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Your client, Jane Hislop, has an investment portfolio which is 30% invested in Fund 1 and 70% invested in Fund 2. Calculate the beta of her portfolio if:
The standard deviation of Fund 1 is 8%, the standard deviation of Fund 2 is 16% and the standard deviation of the market is 10%.
The correlation between Fund 1 and the market is 0.9 and the correlation between Fund 2 and the market is 0.7
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- You have estimated the single index model (SIM) fund B and found that its alpha and beta are 0.035 and 1.1 respectively. The standard deviation of Fund B's excess returns is 30% and the market portfolio excess returns have a standard deviation of 20%. What's the information ratio of Fund B?If $x is invested in mutual fund A, the annual return has an expectation of $0.1x and a standard deviation of $0.02x. If $x is invested in mutual fund B, the annual return has an expectation of $0.1x and a standard deviation of $0.03x. Suppose that the returns on the two funds are independent of each other and that I have $1000 to invest. (a) What are the expectation and variance of my annual return if I invest all my money in fund A? (b) What are the expectation and variance of my annual return if I invest all my money in fund B? (c) What are the expectation and variance of my total annual return if I invest half.Your client, Jane Hislop, has an investment portfolio which is 30% invested in Fund 1 and 70% invested in Fund 2. Calculate the beta of her portfolio if: The standard deviation of Fund 1 is 8%, the standard deviation of Fund 2 is 16% and the standard deviation of the market is 10%. The correlation between Fund 1 and the market is 0.9 and the correlation between Fund 2 and the market is 0.7 Explain to Jane how risky her individual fund investments are, and the risk of her portfolio relative to the market. Relative to return of the market, what return can she expect from her individual funds, and from her overall portfolio?
- An investiment portfolio consists of two securities, X and Y. The weight of X is 30%. Asset X's expected return is 15% and the standard deviation is 28%. Asset Y's expected return is 23% and the standard deviation is 33%. Assume the correlation coefficient between X and Y is 0.37. A. Calcualte the expected return of the portfolio. B. Calculate the standard deviation of the portfolio return. C. Suppose now the investor decides to add some risk free assets into this portfolio. The new weights of X, Y and risk free assets are 0.21, 0.49 and 0.30. What is the standard deviation of the new portfolio?Suppose the total risk of Portfolios A, B and C are 49% ², 64%² and 100% ² respectively. The market price of risk is 8%. The Market Portfolio (M) has an expected return and a total risk of 11% and 100% respectively. (a) You want to form another Portfolio H by investing $7,000 in Portfolio A and $3,000 in Portfolio B. Compute the standard deviation of Portfolio H if the correlation coefficient between Portfolio A and Portfolio B is: i) perfectly positively correlated ii) uncorrelated iii) perfectly negatively correlated (b) If the expected return of Portfolio C is 9.4% and it is lying on the Securities Market Line, what is the beta of Portfolio C? State the answer in %². (c) Is Portfolio C a Market Portfolio as it has same level of total risk (i.e. 100% 2) as the Market Portfolio? Why or Why not?You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 28%. The T-bill rate is 7%. Your client's degree of risk aversion is A = 2.0, assuming a utility function u E(r) = A0². a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment proportion y Expected return Standard deviation - % b. What are the expected value and standard deviation of the rate of return on your client's optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) % %
- You have just been appointed as a fund manager for Gate Way Fund, of which you will be responsible of a portfolio that consists of two assets. The analysts have provided you with the expected returns and standard deviations of returns of which are listed in the table below: Asset A Asset B Expected Return 7% 11% Standard Deviation 15% 21% Calculate the expected return of the portfolio if half is invested in asset A. If the covariance of the two assets is 28, calculate the correlation coefficient of the portfolio. Calculate the variance of the portfolio if the investments in the two assets classes is equal. Calculate the standard deviation of the portfolio if the assets are equally weighted. The two asset portfolio model can be extended to a portfolio with more assets. Explain the implications of this approach for the understanding of portfolio risk and discuss the practical problems of applying the model in this fashion.Suppose that Jerry Tan has surplus funds to invest in both stocks, Alpha and Beta. He has decided to form a portfolio with investment in both stocks. The correlation coefficient between the expected return of both stocks is 0.8 and the weightage of investment is 40% for Stock Alpha and 60% for Stock Beta.Required:(i) Compute the expected return of the portfolio. (ii) Compute the variance of the portfolio. (iii) Compute the standard deviation of the portfolio.A portfolio consists of 70% of investment A and 30% of investment B. The expected returnon investment A is 7% and the expected return on investment B is 9%. The standarddeviation of returns of investment A is 2.19%. The standard deviation of returns ofinvestment B is 4.1%. The correlation coefficient of the returns of investment A andinvestment B=+1. Finda. the expected return from the portfoliob. the standard deviation (risk) of the returns from the portfolio
- Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 46%. The T-bill rate is 4%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund. Required: a. What are the expected return and standard deviation of your client's portfolio? (Round your answers to 1 decimal place.) Expected retum Standard deviation b. Suppose your risky portfolio includes the following investments in the given proportions: 30% 30 40 Stock A Stock B Stock C What are the investment proportions of your client's overall portfolio, including the position in T-bills? (Round your answers to 1 decimal place.) Security T-Bills Stock A Stock B Stock C Investment Proportions % per year % per year % % % % Risky portfolio Client's overall portfolio c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Round your answers to 4 decimal places.) Reward-to-Volatility RatioThe following portfolios are being considered for investment. During the period under consideration, RFR =0.07 Porfolio Return Beta P 0.15 1.00 0.05 Q 0.20 1.50 0.1 R 0.10 0.60 0.03 S 0.17 1.10 0.06 Market 0.13 1.00 0.04 Compute the Sharpe measure for each portfolio and the market portfolio Compute the Treynor measure for each portfolio and the market portfolio Rank the portfolios using each measure explaining the cause for any differences you find in the rankings.You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 36%. The T-bill rate is 6%. Your client's degree of risk aversion is A = 3.1, assuming a utility function u = E(r) A02. a. What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Investment proportion y % b. What are the expected value and standard deviation of the rate of return on your client's optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return % Standard deviation %