5.Risk and Return

# 5.Risk and Return - Chapter 7 Risk and Return Learning...

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Chapter 7 Risk and Return Learning Objectives 1. Explain the relation between risk and return. 2. Describe the two components of a total holding period return, and calculate this return for an asset. 3. Explain what an expected return is, and calculate the expected return for an asset. 4. Explain what the standard deviation of returns is, explain why it is especially useful in finance, and be able to calculate it. 5. Explain the concept of diversification. 6. Discuss which type of risk matters to investors and why. 7. Describe what the Capital Asset Pricing Model (CAPM) tells us and how to use it to evaluate whether the expected return of an asset is sufficient to compensate an investor for the risks associated with that asset. I. Chapter Outline 7.1 Risk and Return The greater the risk, the larger the return investors require as compensation for bearing that risk. Higher risk means you are less certain about the ex post level of compensation. 1

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7.2 Quantitative Measures Return A. Holding Period Returns The total holding period return consists of two components: (1) capital appreciation and (2) income. The capital appreciation component of a return, R CA : 1 0 CA 0 0 P -P CapitalAppreciation P R = InitialPrice P P = = The income component of a return R I : 1 I 0 CF Cash Flow R = InitialPrice P = The total holding period return is simply 1 1 T CA I 0 0 0 CF P+CF P R = R +R = . P P P + = B. Expected Returns Expected value represents the sum of the products of the possible outcomes and the probabilities that those outcomes will be realized. The expected return, E(R Asset ), is an average of the possible returns from an investment, where each of these returns is weighted by the probability that it will occur: ( 29 ( 29 ( 29 ( 29 ( 29 Asset i i 1 1 2 2 1 E R R R R .... R n n n i p p p p = = = + + + 2
If each of the possible outcomes is equally likely (that is, p 1 = p 2 = p 3 = … = p n = p = 1/ n ), this formula reduces to: ( 29 ( 29 i 1 1 2 Asset R R +R +...+R E R n i n n n = = = . 7.3 The Variance and Standard Deviation as Measures of Risk A. Calculating the Variance and Standard Deviation The variance ( σ 2 ) squares the difference between each possible occurrence and the mean (squaring the differences makes all the numbers positive) and multiplies each difference by its associated probability before summing them up: ( 29 ( 29 2 2 R i i 1 Var (R) R E R n i p σ = = = - ° If all of the possible outcomes are equally likely, then the formula becomes: [ ] 2 i 2 1 R R E(R) n i n σ = - = Take the square root of the variance to get the standard deviation ( σ ) . B. Interpreting the Variance and Standard Deviation The normal distribution is a symmetric frequency distribution that is completely described by its mean (average) and standard deviation.

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