4. Suppose you are a money manager of a $10 million investment fund. The fund is invested in three assets with the following investments and betas: Investment Stock A B C $3,000,000 2,000,000 4,000,000 Beta 1.80 0.75 1.20 The remainder is invested in T-bills (risk free asset) with 3% return. a. If the market expected rate of return is 9% what is the fund's expected rate of return? b. Using Funds A and B, create a portfolio (report the portfolio weights and $ investment out of $10 million) with a 0.92 beta.
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- A fund manager can invest in any combination of the three assets with the following expected returns and standard deviations: Asset 1: r1 = 2%, σ1 = 2% Asset 2: r2 = 6%, σ2 = 6% Asset 3: r3 = 4%, σ3 = 4% All three assets returns are uncorrelated: p12 = p13 =p 23 = 0 . Find a portfolio consisting of these three assets that achieves an expected return of 4% with the lowest risk possible. Show all steps.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.An investor is evaluating the historical performance of an investment fund. The following annual returns are provided to the investor: Fund Value Year 0 $120 Year 1 132 Year 2 146 Year 3 133 Year 4 128 Year 5 123 Required: a. Calculate the investment returns for each year. b. Compute the arithmetic mean return. c. Calculate the geometric mean return.
- You plan to invest in either a mutual fund X or mutual fund Y. The following information about the annual return (%) of each of these investments under different demand levels is available, along with the probability that each of these states of nature will OCcur: Demand Probability Fund X Fund Y High 0.4 30% 25% Medium 0.4 22% 34% low 0.2 17% 25% a) Compute expected return, standard deviation for each investment and covariance of the mutual fund X and mutual fund Y. b) Would you invest in the mutual fund X or Y? Explain. c) If you chose to invest in mutual fund X and the state of nature turns up to be the low demand, what do you think about the possibility of the opportunity loss of 8% in comparison to investing in mutual fund Y?Consider the following risk-return characteristics for funds A and B: Expected return Risk Fund A (Equity) 12% 20% Fund B (Debt) 9% 16% The correlation coefficient between the returns of fund A and fund B is 0.4. 1. Which Fund is riskier? Write 1 if your answer is Fund A, write 2 if your answer is Fund B, or write 3 if your answer is undetermined. 2.1 What is the weight of fund A in the minimum variance portfolio? 2.4 What is the risk of the minimum variance portfolio? 2.2 What is the weight of Fund B in the minimum variance portfolio? 2.3 What is the expected return of the minimum variance portfolio?If a fund has a return of 12% and a beta of 1.4, and if the risk-free rate is 2%, and market return rate is 8%, calculate Jensen's Alpha O a. 3.6 Ob. 2.4 O c. 1.6 Od. 1.4
- Net asset value (NAV) of an investment fund is calculated as total portfolio value divided by number of fund shares. Accordingly, if the total portfolio value is 100.000 $ and the number of shares is 55.000, then the NAV would be 100.000 $/55.000 = 1,818 S. Now, suppose that you are a portfolio manager of a bond fund that has 20.000 fund shares outstanding. You consider 3 investments for your portfolio: (a) A T-bill that has a 194 day maturity with a face value of 10.000 $. (b) A zero-coupon bond that has a 10 year maturity with a face value of 100.000 $. (c) A bond that pays quarterly coupon payments with an annual coupon rate of 12%, a face value of 50.000 $ and a maturity of 5 years. You know that the annual market yields are 10%. If you invest them all right now, what would be the NAV of your fund at the time of investment? (1 year = 360 days)Help me pleaseAn insurance fund is analysing the performance of three different fund managers A, B and C. Each manager invests in one third of all asset classes to maintain a well diversified portfolio. The following information is available: A B C Market portfolio Average net return (%) 5 8 9 9 Volatility (%) 18 24 21 20 Beta 0.8 1.1 1.3 A risk free rate is established to be 2%. Calculate for each of the fund managers the expected return using CAPM, ex post Sharpe Ratio, Treynor Ratio, M2 alpha and Jensen’s alpha. Interpret your results.
- Consider the following information about a risky portfolio that you manage and a risk-free asset: E(rp) = 9%, Op = 24%, rf = 2%. Required: a. Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 8%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk-free asset? b. What will be the standard deviation of the rate of return on her portfolio? c. Another client wants the highest return possible subject to the constraint that you limit his standard deviation to be no more than 12%. Which client is more risk averse?Consider the following information about a risky portfolio that you manage and a risk-free asset: E(rp) 13%, op = 17%, rf = 5%. %3D a. Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 7%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk- free asset? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Risky portfolio % Risk-free asset % b. What will be the standard deviation of the rate of return on her portfolio? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Standard deviation %The average returns, standard deviation and betas for three funds and the S&P are given below. The risk-free rate is 3%. Use Fund A the risk-free asset to create a complete portfolio that has the same standard deviation as the market portfolio. What is the expected return of this complete portfolio? Fund Avg. Return Std. Dev Beta A 16% 30% 1.1 B 18% 25% 1.2 C 22% 35% 1.3 S&P 500 14% 20% 1.0