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Q#1. [15 POINTS] You manage a risky portfolio with expected rate of return of 18% and standard
deviation of 28%. The T-bill rate is 8%.
- Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. What is the expected value and standard deviation of the rate of return on his portfolio?
- Suppose that your risky portfolio includes the following investments in the given proportions: STOCK X 25% STOCK Y 32% STOCK Z 43% What are the investment proportions of your client’s overall portfolio, including the position in T- bills?
- What is the reward-to-volatility ratio (S) of your risky portfolio? Your client’s?
- Draw the CAL of your portfolio on an expected return–standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund’s CAL.
- Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 16%.
I. What is the proportion y?
II. Whatareyourclient’sinvestmentproportionsinyourthreestocksandtheT-billfund? III. What is the standard deviation of the rate of return on your client’s portfolio?
F. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio’s standard deviation will not exceed 18%.
I. What is the investment proportion, y?
II. Whatistheexpectedrateofreturnonthecompleteportfolio? G. Your client’s degree of risk aversion is A = 3.5.
I. What proportion, y, of the total investment should be invested in your fund?
Q#2: [EXCEL BASED QUESTION] [50 POINTS] Using the excel example that is discussed in Chapter 7, answer the following questions by first choosing any six assets from your stock trak investment (or the assets of your choice). And for your computation in this question, assume the risk-free rate is 0.2% [TURN- IN ONLY THIS QUESTION BY UPLOADING YOUR EXCEL FILE ON COURSEWORKS]
- [5 Points] Get their monthly price data from yahoo finance for the sample period of 02/1/2011 – 02/1/2022 and compute the realized returns and excess returns.
- [5 Points] Calculate their average monthly returns, monthly variance and standard deviation.
- [5 Points] Calculate their average annual returns, annual variance and standard deviation.
- [5 Points] Compute the variance-covariance matrix of these six assets.
- [5 Points] Find the minimum variance efficient portfolio.
- [5 Points] Find the optimal risky (tangent) portfolio.
- [5 Points] Give an interpretation of your findings.
H. [15 POINTS] Now (i) collect the S&P 500 stock price data for the same sample period as the assets and compute the rate of returns for it. (ii) Run six regressions (i.e., one for each asset) of the returns of your assets on the rate of return of the market portfolio (i.e., S&P 500). (iii) Interpret your regression results of the six assets.
Q#3: [10 POINTS] Index Model: The following are estimates for two stocks.
Stock Return Beta
A 13% 0.8 B 18% 1.2
Firm-Specific Standard Deviation
The market index has a standard deviation of 22% and the risk-free rate is 8%.
- What are the standard deviations of stocks A and B?
- Suppose that we were to construct a portfolio with proportions: Stock A: .30 Stock B: .45 T- bills: .25. Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio.
Q#4: [15 POINTS] Index Model: Consider the two (excess return) index model regression results for A
R-square = .576
Residual standard deviation = 10.3% 𝑹𝑩 =−𝟐%+𝟎.𝟖𝑹𝑴
R-square = .436
Residual standard deviation = 9.1%
- Which stock has more firm-specific risk?
- Which has greater market risk?
- For which stock does market movement explain a greater fraction of return variability?
- If rf were constant at 6% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A?
Q#5: [10 PONITS] Using the two assets in question 3 above, assuming that the coefficient of risk aversion (A) and the correlation of the two assets are 4 and 0.6, respectively, find the portfolio that maximizes the individual’s utility given below:
𝑼=𝑬(𝒓 )− 𝟏𝑨𝝈𝟐 𝑷𝟐𝑷
[Hint: first define 𝐸(𝑟 ) and 𝜎’ as a function of the two assets and substitute them in the utility function &&
before you optimize it]