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Finance

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Jan 9, 2024

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Uploaded by ProfessorLapwing6374

Page 1 of 3 FIN222 Week 5 Workshop Solutions on Risk and Return 1. If FALSE, correct the sentence. a. Beta is a measure of systematic risk. TRUE b. The market will compensate investors for bearing both systematic risk only and unsystematic risk . FALSE This is because unsystematic risk can be diversified away. c. The beta of a stock is primarily determined by how its returns co-vary with the market returns. TRUE d. An investor investing in a two-asset portfolio can achieve diversification benefit as long as two assets are less than perfectly positively correlated (i.e. as long as Corr < 1) only when two assets are negatively correlated . FALSE e. Assuming a two-asset portfolio, a maximum reduction in portfolio risk occurs when the correlation coefficient between the two assets is equal to minus onezero . FALSE 2. Which one of the following is TRUE ? If it is FALSE, correct the sentence. a. The intercept of the SML is a risk free ratereturn on the market . FALSE b. In equilibrium, all assets are priced according to their systematic riskstandard deviation . FALSE c. A security having a higher betastandard deviation will always have a higher required rate of return than a security having a lower standard deviationbeta . FALSE Although a security has a lower standard deviation, if the beta of this security is greater, then the security having a lower standard deviation would require a higher return. d. A stock is called overpriced when it is located belowabove the SML. FALSE e. A stock is said to be underpriced when its expected return is greater than the required return. TRUE

Page 2 of 3 3. What is the portfolio's standard deviation if you invest 45% of your money into stock 1 which has a standard deviation of returns of 15% and the rest into stock 2 which has a standard deviation of returns of 10%? Assume that the correlation coefficient between the returns of the two stocks is +0.80. 𝑉𝑎𝑟൫𝑅 ௣ ൯ ൌ 𝑊 ଵ ଶ 𝑆𝐷ሺ𝑅 ଵ ሻ ଶ ൅ 𝑊 ଶ ଶ 𝑆𝐷ሺ𝑅 ଶ ሻ ଶ ൅ 2 𝑊 ଵ 𝑊 ଶ 𝐶𝑜𝑟𝑟ሺ𝑅 ଵ , 𝑅 ଶ ሻ𝑆𝐷ሺ𝑅 ଵ ሻ𝑆𝐷ሺ𝑅 ଶ ሻ W 1 =0.45, SD 1 =0.15, W 2 = 1-W 1 =0.55, SD 2 =0.1, Corr = +0.8 𝑉𝑎𝑟൫𝑅 ௣ ൯ ൌ ሺ 0.45 ሻ ଶ ሺ 0.15 ሻ ଶ ൅ ሺ 0.55 ሻ ଶ ሺ 0.1 ሻ ଶ ൅ 2 ሺ 0.45 ሻሺ 0.55 ሻሺ 0.8 ሻሺ 0.15 ሻሺ 0.1 ሻ ൌ 0.013521 𝑆𝐷൫𝑅 ௣ ൯ ൌ √ 0.013521 ൌ 0.1163 4. The covariance of the market's returns with the stock's returns is .006. The standard deviation of the market's returns is 8% and the standard deviation of the stock's returns is 15%. What is the correlation coefficient between the stock and market's returns? 𝐶𝑜𝑟𝑟 ଵ , ଶ ൌ 𝐶𝑜𝑣 ଵ , ଶ 𝑆𝐷 ଵ ∗ 𝑆𝐷 ଶ 𝐶𝑜𝑟𝑟 ଵ , ଶ ൌ 0.006 0.08 ∗ 0.15 ൌ 0.5 5. The risk- free rate is 6% and the expected market return is 15%. An investor sees a stock with a beta of 1.20 selling for $25. The investor thinks that the stock will sell for $29 at year end. The stock is ______ so the investor should _______ : a. overpriced, buy it b. overpriced, sell it c. underpriced, buy it d. underpriced, sell it E(R i )=rf + Beta (E(R Mkt -r f )) =0.06+ 1.2 (0.15 – 0.06) = 0.168 (required return) Expected return = 29 െ 25 25 ൌ 0.16 ሺ𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛ሻ

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