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- 1. Essentials of Investments BODIE, KANE, MARCUS, 8TH EDITION Problem + Solution for Chapter 5, Problem 12
- 2. PreambleAssume you manage a risky portfolioExpected Return of 17%Standard Deviation of 27%T-Bill rate is 7%
- 3. E(r) = 17% σ = 27% T-bill=7%Client chooses to place:70% of their portfolio in your fund30% in Tbill money marketWhat is the E(r) and σ of your client’s portfolio?
- 4. Gather the Data Security E(r) σ p(s)Standard deviation of T-bills is always 0% Risky Fund 17 27 70%This is by definition. Because they can notlose value, they are considered “risk-free”. T-Bill 7 0 30%
- 5. Expected Return70% will have an E(r) of 1730% will have an E(r) of 7.7 (17) + .3 (7) =11.9 + 2.1 = 14Expected Return of the Portfolio is 14
- 6. Standard DeviationFirst, calculate the variance.This is easy, since standard deviation of a t-bill is 0.
- 7. Quick SolveIgnore the T-bill, since that is 0Weight the Standard Deviation of the Risky Portfolio
- 8. Standard Deviation70% of 27%.7 * 27% = 18.9
- 9. Answers to 12(a)Mean Expected Return = 14%Standard Deviation = 18.9%
- 10. Part B Stock A 27%Suppose your risky portfolio includesthe following investments in thegiven proportions. Stock B 33%What are the investment proportionsof your client’s overall portfolio, includingthe position in T-bills. Stock C 40%
- 11. A Portfolio Partition? My Risky Portfolio 27% 40% 33%Remember, each stock in My Risky Portfolio will Stock A Stock B Stock Conly take up a portion of 70% of the client’sportfolio. Client’s Portfolio 30% 70% My Risky Portfolio T-Bills
- 12. Compute!Stock A: 27% *.7 = 18.9Stock B: 33% * .7 = 23.1Stock C: 40% * .7=28.0
- 13. 12(b) Solution Stock A Stock B Stock C T-BillsT-Bills = 30% 18.9%Stock A = 23.1 30.0%Stock B = 18.9Stock C= 28.0 23.1% 28.0%
- 14. 12(c) Sharpe RatioWhat are the reward-to-volatility ratios (S) of your RiskyPortfolio and your client’s portfolio?
- 15. How to find Sharpe Portfolio Risk PremiumSharpe = S = Standard Deviation of Portfolio Excess Return
- 16. Risk Premium? Excess Return?The Portfolio Risk Premium is the E(r) above the risk-free rate.In this case, the risk-free rate is the T-bill rate of 7%The standard deviation is the same, since the T-bill SD is 0.
- 17. Sharpe RatiosMy Risky Portfolio has a Portfolio Risk Premium of 17% - 7% = 10%My Client’s Portolio has a PRP of 14%-7% = 7%
- 18. 12(c) Sharpe Ratios My Risky My Client’s Portfolio Portfolio Portfolio RiskWhat! The Sharpe Ratios are the same! 10 7 PremiumHow can that be, since My Risky Portfolio Standardis riskier than My Client’s Portfolio? 27 18.9 Deviation 0.370 0.370 Sharpe Ratios
- 19. What The Sharpe Ratio SaysThe Sharpe Ratio compares the reward, per unit of volatilityA higher Sharpe Ratio indicates a higher reward.Higher is better.
- 20. Sharpe Ratio Equation E(rp) - rfS= σp
- 21. 12(d) Draw the CALDraw the CAL of your portfolio on an expected return/standard deviation diagram.What is the slope of the CAL?Show the position of your client’s fund on the CAL.
- 22. What is a CALCAL stands for Capital Allocation LineWhen graphed, The Y axis is the E(r) return, and the X axis is risk/standard deviation
- 23. CAL for My Risky Portfolio CAL CLIENTThe CAL starts at 0 risk + 7% return (TBills)20 17The CAL ends at 17% return and 27% risk 15 14Rise/Run = Slope 1010/27 =.3704 7 5My Client appears at X-axis18.9% riskwith a 14% return. 0 0 18.9 27 40

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