the estimated probability of a major hurricane was wrong. Please calculate the probability of a major hurricane that would make you indifferent between investing and not investing in the CAT bond.
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