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# Lec3 - LECTURE 3 Risk and Return Efficient Diversification...

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AF3316 Investments Shaojun (Shaun) Zhang, Ph.D. ASA School of Accounting and Finance The Hong Kong Polytechnic University LECTURE 3 LECTURE 3 Risk and Return, Risk and Return, Efficient Efficient Diversification Diversification

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3-2 AF3316 Lecture 3 INFLATION AND REAL RATES OF RETURN
3-3 AF3316 Lecture 3 Real vs. Nominal Rates ! " # ! ! " " \$ ! ! \$ ! ! " # ! # " \$ ! \$ ! " ! # Today’s price of \$1000-worth 20-year bond is \$103.7. Nominal rate is 12% per annum. Purchasing power =1000/ 1+i ^20, i is inflation rate. Real rate of return is r=[(1+R)/(1+i)]-1 If nominal rate is 12% and inflation rate is 4% real rate is [(1+0.12)/(1+0.04)]-1=1.07692-1=0.07692=7.692%.

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3-4 AF3316 Lecture 3 Real vs. Nominal Rates Fisher effect: Example R = 9%, i = 6% r = 2.83% = (9%-6%) / (1.06) Approximation: real rate = nominal rate - inflation premium r = R - i Example r = 9% - 6% = 3% i i R i R r + - = - + + = 1 1 1 1
3-5 AF3316 Lecture 3 THE HISTORICAL RECORD -- Looking Back The historical record provides the basis for forecasting the future.

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3-6 AF3316 Lecture 3 Figure 5.2 Rates of Return on Stocks, Bonds and T-Bills
3-7 AF3316 Lecture 3 Figure 5.4 Interest, Inflation and Real Rates of Return

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3-8 AF3316 Lecture 3 Annual Holding Period Returns Table 5.3 Geom. Arith. Stan. Series Mean% Mean% Dev.% World Stk 9.80 11.32 18.05 US Lg Stk 10.23 12.19 20.14 US Sm Stk 12.43 18.14 36.93 World Bonds 5.80 6.17 9.05 LT Treas. 5.35 5.64 8.06 T-Bills 3.72 3.77 3.11 Inflation 3.04 3.13 4.27
3-9 AF3316 Lecture 3 Nominal and real wealth indexes for investments in Treasury bills, 1966-2005 (inset figure is for 1925-2005)

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3-10 AF3316 Lecture 3 RISK AND RISK PREMIUMS -- Looking Forward The future is uncertain.
3-11 AF3316 Lecture 3 Mean (or expected) return Mean (or expected) return p(s) = probability of a state r(s) = return if a state occurs 1 to S states p(s) = probability of a state r(s) = return if a state occurs 1 to S states Measuring Mean: Scenario or Subjective Returns

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3-12 AF3316 Lecture 3 Numerical Example: Subjective or Scenario Distributions State State Prob. of State Prob. of State r r in State 1 1 .1 .1 - - .05 .05 2 2 .2 .2 .05 .05 3 3 .4 .4 .15 .15 4 4 .2 .2 .25 .25 5 5 .1 .1 .35 .35 E(r) = (.1)( E(r) = (.1)( - - .05) + (.2)(.05)...+ (.1)(.35) .05) + (.2)(.05)...+ (.1)(.35) E(r) = .15 or 15% E(r) = .15 or 15%
3-13 AF3316 Lecture 3 Expected return is an illusionary concept! Actual (or realized) return is expected return plus surprises R = E( R ) + u Such surprises may be: Company specific ones Industry specific ones Economy wide factors Actual returns are uncertain!

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3-14 AF3316 Lecture 3 Measuring Variance (or Dispersion) of Returns Variance Standard Deviation
3-15 AF3316 Lecture 3 Measuring Variance (or Dispersion) of Returns Using the above example: Var = [(.1)( Var = [(.1)( - - .05 .05 - - .15)^2+(.2)(.05 .15)^2+(.2)(.05 - - .15)^2...+ .1(.35 .15)^2...+ .1(.35 - - .15)^2] .15)^2] = .01199 = .01199 SD = [ .01199] ^(1/2) = .1095 or 10.95% SD = [ .01199] ^(1/2) = .1095 or 10.95%

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Lec3 - LECTURE 3 Risk and Return Efficient Diversification...

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