Yahoocombondscompositebondrates we usually use 3 month

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Unformatted text preview: We usually use 3-month Treasury bill (3M T-bill) yield We as the risk-free investment return (risk-free rate, or “rf”), and its volatility (std) can be assumed = 0 ”), 5-15 (why?) (why?) Risk premiums (excess returns) Why should all assets’ expected returns be higher Why than 3-M T-bill? than Investors expect to receive higher returns on all Investors other assets as compensation for risk because they are riskier than 3-M T-bill they In general, In excess return = simple return – 3-M T-bill rate, excess this can be called “risk premium” this More details will be given in Sharpe ratio and More 5-16 Sharpe ratio – by William Sharpe 5-17 Back to risk premiums: The premium for taking the risk If T-Bill denotes the risk-free rate, rf , and variance, If σp , denotes volatility of returns then: denotes The risk premium of a portfolio (p) is: E (rP ) − rf • Note 1: A portfolio could be one stock • Note 2: The risk premium is the total Note compensation for the investor to bear for all risks on the portfolio/stock on 5-18 The Sharpe (Reward-to-Volatility) Ratio portfolio risk premium S= standard deviation of portfolio excess return = E (rP ) − rf σP • Sharpe ratio provides a standard to measure “How much you earn for bearing one unit of volatility (standard deviation)” 5-19 Sharpe ratio for Dell using Excel • Check the excel template: “IndexData” tab • Let riskfree rate = 0.1% per month Monthly DJIA NASDAQ Mean ret 0.7% 1.0% St dev. 4.3% 6.9% Risk prem. 0.6% 0.9% Sharpe 0.14 0.13 • Thus, in DJIA, we get 0.14 of risk premium per unit of volatility; in NASDAQ, we get 0.13 of risk premium per unit of volatility 5-20 Exercise 4 • Now, if we short 1$ of DJIA and use the cash to buy $1 in NASDAQ • What’s the mean return, st. dev. and Sharpe ratio of such a portfolio? • Ans: Mean = 0.29%, Volatility = 4.93%, Sharpe = 0.039 • Will the answer change when we short $1000 of DJIA and long $1000 of NASDAQ? 5-21 Capital allocation line of 1 risky asset and 1 risk-free asset 5-22 A portfolio consisting of two assets: one stock and one T-bill rf = 7% σ f = 0% E(rs) = 15% σ s = 22% y = % in stock (1-y) = % in T-bill 5-23 Expected Returns for Combined Portfolio E(rp) = y E(rs) + (1 - y) rf E(rp)= expecte...
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