on A Return on B Boom .20 20% 5% Normal .50 10% 8% Bust .30 8% 12% What is the variance of a portfolio with 80% of the funds invested in A? What is the standard deviation of a portfolio with 80% of the funds inv
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Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
State Probability Return on A Return on B Boom .20 20% 5% Normal .50 10% 8% Bust .30 8% 12%
What is the variance of a portfolio with 80% of the funds invested in A?
What is the standard deviation of a portfolio with 80% of the funds invested in A?
Step by step
Solved in 3 steps with 2 images
- EXAMPLE: PORTFOLIO VARIANCE• Consider the following information on returnsand probabilities:▪ Invest 50% of your money in Asset A State Probability A B PortfolioBoom .4 30% -5% 12.5%Bust .6 -10% 25% 7.5%• What are the expected return and standarddeviation for each asset?• What are the expected return and standarddeviation for the portfolio?Consider the information for assets A, B, and C below: Probability Return on A 0.2 0.4 0.4 State Boom Average Bust 0.3 0.2 0.1 Return on B Return on C 0.05 9.15 0.2 0.1 0.25 0.3 Consider Portfolio (Y) comprising 60% Asset A and 40% Asset C. What is the variance of portfolio Y™?Analyze investment M and investment J using the below. Scenario Probability M Return J Return Strong .30 18% 20% Normal .30 15% 12% Weak .40 9% 5% 1. What is the range for M? 2. What is the average exp. return for M ? 3. What is the standard deviation* M? 3.85 (given) 4. What is the CV for M? 5. What is the range for J? 6. What is the average exp. return for J? 7. What is the standard deviation J? 6.22 (given) 8. What is the CV for J? 9. Which is the better choice?
- 5. Consider the following portfolio (assume an equal probability of a boom or a bust): Asset Port. Weight ReturnBoom ReturnBust .25 15% .25 20% .50 35% A B D 5% 10% -10% (a) what is the expected portfolio return given the following information? (b) what is the portfolio's variance? What is its standard deviation?c. Suppose the risk-free rate is 4.2 percent and the market portfolio has an expected return of 10.9 percent. The market portfolio has a variance of .0382. Portfolio Z has a correlation coefficient with the market of .28 and a variance of .3285. According to the capital asset pricing model, what is the expected return on Portfolio Z?Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084. 1. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio? 2. In addition to the funds A and B in the previous question, now you decide to include fund C to your portfolio. Its expected return is 10, its variance 0.0625, its correlation with A is 0.1050 and its correlation with B is 0.07. You want to achieve an expected return of 16% on your portfolio, with the minimum possible risk (measured by the standard deviation). Derive analytically (that is, without the help of solver, but trough calculus) the weights of such desired portfolio, and its standard deviation.
- Consider the following information: Probability State of of State of Economy Boom Good Foor Bust Economy 0.20 0.25 0.10 0.45 Variance Rate of Return if State Occurs Stock A 0.19 0.16 0.00 -0.00 Stock B 0.38 0.23 -0.09 -0.32 Standard deviation Stock C 0.28 0.10 a. Your portfolio is invested 25 percent each in Stocks A and C and 50 percent in Stock B. What is the expected return of the portfolio? Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Expected return -0.05 -0.10 b-1. What is the variance of this portfolio? Note: Do not round intermediate calculations. Round your answer to 5 decimal places. b-2. What is the standard deviation? Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.1. Given the following summary statistics, Mean S.D. 1.235 0.997 Asset A 0.52 Asset B. 0.44 (a) If the correlation between the two financial series is 0.25. What are the optimal portfolio weights to minimize risk? (b) What are the expected return and standard deviation of the optimal port- folio? (c) Compute the 1% Value-at-Risk for the next 5 days (d) Compute the expected shortfallUse the following information: E[rXOM] = 15.6%, standard deviationyOM = 15.9% %3D E[IMSI=29.7%, standard deviationMS = 35.2% Correlation of returns: PXOM.MS = 0.139, r=10% If the optimal amount to invest in the first asset (w) is 0.43, what is the variance of the risky portfolio when w=0.43? (write in decimal format using 5 decimal places)
- Consider the following information on a portfolio of three stocks: Probability of State Stock A Rate of Economy of Return State of Economy Boom Normal Bust .25 .60 15 a. Expected return Variance Standard deviation b. Expected risk premium 0.10 % .04 .09 15 0.00993 Stock B Rate of Return a. If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio's expected return? The variance? The standard deviation? Note: Do not round intermediate calculations. Round your variance answer to 5 decimal places, e.g., 16161. Enter your other answers as a percent rounded to 2 decimal places, e.g., 32.16. 0.10 % % .33 . 13 . 14 b. If the expected T-bill rate is 3.4 percent, what is the expected risk premium on the portfolio? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16. Stock C Rate of Return .55 . 19 -.28Consider the following information: State of Economy Boom Good Poor Bust a. Probability of State- of Economy a. Expected return b-1. Variance b-2. Standard deviation .20 .50 .20 .10 Rate of Return if State Occurs Stock A Stock B Stock C .48 .28 .19 12 38 14 -.05 -.19 Your portfolio is invested 22 percent each in A and C, and 56 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b-1. What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.) b-2. What is the standard deviation? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) % -.08 -.23 % -.06 -.09Portfolio Suppose rA ~ N (0.05, 0.01), rB ~ N (0.1, 0.04) with pA,B = 0.2 where rA and rB are CCR’s. a) Suppose you construct a portfolio with 50% for A and 50% for B. Find the variance of the portfolio CCR. b) Find the portfolio expected gross return. c) Find the expected portfolio CCR.