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Chapter 6 Foundation Of Risk Analysis ®1999 South-Western College Publishing 1 How Do Asset Prices Change With Risk? • The Higher the Volatility (Risk) • The Higher the E(R) • The Lower the Price ®1999 South-Western College Publishing 2 Market Scenario Certainty 1. The mean return equals the riskless interest rate. 2. The variance is 0. Uncertainty 1. The mean return is greater than the riskless interest rate. 2. The variance is greater than 0. 3. The risk premium is zero. 3. The risk premium is positive. (with risk aversion) ®1999 South-Western College Publishing 3 • Certainty There is only one future return that is known with a probability of 1. • Uncertainty There is more than one possible future return. The probability of each outcome is unknown. ®1999 South-Western College Publishing 4 Probabilities • Objective Probability – Actual probabilities are known • Subjective Probability – Probability estimates • Actual probabilities are not known – Based on historical data ®1999 South-Western College Publishing 5 Have different average rates of return Assets Requires criteria for selection Have different degrees of risk ®1999 South-Western College Publishing 6 Investment Criteria • MRC – Selects the asset with the highest rate of return – Does not rank investments • MERC – Compares assets with uncertain returns – Gives a clear ranking of investments – Chooses highest E(R) – Does not relate risk to return ®1999 South-Western College Publishing 7 Attitudes Toward Risk • Risk Averters Most investors – Dislike volatility or risk – Require a risk premium for taking on additional risk • Risk Neutral Use MERC – Ignore variance – Decisions based only on E(R) • Risk Seekers Buy lottery tickets – Like risk and variance ®1999 South-Western College Publishing 8 E(R) = Mean Rate of Return + Risk on Riskless Asset Premium Risk Premium is Required by the Market to Compensate Investors for Risk Variance and Standard Deviation Measures Risk ®1999 South-Western College Publishing 9 Calculating Variance and Standard Deviation • Variance – Measure of the dispersion around the mean m 2 = Pi[Ri - E(R)]2 i=1 • Standard Deviation – Measure of how much the actual return is likely to deviate from its expected return = Square root of the variance ®1999 South-Western College Publishing 10 Mean-Variance Criterion MVC • Most Investors are Risk Averse • Risk Aversion Characteristics – Select assets with the lowest variance for the same E(R) – Select assets with the highest E(R) for the same variance • Assumes – Investors like higher E(R’s) – Investors dislike higher variances ®1999 South-Western College Publishing 11 MVC Return C A . B . . (see next slide) Risk Investors prefer investments A and C to B ®1999 South-Western College Publishing 12 • C Gives a Greater Return Than B for the Same Level of Risk. C B • A Gives the Same Return as B for a Lower Level of Risk. A B ®1999 South-Western College Publishing 13 Risk-Return Relationship • Confirmed by Historical Returns – The higher the risk • Higher variance and standard deviation – The higher the average rates of return • An Asset’s Variability Determines its Risk Premium ®1999 South-Western College Publishing 14