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- Suppose my utility function for asset position x is given by u(x) = In(x). **Am I risk-averse, risk-neutral, or risk-seeking? I now have $20,000 and am considering the following two lotteries: L1: With probability 1, I lose $1,000. L2: With probability .9, I gain $0. L2: With probability .1, I lose $10,000. Determine which lottery I prefer and the risk premium of L2.The accompanying data represent the annual rates of return of two companies' stock for the past 12 years. Complete parts (a) through (k). O A. OB. 0.50- 0.50- 0.00- 0.00- -0.50- -0.50- -0.3 RR of Company 2 0.0 0.3 -0.3 0.0 0.3 RR of Company 1 OC. 0.30- 0.50- 0.00- 0.00- -0.30- -0.50- o.0 0'5 0.0 0.3 -0.5 RR of Company 2 0.5 -0.3 RR of Company 1 (b) Determine the correlation coefficient between rate of return of Company 1 and Company 2. The correlation coefficient is 0.966. (Round to three decimal places as needed.) (c) Based on the scatter diagram and correlation coefficient, is there a linear relation between rate of return of Company 1 and Company 2? Yes No (d) Find the least-squares regression line treating the rate of return of Company 1 as the explanatory variable. y=x+O (Round to four decimal places as needed.) RR of Company 1 RR of Company 1 RR of Company 2 RR of Company 2Asset X pays 2 if state 1 occurs and 4 if state 2 occurs and costs 3. Asset Y pays 3 if state 1 occurs and 1 if state 2 occurs and costs 2. The risk free rate of interest is -0.01 0.00 0.01 0.02
- The accompanying data represent the annual rates of return of two companies' stock for the past 12 years. Complete parts (a) through (k). Year Rate of Return of Company 1 Rate of Return of Company 21996 0.203 0.3981997 0.310 0.5101998 0.267 0.4101999 0.195 0.4362000 -0.101 -0.0602001 -0.130 -0.1512002 -0.234 -0.3572003 0.264 0.3282004 0.090 0.2072005 0.030 -0.0142006 0.128 0.0932007 -0.035 0.027 (j) Plot residuals against the rate of return of Company 1. Does the residual plot confirm that the relation between the rate of return of Company 1 and Company 2 is linear? Yes or No? (k) Are there any years where the rate of return of Company 2 was unusual? Yes or No?From the graph below relating the holding-period returns for Aram Inc. (in the Y-axis) to the S&P 500 Index (in the X-axis), estimate the firm's beta. Aram's beta is estimated to be about?In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected return is given by E[R].
- The diversifiable risk of a portfolio:a. Is correlated with systematic risk.b. Can be made sufficiently small.c. Is zero in the real world.d. Is the risk that investors lose because of transaction costs.Example 1: Let's consider two portfolios. Calculate Sharpe's ratio. Portfolio Return (Rp) Risk Free (Rr) Excess return (Rp- Rr) Portfolio risk (SD) A 21 8. 13 10 17 8. 9. 8.7. For a sample of 20 monthly observations, a financial analyst wants to regress the percentage rate of return (Y) of the common stock of a corporation on the percentage rate of return ( X) of standard and Poor's 500 Index. The following information is available: 20 20 20 20 20 >y = 22.6 , x = 25.4 , ) xỉ = 145.7 ,) yf = 180.5 , *Y = 150.5 a. Compute the sample correlation coefficient and interpret your answer. b. Test to determine the significance of the linear relationship between x and y. c. Estimate the lincar regression of Y on X, and interpret your results. Hence write the regression line and estimate Y when X is 8%.
- Returns earned over a given time period are called realized returns. Historical data on realized returns is often used to estimate future results. Analysts across companies use realized stock returns to estimate the risk of a stock. Consider the case of Celestial Crane Cosmetics Inc. (CCC): Five years of realized returns for CCC are given in the following table. Remember: 1. While CCC was started 40 years ago, its common stock has been publicly traded for the past 25 years. 2. The returns on its equity are calculated as arithmetic returns. 3. The historical returns for CCC for 2014 to 2018 are: 2014 2015 2016 2017 2018 Stock return 18.75% 12.75% 22.50% 31.50% 9.75% Given the preceding data, the average realized return on CCC’s stock is . The preceding data series represents of CCC’s historical returns. Based on this conclusion, the standard deviation of CCC’s historical returns is . If investors expect the…If the expected return on the market is 8% and the risk free rate is 4% and the expected return is 12%, what is the market risk premium ?Consider a special fully discrete 20 year endowment insurance on (30). The death benefit, payable at the end of the year of death if death occurs within 20 years, is 250,000, while the endowment benefit which is payable at time 20 is 500,000. Premiums are level and payable at the beginning of each year for 20 years. Using the Standard Ultimate Life Table ( S.U.L.T) with i = 5% determine each of the following: (a.) the premium 7. (b.) 10 V, the reserve at time 10.