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i. (1) Suppose interest rates go up by 3 percentage points over the current 4% risk-free rate. What effect would higher interest rates have on the SML and on the returns required on high- and low-risk securities? (2) Suppose instead that investors' risk aversion increased enough to cause the market risk premium to increase by 3 percentage points. (Assume the risk-free rate remains constant.) What effect would this have on the SML and on returns of high- and low-risk securities? Base Case Higher Risk- Higher Market Risk Free Rate Premium TRF 4% 7% 4% RPM 5% 5% 8% Base Case Risk- Free Rate SML: Higher Risk-Free Rate SML: Higher Market Risk Premium Beta 0.00 0.50 1.00 1.50 2.00 SML: Base Case 4.0% 6.5% 9.0% 11.5% 14.0% 4% 4% 4% 4% 4% c. The table below shows how the standard deviation is calculated. Use the SUMPRODUCT and SQRT Excel functions to calculate the mean, variance and standard deviation below the table. What figure from the table sumarizes the return from the bond portfolio? What figure from the table sumarizes the risk of the bond portfolio? Calculating Expected Returns and Standard Deviations: Discrete Probabilities Inputs: Expected Return Standard Deviation Product of Probability of Probability and Deviation from Squared Scenario Rate of Return Return Expected Return Deviation Sq. Dev. Prob. Scenario (1) (2) (1) x (2) = (3) (2) - Exp. r = (4) (4) = (5) (1) x (5) = (6) Worst Case 0.10 -14% -1.4% -20% 4.0% 0.4% Poor Case 0.20 -4% -0.8% -10% 1.0% 0.2% Most Likely 0.40 6% 2.4% 0% 0.0% 0.0% Good Case 0.20 16% 3.2% 10% 1.0% 0.2% Best Case 0.10 26% 2.6% 20% 4.0% 0.4% 1.00 Exp. ret. = Sum = 6.0% Sum = Variance = 1.20% Std. Dev. = Square root of var. = 10.95% root of variance =