Peter invests $10,000 in debt securities that mature in one year and have a yiel

Question

Peter invests $10,000 in debt securities that mature in one year and have a yield to maturity of i = 4%. The following table shows three expected inflation rates which may occur with different probabilities. According to the probability distribution A, there is a 50% probability of the inflation rate of 3%, whereas the distribution B assigns a 30% probability to the inflation rate of 3%. Complete the following table by calculating the expected inflation rate, the expected real interest rate, and the risk to Peter's investment.

Explanation / Answer

Distribution A:
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Expected Inflation=(25%*0)+(50%*3%)+(25%*6%)=3%
Expected real interest rate=[(1+nominal)/(1+inflation)]-1
=[(1+4%)/(1+3%)]-1
=0.97%

Risk(%)= standard deviation of inflation
variation=[0.25*(3%-0)^2]+[0.5*(3%-3%)^2]+[0.25*(3%-6%)^2]
=0.05%
standard deviation= variance^.5
=2.121%

Distribution B:
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Expected Inflation=(35%*0)+(30%*3%)+(35%*6%)=3%
Expected real interest rate=[(1+nominal)/(1+inflation)]-1
=[(1+4%)/(1+3%)]-1
=0.97%

Risk(%)= standard deviation of inflation
variation=[0.35*(3%-0)^2]+[0.3*(3%-3%)^2]+[0.35*(3%-6%)^2]
=0.06%
standard deviation= variance^.5
=2.51%

The higher the probability of higher than expected inflation Higher the risk to peter's iinvestment

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