1. What is the partfolio nisk of holding 11 positions with identi cal volatility

Question

1. What is the partfolio nisk of holding 11 positions with identi cal volatility (any arbitrary volatility) wath one position being 50% ofthe portfolio and the remaining 10 being 5% each? Assume positions are uncorrelated. There are two approaches to thisproblem The direct approach works ith all 11 positions at once. The indirect approach considers a portfolio of portfolios. The following questions assume there are three risky asset classes in the economy Market Capitalization $ trillion) Volatility 20 15 Beta Asset Small Cap Equity Large Cap Equity Corporate & Govt Bonds 1.9 12 20 0.4 2. What are the weights and beta of the market portfolio?

Explanation / Answer

1. let volatility be x; weight of weight of other 10 = 0.05 each

vol of portfolio = square root of ((0.5x)2 + 10*(0.05x)2)

vol of portfolio = 0.5244x................where x is the standard deviation of each asset

2.

weight = market cap/total market cap

beta = 1.00

9

weight beta weight*beta small cap 0.2 1.90 0.38 large cap 0.3 1.40 0.42 bonds 0.5 0.40 0.20

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