# Over the last five years annual returns have been 15

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You invested \$100 in a stock five years ago. Over the last five years, annual returns have been 15%, -8%, 12%, 18% and -11%. What is your average annual rate of return? What is your investment worth today?FV=\$100(1+.15)(1-.08)(1+.12)(1+.18)(1-.11) FV=\$124.44 %47.412444.1)1(100\$44.124\$515GGGRRR5.2R5)11(1812)8(15Return AverageArithmeticAARExpected Returns State Probability C T Boom 0.3 0.15 0.25 Normal 0.5 0.1 0.2 Recession 0.2 0.02 0.01 RC= .3(.15) + .5(.10) + .2(.02) = .099 = 9.9% RT= .3(.25) + .5(.20) + .2(.01) = .177 = 17.7% Variance: Stock C = .3(.15-.099)2 + .5(.1-.099)2 + .2(.02-.099)2 = .002029 = .045 Stock T = .3(.25-.177)2 + .5(.2-.177)2 + .2(.01-.177)2 = .007441= .0863 Efficient Markets: Strong Form Efficiency- If the market is strong form efficient, then investors could not earn abnormal returns regardless of the information they possessed Semistrong- If the market is semistrong form efficient, then investors cannot earn abnormal returns by trading on public information Weak Form- If the market is weak form efficient, then investors cannot earn abnormal returns by trading on market information Efficient markets are a result of investors trading on the unexpected portion of announcements Portfolio Weights: \$15000 to invest; 2000 ABC, 3000 DEF, 4000 GHI, 6000 JKL ABC: 2/15 = 0.133 ; DEF: 3/15=0.2 ; GHI 4/15 = 0.267 ; etc. Returns: Total Return = expected return + unexpected return Unexpected return = systematic portion + unsystematic portion Total Return = expected return + systematic portion + unsystematic portion Portfolio Beta Security Weight Beta ABC 0.133 3.69 DEF 0.2 0.64 GHI 0.267 1.64 JKL 0.4 1.79 What is the portfolio beta?.133(3.69) + .2(.64) + .267(1.64) + .4(1.79) = 1.773 Reward-to-Risk: Slope = (E(RA) Rf) / (A 0) MfMAfARRERRE)()((market equilibrium) Capital Asset Pricing (CAPM): Rf) CAPM Example Security Beta Expected Return ABC 3.69 4.5 + 3.69(8.5) = 35.865% DEF 0.64 4.5 + .64(8.5) = 9.940% GHI 1.64 4.5 + 1.64(8.5) = 18.440% JKL 1.79 4.5 + 1.79(8.5) = 19.715% Arbitrage Pricing Theory
Portfolio Variance: Invest 60% of money in Asset A: State Probability A Bond: A bond with a \$5000 face value and 20 years to maturity has a coupon rate of 5% oer year compounded semi-annually. If its YTM is 3.6% per year compounded semi-annually, what is the PV? N= 20 * 2 i= 3.6 B
10%
30% If A and B are your only choices, what percent are you investing in Asset B? Asset A: E(R
PV Semi-annual Bond: A bond with a \$5000 face value and 20 years to maturity has a coupon rate of 5% oer year compounded semi-annually. If its YTM is 3.6% per year compounded semi-annually, what is the PV? N= 20 * 2 i= 3.6
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