The president of the United States is considering two different candidates to chair the Federal Reserve. If he chooses Alan, the probability that inflation will be 2 percent is 0.4 and the probability that inflation will be 4 percent is 0.6. If the president chooses Ben, the probability that inflation will be 2 percent is 0.6 and the probability that inflation will be 3 percent is 0.4. If you are an investor with your funds invested in bonds paying 7 percent, calculate the standard deviation of your real return if Alan is chosen to chair the Fed and if Ben is chosen to chair the Fed. Which candidate would you prefer? Explain why.
What will be an ideal response?
Your real interest rate is 7 percent minus the inflation rate.Under Alan, the probability is 0.4 that your real interest rate is 7% ? 2% = 5% and the probability is 0.6 that your real interest rate is 7% ? 4% = 3%. Your expected real interest rate is (0.4 × 5%) + (0.6 × 3%) = 3.8%. The standard deviation of your real interest rate is {[.4 × (0.05 ? 0.038)2] + [0.6 × (0.03 ? 0.038)2]}1/2 = 0.98%.Under Ben, the probability is 0.6 that your real interest rate is 7% ? 2% = 5% and the probability is 0.4 that your real interest rate is 7% ? 3% = 4%. Your expected real interest rate is (0.6 × 5%) + (0.4 × 4%) = 4.6%. The standard deviation of your real interest rate is {[0.6 × (0.05 ? 0.046)2] + [0.4 × (0.04 ? 0.046)2]}1/2 = 0.49%.You would prefer Ben because your expected real return is higher and your risk is lower.
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