Question

Suppose that in 2019 the Federal Reserve Bank can take three actions with equal probability: 1)...

  1. Suppose that in 2019 the Federal Reserve Bank can take three actions with equal probability: 1) not increasing short-term interest; 2) increasing short-term interest rate moderately; 3) increasing short-term interest rate aggressively. Further assume that the returns on the stock market will be 10%, 8%, and 3% respectively in these three scenarios, and the returns on the bond market will be 4%, 6%, and 8% in these three scenarios. Suppose that you can only invest in either the stock market or the bond market and your goal is to minimize your risk (hint: standard deviation). Will you invest in stocks or bonds?

  1. Over the last twenty years, the average return and standard deviation of returns of large cap value stocks are 8.5% and 15.2%, and the average return and standard deviation of returns of fixed income portfolio are 5.3% and 3.4%. Suppose that over the next year the expected returns and risks of the two asset classes will remain the same as what happened in the last twenty years. Further assume that you can invest in a riskless asset with 2% return over the next year (you can also borrow money with an interest rate of 2%).

Suppose that you can invest in the risk-free asset, and either the large cap value stocks portfolio or the fixed income portfolio. Which portfolio will you choose and why?

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The standard deviation of a portfolio is given by sqrt(P1*(Ret1-Exp.Ret)^2+P2*(Ret2-Exp Ret)^2+P3*(Ret3-Exp Ret))Stock Condition Not increasing short term rates Increasing short term rates moderately Increasing short term rates aggressively Return Pr Pr (Ret Exp Ret)A2 10% 0.333333 0.000 8% 0.333333 0.000 3% 0.333333 0.001 Total 0.001 Exp Return Standard Dev 2.94% Bonds Condition Not increasing short term rates Increasing short term rates moderately Increasing short term rates aggressively Return Pr Pr (Ret - Exp Ret)A2 4% 0.333333 0.000 6% 0.333333 0.000 8% 0.333333 0.000 Total 0.000 Exp Return Standard Dev 6.00% 1.63% The risk is minimized in the case of investment in bond Rf 2% SD 15.20% 3.40% Optimal Weight 0.5 0.5 Portfolio Ret Port SD Sharpe ratio Stock Bond Return 8.50% 5.30% 5.25% 3.65% 7.60% 0.4276 1.70% 0.9706 Investment in bond is good because it has higher Sharpe Ratio

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