ReviewMidTerm1_examples

# ReviewMidTerm1_examples - rate of return of 11.0 and a...

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2/11/2011 1 Examples Normal Distribution and VaR • If the return on an asset follows normal distribution, with a mean of 16%, and a standard deviation of 25%, what is the probability of return being less than 10% over the next year? % 10 P R ob %) ( Pr % 25 % 16 % 10 % 25 % 16 Pr %) 16 % 10 % 16 ( Pr R ob R ob ) 24 . 0 ( Pr Z ob ) 24 . 0 ( NORMSDIST 4052 . 0 Examples Normal Distribution and VaR Assume that you are a manager of a mutual fund with \$100 million in assets. You know that your fund has a expected annual rate of return of 16%, and an annual standard deviation of 25%. What is the probability that by the end of next year your asset will be at least \$95 million? Prob(Asset Value>=\$95 million) = Prob (R>=-5%) = 1 – Prob (R<-5%) %) 16 % 5 % 16 ( Pr %) 5 ( Pr R ob R ob 200 . 0 ) 84 . 0 ( NORMSDIST ) 84 . 0 ( Pr % 25 % 16 % 5 % 25 % 16 Pr Z ob R ob Prob(Asset Value>=\$95 million) = Prob (R>=-5%) = 1 – Prob (R<-5%) = 1 – Prob (R<-5%) =1 - 0.200 = 0.800 Examples Normal Distribution and VaR • A mufual fund has an annual expected
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Unformatted text preview: rate of return of 11.0%, and a standard deviation of 20%. What is the 5% VaR for small stocks? 5% VaR = + * NORMSINV(0.05) = 11.0% + 20.0% * (-1.645) = -21.9% Examples Bear Normal Bull Prob .2 .3 .5 Return-25% 10% 24% Find the expected rate of return E(r) = [0.2 × ( − 25%)] + [0.3 × 10%] + [0.5 × 24%] =10% Ch 5. Q12 25% Examples • Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 18%. T-bills offer a risk-free 7% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to bills? • Utility for bills: 0.07 • Utility for the portfolio: U P =0.12-0.5 A 0.18 2 = 0.12 – 0.0162 A • For investors to prefer the risky portfolio U P >0.07 or 0.12 – 0.0162 A > 0.07 A < 0.05/0.0162 = 3.09 CH6. Q2...
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