# Ch09 - Chapter 9 Risk Road Map Part A Introduction to...

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Chapter 9 Risk Road Map Part A Introduction to Finance. Part B Valuation of assets, given discount rates. Part C Determination of discount rates. Historic asset returns. Time value of money. Risk. Portfolio theory. Capital Asset Pricing Model (CAPM). Arbitrage Pricing Theory (APT). Part D Introduction to corporate ±nance. Main Issues De±ning Risk Risk and Horizon Estimating Return and Risk

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9-2 Risk Chapter 9 Contents 1 In t r odu c t i on . ......................... 9 - 3 2 D efn in gR i s k.......................... 9 - 4 3 R i s kandH o r i z on. ....................... 9 - 6 4 E s t im a t i s kandR e tu rn . ................. 9 - 9 5 v e s t gF o rth eL on g -Run. .................. 9 - 1 2 6 Appendix: Probability and Statistics . . . . . . . . . . . . . . 9-13 6 . 1 M om e n t s .............................. 9 - 1 3 6 . 2 C e n t s............................. 9 - 1 4 6.3 Properties oF Moments and Comoments . . . . . . . . . . . . . . 9-16 6 . 4 L i n e a rR e g r e s s i o n .......................... 9 - 1 6 7 H ew o r k ........................... 9 - 1 9 15.407 Lecture Notes ±all 2003 c ° Jiang Wang
Chapter 9 Risk 9-3 1 Introduction Return on an asset is a random variable , characterized by all possible outcomes, and probability of each outcome (state). Example. The S&P 500 index and the stock of MassAir, a regional airline company, give the following returns: State 123 Probability 0.20 0.60 0.20 Return on S&P 500 (%) - 5 10 20 Return on MassAir (%) - 1 01 04 0 Asset returns are risky (uncertain). Expected rate of return: ¯ r r F + π where r F is the risk-free rate and π is the risk premium. Excess return: ˜ q ˜ r r F . Questions : 1. How do we deFne and measure risk? 2. How are risks of di±erent assets related to each other? 3. How is risk priced (how is π determined)? c ° Jiang Wang ²all 2003 15.407 Lecture Notes

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9-4 Risk Chapter 9 2 Defning Risk Example. Moments of return distribution. Consider three assets: Mean StD ˜ r 0 (%) 10.0 0.00 0 ˜ r 1 (%) 10.0 10.00 0 ˜ r 2 (%) 10.0 20.00 0 -0.4 -0.2 0 0.2 0.4 0.6 0 0.5 1 1.5 2 2.5 3 3.5 4 Probability Distribution of Returns return probability riskless return of 10% risky return of mean 10% and volatility 10% risky return of mean 10% and volatility 20% Between Asset 0 and 1, which one would you choose? Between Asset 1 and 2, which one would you choose? Investors care about expected return and risk. 15.407 Lecture Notes Fall 2003 c ° Jiang Wang
Chapter 9 Risk 9-5 Key Assumptions On Investor Preferences for 15.401 1. Higher mean in return is preferred: ¯ r = E r ] . 2. Higher standard deviation (StD) in return is disliked: σ = p E [(˜ r ¯ r ) 2 ] . 3. Investors care only about mean and StD (or variance). 4. Investors do not care about higher moments, such as skewness. Under 1-4, standard deviation (StD) gives a measure of risk. Investor Preference for Return and Risk - 6 @ @ @ @ @ @ @ @ @ @ @ @ @ @ @I 6 ¾ increasing return decreasing risk Risk ( σ ) Expected return ( ¯ r ) c ° Jiang Wang Fall 2003 15.407 Lecture Notes

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9-6 Risk Chapter 9 3 Risk and Horizon In previous discussions, we considered return and risk over a fxed horizon. However, in many cases, we need to know: How do risk and return vary with horizon?
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Ch09 - Chapter 9 Risk Road Map Part A Introduction to...

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