Microsoft Word - Week 5__W

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University of Wollongong *

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222

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Finance

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Jan 9, 2024

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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 𝑆𝐷ሺ𝑅 ൅ 𝑊 𝑆𝐷ሺ𝑅 2 𝑊 𝑊 𝐶𝑜𝑟𝑟ሺ𝑅 , 𝑅 ሻ𝑆𝐷ሺ𝑅 ሻ𝑆𝐷ሺ𝑅 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 0.15 ൅ ሺ 0.55 0.1 2 0.45 ሻሺ 0.55 ሻሺ 0.8 ሻሺ 0.15 ሻሺ 0.1 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 , 𝐶𝑜𝑣 , 𝑆𝐷 ∗ 𝑆𝐷 𝐶𝑜𝑟𝑟 , 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
Page 3 of 3 6. The market risk premium is 6% and the risk-free rate is 2.65%. Mcdonald has a beta of 0.5. Assuming the realised return of 8%, is the security fairly priced? Yahoo has a beta of 1.46. Assuming the realised return of 5%, is this security fairly priced? Answer the questions by completing the below and drawing the SML. Hints: Fill the gap as you develop ideas for the question. The Security Market Line (SML) shows the relationship between required return and beta . From the question, we know o r f = 2.65% and Market risk premium= 6% . Given above, let’s establish CAPM equation E(Ri)=_ r f + B[E(R MKt )–r f ]=2.65 + 6B To determine whether a security is correctly priced, we need to compare required rate of return to realised rate of return. Beta Realised return Required return (Compute!) Overpriced? Underpriced? Buy or Sell? Mcdonald 0.5 8% 2.65+ 0.5*6=5.65% Underpriced Buy Yahoo 1.46 5% 2.65+ 1.46*6=11.41% Overpriced Sell E(Ri) 11.41% Mc 5.65% ( r f ) 2.65% 0.5 1.46 Beta 8% 5 % yaho o I am E(R MKt )–r f
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