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Unformatted text preview: 55E(r) = [0.3 ×44%] + [0.4 ×14%] + [0.3 ×(–16%)] = 14% σ2= [0.3 ×(44 – 14)2] + [0.4 ×(14 – 14)2] + [0.3 ×(–16 – 14)2] = 540 σ= 23.24% 57Timeweighted average returns are based on yearbyyear rates of return. Year Return = [(capital gains + dividend)/price] 20072008 (110 – 100 + 4)/100 = 14.00% 20082009 (90 – 110 + 4)/110 = –14.55% 20092010 (95 – 90 + 4)/90 = 10.00% Arithmetic mean: 3.15% Geometric mean: 2.33% Time Cash flow Explanation 0 300 Purchase of three shares at $100 per share 1 208 Purchase of two shares at $110, plus dividend income on three shares held 2 110 Dividends on five shares, plus sale of one share at $90 3 396 Dividends on four shares, plus sale of four shares at $95 per share Dollarweighted return = Internal rate of return = –0.1661% 59For the period 1926 – 2008, the mean annual risk premium for large stocks over Tbills is 9.34% E(r) = Riskfree rate + Risk premium = 5% + 7.68% =12.68% 396     110      Date: 1/1/07 1/1/08 1/1/09 1/1/10          208 300 511The expected cash flow is: (0.5 ×$50,000) + (0.5 ×$150,000) = $100,000 With a risk premium of 10%, the required rate of return is 15%. Therefore, if the value of the portfolio is X, then, in order to earn a 15% expected return: X(1.15) = $100,000 ⇒X = $86,957 If the portfolio is purchased at $86,957, and the expected payoff is $100,000, then the expected rate of return, E(r), is: 957,86$957,86$000,100$−= 0.15 = 15.0% The portfolio price is set to equate the expected return with the required rate of return. If the risk premium over Tbills is now 15%, then the required return is: 5% + 15% = 20% The value of the portfolio (X) must satisfy:X(1.20) = $100, 000 ⇒X = $83,333 For a given expected cash flow, portfolios that command greater risk premia must sell at lower prices. The extra discount from expected value is a penalty for risk. 512E(rP) = (0.3 ×7%) + (0.7 ×17%) = 14% per year σP= 0.7 ×27% = 18.9% per year Security Investment Proportions TBills 30.0% Stock A 0.7 ×27% = 18.9% Stock B 0.7 ×33% = 23.1% Stock C 0.7 ×40% = 28.0% Your Rewardtovariability ratio = S =27717−= 0.3704 Client's Rewardtovariability ratio =9.18714−= 0.3704 E(r)σ σ σ σ 7 271417P CAL ( slope=.3704)% % 18.9client514Portfolio standard deviation = σP= y ×27% If the client wants a standard deviation of 20%, then: y = (20%/27%) = 0.7407 = 74.07% in the risky portfolio. Expected rate of return = 7 + 10y = 7 + (0.7407 ×10) = 14.407% 515Slope of the CML =25713−= 0.24 b. 0 2 4 6 8 1012141618200 102030σ (%) σ (%) σ (%) σ (%) CAL (slope=.3704)CML (slope=.24) My fund allows an investor to achieve a higher expected rate of return for any given standard deviation than would a passive strategy, i.e., a higher expected return for any given level of risk....
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This note was uploaded on 11/23/2010 for the course FINANCE 08FB40447 taught by Professor Raymond during the Spring '10 term at University of Manchester.
 Spring '10
 RAYMOND

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