Suppose the following version of the APT is a good model of risk in the stock ma

Question

Suppose the following version of the APT is a good model of risk in the stock market. There are three factors: (1) the stock market’s excess return, in percentage points; (2) the unemployment rate minus its natural rate (the level the unemployment rate would be if the economy were at full employment), in percentage points; and (3) the real federal funds rate minus its long-run equilibrium value. Suppose the natural rate of unemployment is 4.5 percent and the long-run equilibrium value of the real federal funds rate is 3.0 percent.   Each of the following stocks has the beta coefficients shown in the table below:

a.         If your forecast for next year is that the risk-free interest rate next year will be 1.0 (Rf) percent, the overall stock market will return 10.0 percent, the unemployment rate will be 5.0 percent, and the real federal funds rate will be 2.0 percent, what is the expected return (in percent, with two decimals) to each of the three stocks? Show your calculations.

b.         If your forecast for next year is that the risk-free interest rate next year will be 2.0 (Rf) percent, the overall stock market will return 20.0 percent, the unemployment rate will be 4.0 percent, and the real federal funds rate will be 4.0 percent, what is the expected return (in percent, with two decimals) to each of the three stocks?   Show your calculations.

Explanation / Answer

a.        RP1 - RF RP2-RF-4.5% RP3-RF-3% Expected Return Company Risk free Rate (RF) Stock market Return (RM) Unemployment Rate Real Federal Rate B1 B2 B3 Market Risk premium RP1 Unemployment Risk Premium RP2 Real Fedreal risk premium RP3 E(rj) = rf + bj1RP1 + bj2RP2 + bj3RP3 Royal Dutch Shell 1% 10% 5% 2% 3 -3 4 9% -1% -2% 21.50% Merck 1% 10% 5% 2% 2 6 0 9% -1% -2% 16.00% Wells Fargo 1% 10% 5% 2% 1 -3 -8 9% -1% -2% 27.50% The APT formula is: E(rj) = rf + bj1RP1 + bj2RP2 + bj3RP3 + bj4RP4 + ... + bjnRPn where: E(rj) = the asset's expected rate of return rf = the risk-free rate bj = the sensitivity of the asset's return to the particular factor RP = the risk premium associated with the particular factor b.        RP1 - RF RP2-RF-4.5% RP3-RF-3% Expected Return Company Risk free Rate (RF) Stock market Return (RM) Unemployment Rate Real Federal Rate B1 B2 B3 Market Risk premium RP1 Unemployment Risk Premium RP2 Real Fedreal risk premium RP3 E(rj) = rf + bj1RP1 + bj2RP2 + bj3RP3 Royal Dutch Shell 2% 20% 4% 4% 3 -3 4 18% -3% -1% 59.50% Merck 2% 20% 4% 4% 2 6 0 18% -3% -1% 23.00% Wells Fargo 2% 20% 4% 4% 1 -3 -8 18% -3% -1% 35.50%

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