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what is the return in a recession for a portfolio of the two assets

Use the following information to answer questions 1 through 3: Your portfolio is comprised of $8,000 in Barbie and $3,500 in Ken. State of Probability Returns if State Occurs Economy of State Recession Growth Barbie Ken 25% 75% -3% 7% 8% 2% 1. What is the return in a recession for a portfolio of the two assets? 2. What is the expected return for a portfolio of the two assets? 3. What is the variance of return for a portfolio of the two assets? (Hint: Find the portfolio return in each state first, then use the probabilities in the same manner as for a single asset. You dont need the correlation coefficient when using this method.) 4. The expected value of a normal distribution of prices for a stock is $36. If you are 99 percent sure that the price of the stock will be between $9 and $63, then what is the variance of the stock price? 5. What type of risk can be diversified away? 6. The security market line is shown below. Based on the graph, what is the required return for a stock with a beta of 0.5? 4.5 % 1% Beta
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Answer #1

Expected return and variance found by calculating the expected return of the

portfolio in each state.

Probability of Return if the state State State of econo occurs Barbie Ken Recession 25% 75% Growth Barbie Ken Total $8,000$3,500 $11,500 0.30 Amount invested Wei 0.70 13 Portfolio return in each state can be calculated as follows: Expected portfolio returm, Ip -XV 17 Where w and r are the weights and return of assets Probability of Return if the state Portfolio State 21 State of econo occurS Return Barbie Ken Recession 25% 896 | 0.35%|-D10E234E10°F23 24 25 Thus portfolio return in recession is 0.35% 2б Probability of Return if the state Portfolio State State of econo occurs Return Barbie Ken 25% 75% 31 Recession 8%) 0.35% Growth 2% 5.48% 34 Expected Portfolio return -25%*0.35%+75%5.48% 35 4.20%-D31 G31+D32 G32 37 38 39 Hence Expected Portfolio return is 4.20% Probability of Return if the statePortfolio State State of econo occurS Return BarbieKen 25% 75% 8% 2% 0.35% 5.48% 43 Recession Growth Variance and standard deviation of stocks can be calculated from following formula 47 variance Var)-yp, (r-r) 49 Variance of portfolio -Sum of product of probability and square of excces return in each state :0.25*((0.35%-4.20%)^2)+0.75*(( 5.48%-4.20%)^2) 51 53 0.04996-SUMPRODUCT(D43:D44(G43:G44-D37)^2) Hence variance of tfolio is 0.049%

57 59 value of Z for 99% confidence level is 2.58 the upper and lower value of the confidence interval will be μ-2586 and μ-2.53c where μ is the mean and σ is the standard deviation of the interval 61 63 Thus 36 μ-2.580 69 36-2.58ơ 9 71 72 Solving the above equation $10.47(D65-D67)/2.58 Hence the value of standard deviation of stock price is $10.47 74 75 76 (Standard Deviation)A2 $109.52 Variance 78 Hence the value of variance of stock price is $109.52 81 Stock specific risk suck as performance of the company, labor strike etc. can be diversified using the portfolio of different stock. 83 86 87 As Per CAPM, Expected rate of return can be calculated as 89 91 92 93 Using the Following data Beta (P Risk free rate (r) Market Return (rm) 0.5 196 5% Expected rate of return can be calculated as follows: Expected rate of return 95 -rf +B*(rm-rf -1%+0.5* (4.5%-1%) 97 2.75% D92+D91*(D93-D92) 100 101 Hence required return is 2.75%

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