Question

Problem 6-20 Refer the table below on the average risk premium of the S&P 500 over T-bills and the standard deviation of that risk premium Suppose that the S&P 500 is your risky portfolio Sharpe Period 1926-2015 1992-2015 1970-1991 1948-1969 1926-1947 Average Annual Returns S&P 500 1-Month Portfolio T-Bills T 11.77 3.47 110.79 2.66 12.87 14.14 2.70 9.25 8.91 Risk Premium 8.30 8.13 5.33 11.44 S&P 500 Portfolio Standard Deviation 20.59 18.29 18.20 17.67 27.99 0.40 0.44 0.29 0.3e o. If your risk-aversion coefficient is A = 3.6 and you believe that the entire 1926-2015 period is representative of future expecte performance, what fraction of your portfolio should be allocated to T-bills and what fraction to equity? Assume your utility functio ED) - 0.5 * Ao? (Do not round intermediate calculations. Round your answers to 2 decimal places.) T-bills Equity ndows

Answer 1

a) The Utility Score of the Investor is

U = E(r) - 0.5*A * Variance where Variance is the square of Standard Deviation

As the entire period of 1926 -2015 is representative of future expectation

= 0.1177 -0.5* 3.6* 0.2059^2

= 0.041389

Now, as the portolio has to be formed by using the Risk free asset and the Risky portfolio (S&P500 portfolio)

the optimal weight assigned to the Risky asset (W) is calculated as

W = Risk premium / ( A* variance)

= 0.083 / (3.6*0.2059^2)

=0.54383 or 54.38%

So, amount invested in Equity (S&P 500 portfolio) = 54.38%

and amount invested in T-Bills (Risk free asset) = 100%-54.38% = 45.62%

b) The Utility Score of the Investor is

U = E(r) - 0.5*A * Variance where Variance is the square of Standard Deviation

As the period of 1970-1991 is representative of future expectation

= 0.1287 -0.5* 3.6* 0.1820^2

= 0.069077

Now, as the portolio has to be formed by using the Risk free asset and the Risky portfolio (S&P500 portfolio)

the optimal weight assigned to the Risky asset (W) is calculated as

W = Risk premium / ( A* variance)

= 0.0533 / (3.6*0.1820^2)

=0.446974 or 44.70%

So, amount invested in Equity (S&P 500 portfolio) = 44.70%

and amount invested in T-Bills (Risk free asset) = 100%- 44.70% = 55.30%