Risk Modelling-01(Active)

# Risk Modelling-01(Active) - Risk Return Portfolio Theory...

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Risk, Return, Portfolio Theory and CAPM Where does the discount rate (for stock valuation) come from?

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So far discount rate , We have taken the discount rate as given. We have also learned the factors that determine the discount rate in bond valuation. What is the appropriate discount rate in stock valuation? 2
Topics Risk and returns How to measuring risk Individual security risk Portfolio risk Diversification Unique risk Systematic risk or market risk Measure market risk: beta CAPM 3

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4 The Value of an Investment of \$1 in 1926 Source: Ibbotson Associates Index Year End 1 6402 2587 64.1 48.9 16.6
5 Source: Ibbotson Associates Index Year End 1 660 267 6.6 5.0 1.7 Real returns The Value of an Investment of \$1 in 1926

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6 Rates of Return 1926-2000 Source: Ibbotson Associates Year Percentage Return
Selected Realized Returns, 1926 – 2001 Average Standard Return Deviation Small-company stocks 17.3% 33.2% Large-company stocks 12.7 20.2 L-T corporate bonds 6.1 8.6 L-T government bonds 5.7 9.4 U.S. Treasury bills 3.9 3.2 Source: Ibbotson Associates. 7

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Risk premium Risk aversion – in Finance we assume investors dislike risk, so when they invest in risky securities, they require a higher expected rate of return to encourage them to bear the risk. The risk premium is the difference between the expected rate of return on a risky security and the expected rate of return on a risk-free security, e.g., T-bills. Over the last century, the average risk premium is about 7% for stocks. 8
Measuring Risks How to measure the risk of a security? Standard-alone risk: when the return is analyzed in isolation. This provides a starting point . Portfolio risk: when the return is analyzed in a portfolio. This is what matters in reality when people hold portfolios. 9

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PART I: Standard alone risk The risk an investor would face if he/she held only one asset. Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment. The greater the range of possible events that can occur, the greater the risk 10
Probability distributions Which firm is more likely to have a return closer to its expected value? A listing of all possible outcomes, and the probability of each occurrence. Can be shown graphically. 11 Expected Rate of Return Rate of Return (%) 100 15 0 -70 Firm X Firm Y

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Measuring Risk In financial markets, we use the volatility of a security return to measure its risk. Variance – Weighted average value of squared deviations from mean. Standard Deviation – Squared root of variance. 12
Some basic concepts N i i X i p X E X 1 ) ( ) ( ] [ 13 Some basic formula for Expectation and Variance Let X be a return of a security in the next period. Then we have N i X i X i p X Var 1 2 ) ) ( )( ( ] [

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Investment alternatives Economy Prob. T-Bill HT Coll USR MP Recessio n 0.1 8.0% - 22.0% 28.0% 10.0% - 13.0% Below avg 0.2 8.0% -2.0% 14.7% - 10.0% 1.0% Average 0.4 8.0% 20.0% 0.0% 7.0% 15.0% Above avg 0.2 8.0% 35.0% - 10.0% 45.0% 29.0% Boom 0.1 8.0% 50.0% - 20.0% 30.0% 43.0% 14
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