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Investment Analysis Bus350 Return and Risk Calculation • Professor Tao Wang • Tel: x5445 • E-mail: [email protected] • Room: PH154 • Office Hour: W, F 12:15pm – 1:15pm • Coursepage: http://www.qc.edu/~twang/course/350/i nvestments.html. Announcements, homework, cases, exam dates are all on the webpage. Course Overview • Book: Investment Analysis and Portfolio Management by Reilly and Brown • CFA-designated Textbook • Group case (10%), three homework (5%), two midterms (50%) and one final (30%). Class participation is 5%. Contents • Calculate return and risk based on distribution for a single asset • Calculate return and risk for a portfolio of assets • Holding Period Return • Real life indices • Calculate return and risk from index example, geometric mean and arithmetic mean comparison Probability Distributions of Returns • Assume that there are two stock available, GENCO and RISCO, and each responds to the state of the economy according to the following table Returns on GENCO & RISCO State of Return on Return on ProbEconomy RISCO GENCO ability Strong 50% 30% 0.20 Normal 10% 10% 0.60 Weak -30% -10% 0.20 •Probability Distributions of Returns of GENCO and RISCO •0.6 •0.5 •0.4 •Probability •0.3 •0.2 •0.1 •0 •50% •GENCO •30% •Return •10% •RISCO •-10% •-30% Observation • Both companies have the same expected return, but there is considerably more risk associated with RISCO Equations: Mean r E r P1r1 P2 r2 P3r3 ...Pn rn P r n Pi ri i 1 r 0.2 0.3 0.6 0.10 0.2 (0.10) r 0.10 10% GENCO GENCO Also : rRISCO 10% Equations: Standard Deviation r E r E r 2 P1 r1 r P2 r2 r ... Pn rn r 2 n 2 2 Pi ri r 2 i 1 r 0.2 0.30 0.10 0.6 0.10 0.10 0.2 (0.10 0.10) 2 r 0.016 0.1265 GENCO GENCO 2 Also : rRISCO 0.2530 2 Observation • The expected returns of GENCO and RISCO happen to be equal, but the volatility, or standard deviation, of RISCO is twice that of GENCO’s • Which stock would a typical investor prefer Example 1. Calculate the expected return and standard deviation of the following stock A: State Probability Return 1 20% 15% 2 60% 10% 3 20% -8% The mean is 0.2*0.15+0.6*0.1+0.2*(-0.08) = 7.4% The standard deviation is: S.D. = Sqrt[0.2*(0.15-0.074)^2+0.6*(0.10.074)^2+0.2*(-0.08-0.074)^2] = 7.9% Portfolio Return and Risk • Suppose you invest in two assets: stocks and bonds. • Stocks offer a return of 10% with standard deviation of 15% • Bonds offer a return of 6% with standard deviation of 8% Portfolio weight • If the investment weight on stocks is 50%, on bonds is 50%, what’s the return on the portfolio? • What about the risk of the portfolio? Holding Period Return Ending Price - Beginning Price Dividend HPR Beginning Price $220 200 10 0.15 $200 Measures of Historical Rates of Return Arithmetic Mean : AM HPR/ n where : HPR the sum of annual holding period yields Measures of Historical Rates of Return • Geometric Mean GM (1 HPR) 1 n 1 where : the product of the annual holding period returns as follows : 1 HPR 1 1 HPR 2 1 HPR n • Arithmetic mean is used for forecasting future returns • Geometric mean is used to calculate real past returns • Geometric mean has upward bias Measure volatility • Historical volatility – Standard deviation – Realized volatility • Future volatility Stylized facts • Stock/Bond returns are fairly difficult to predict • But return volatilities are predictable to a degree Yahoo finance • Most indices historical data can be downloaded from http://finance.yahoo.com