Given her evaluation of current economic conditions, Ima Nutt believes there is a 20 percent probability of recession, a 50 percent chance of continued steady growth, and a 30 percent probability of inflationary growth. For each possibility, Ima has developed an interest rate forecast for long-term Treasury bond interest rates:
ECONOMIC FORECAST INTEREST RATE FORECAST
Recession 6 percent
Constant growth 9 percent
Inflation 14 percent
A. What is the expected interest rate under Ima's forecast?
B. What is the variance and standard deviation of Ima's interest rate forecast?
C. What is the coefficient of variation of Ima's interest rate forecast?
D. If the current long-term Treasury bond interest rate is 8 percent, should Ima consider purchasing a Treasury Bond? Why or why not?
A. To calculate the expected interest rate under Ima's forecast, we multiply each interest rate forecast by its corresponding probability and sum them up.
Expected interest rate = (Probability of recession * Interest rate during recession) + (Probability of constant growth * Interest rate during constant growth) + (Probability of inflation * Interest rate during inflation)
Expected interest rate = (0.20 * 6%) + (0.50 * 9%) + (0.30 * 14%)
B. Variance is a measure of the spread of data around the mean. To calculate the variance of Ima's interest rate forecast, we use the formula:
Variance = (Probability of recession * (Interest rate during recession - Expected interest rate)²) + (Probability of constant growth * (Interest rate during constant growth - Expected interest rate)²) + (Probability of inflation * (Interest rate during inflation - Expected interest rate)²)
Standard deviation is the square root of the variance.
Standard deviation = √Variance
C. The coefficient of variation measures the relative variability of the interest rate forecast, normalized by the mean. It is calculated by dividing the standard deviation by the expected interest rate and multiplying by 100.
Coefficient of variation = (Standard deviation / Expected interest rate) * 100
D. Ima should consider purchasing a Treasury Bond if its yield is higher than the current long-term Treasury bond interest rate. If the yield is lower, it may not be as attractive of an investment.
Therefore, we compare the expected interest rate to the current long-term Treasury bond interest rate.
If the expected interest rate is higher than the current interest rate, Ima should consider purchasing a Treasury bond. If it is lower or equal, it may not be the best investment choice.
Please note that factors other than interest rates, such as risk tolerance and investment objectives, should also be considered before making an investment decision.