Look at the Q then see my comment afterward. Thanks Ben Jacobs, CFA, is attempting to calculate a historical equity risk premium. His first estimate uses geometric mean equity returns and long-term bond yields. His second estimate uses arithmetic mean returns and short-term bond yields. The effect of the changes in methodology in the second estimate, relative to the first, will: A) both decrease the size of the risk premium. B) have offsetting effects. C) both increase the size of the risk premium. Your answer: B was incorrect. The correct answer was C) both increase the size of the risk premium. Switching from a geometric mean to an arithmetic mean will increase the mean equity return. All else being equal, that will increase the estimated risk premium. When the yield curve slopes upward, short-term bonds yield less than long-term bonds. Thus, the equity risk premium estimate will be larger when short-term bond rates are used. *Comment/Question* " Switching from a geometric mean to an arithmetic mean will increase the mean equity return." Fine, I get that, moving on, When the yield curve slopes upward, short-term bonds yield less than long-term bonds. Thus, the equity risk premium estimate will be larger when short-term bond rates are used. What ? How? If the curve is upward sloping, Kd is lower on the short end, higher on the long end. Since Ke=Kd+ b(Rm-Rf), wouldn’t the Premium just increase with the Rf *OR* Kd would increase? (maintain the spread) just raising Ke?
The equity risk premium is the difference between the return on equity and the return on bonds in this case. Since geometric equity return is lower than aritmetic and long term yields are higher than short term yields, the difference between geometric and long yields will be less than the difference between aritmetic and short term yields (they are farther apart) therefore switiching to the second methodology increases the equity risk premium.
yeah, this one is tricky one… I’m going to add to Anna237’s response… “equity risk premium is the difference between the return on equity and the return on bonds in this case”. So Ke being the Cost of Equity is not the same as Equity Premium being – [Ke-Kd=Equity premium] Look at it this way…at one point in time, weigh the cost of capital… typically is as follow: EQUITYarithmetic > EQUITYgeometric > longterm bongs > short term bonds And so… [EQUITYarithmetic-short term bonds] > [EQUITYgeometric-longterm bonds] or… EQUITY RISK PREMIUM ar-stb > EQUITY RISK PREMIUM gm - ltb ar- arithmetic mean stb-short term bonds gm-geometric mean ltb-long term bonds I don’t think Kd is synonymous with Rf. The problem does not specify the type of bonds the calculation is using. As you know, Kd for a corporation includes default risk while Kd for the government is calculated default-risk free…
This might be an overly simplistic way to answer this question, but it worked for me. Visualize the spread as two parallel lines, the top line being the Equity Return, the bottom line being the Bond Yield. If you move from Geometric to Arithmetic, the top line will move up, increasing the spread. If you move from LT Bonds to ST Bonds, the bottom line will move down, increasing the spread.
Equity Risk premium = (Rm - Rf) if Rf is lower, (Rm - Rf) increases. That’s all the Q is asking - Don’t read too much into it.