What is the portfolio risk of holding 11 positions with identical volatility (an
ID: 2798827 • Letter: W
Question
What is the portfolio risk of holding 11 positions with identical volatility (any arbitrary volatility) with one position being 50% of the portfolio and the remaining 10 being 5% each? Assume positions are uncorrelated. 1. There are two approaches to this problem. The direct approach works with all 11 positions at once. The indirect approach considers a portfolio of portfolios. The following questions assume there are three risky asset elasses in the economy Market Capitalization Asset Small Cap Equity Large Cap Equity Corporate & Govt Bonds ($ trillion) Beta 1.9 1.4 0.4 8 12 20 Volatility 20 15 9 2. What are the weights and beta of the market portfolio? What is the expected return of Large Cap Equity if the market portfolio has an expected return of 10% and the risk free rate is 1%? 3. The following is the correlation matrix for the three risky assets. Corporate & Govt Bonds 0.2 Small CapLarge Cap Equity 0.6 Equity Small Cap Equity 0.4 Large Cap Equity 0.6 Corporate & Govt Bonds0.2 0.4 4. What is the expected return and volatility o fthe portfolio that is 60% Large Cap Equity and 40% Corporate and Govt Bonds?Explanation / Answer
2. What are the weights and beta of the market portfolio?
Total = 8+12+20 = 40
Weight of Small Cap equity = 8/40 =0.2
Weight of Large Cap equity = 12/40 = 0.3
Weight of Corporate and government bonds = 20/40 = 0.5
Beta of the market portfolio = Weighted average beta = 0.2*1.9 +0.3*1.4+0.5*0.4 = 1
Beta of market portfolio = 1
3. What is the expected return of Large Cap equity?
As per CAPM, Re = Rf + beta*(Rm-Rf)
Re = 1 + 1.4*(10-1) = 13.6%
Expected return of large cap = 13.6%
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