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- 1. Suppose there is a mutual fund and each consumer buys a share in it for her endowment at t = 0. The mutual fund | maximises the wealth of its shareholders when choosing IF, the investment in the long term technology. At t =1, the mutual fund pays dividend d to each of its shareholders. At t = 1, the shares can be traded at price p". a. Set up the mutual fund's optimisation problem and derive and interpret the first order condition. What happens when R increases and why? b. What is the optimal consumption profile cf, c and the optimal investment IF? | c. Calculate (i.e. derive an expression for) d and p".Consider the information on the market, the risk-free asset, and a mutual fund. You want to build a two-asset portfolio comprising the market portfolio and the risk-free asset such that your portfolio beta is the same as the mutual fund. What is the portfolio weight on the market in your portfolio? Mutual Fund Market Risk Free E(k) 11.1% 8.5% 2.0% Beta 1.4 1 0A mutual fund that aggressively seeks capital growth: # O A. will have an MER that is higher than a global fund. OB. will have an MER that is approximately the same as a T-bill fund. OC. will have an MER that reflects the increased costs of research. OD. will have an MR similar to that of a fixed-income fund.
- You have been given the following return information for a mutual fund, the market index, and the risk-free rate. You also know that the return correlation between the fund and the market is 0.91. Year 2018 2019 2020 2021 2022 Fund -20.60% 25.10 13.90 7.60 -2.10 Market -39.50% 21.00 13.90 8.80 -5.20 Risk-Free 1% 3 2 4 2 Calculate Jensen's alpha for the fund, as well as its information ratio. Note: Do not round intermediate calculations. Enter the alpha as a percent rounded to 2 decimal places. Round the ratio to 4 decimal places.You Answered Correct Answer Jensen (1968) E proposed a very influential idea: when assessing mutual fund performance, we should compare funds only after accounting for the risks they take (rather than simply comparing returns). To see his argument, draw a SML, and put one dot above the SML (call it A) and one dot below it (call it B) while A and B have the same beta. (a) Describe the investment opportunities here. Buy B and sell A in a way that the portfolio has zero market beta Buy A and sell B in a way that the portfolio has zero market beta Just buy A to reach the highest possible returnSuppose you have some money to invest-for simplicity, $1-and you are planning to put a fraction w into a stock market mutual fund and the rest, 1 w, into a bond mutual fund. Suppose that $1 invested in a stock fund yields R after 1 year and that $1 invested in a bond fund yields Rp. suppose that R, is random with mean 0.08 (8%) and standard deviation 0.07, and suppose that R, is random with mean 0.05 (5%) and standard deviation 0.04. The correlation between R. and R, is 0.27. If you place a fraction w of your money in the stock fund and the rest, 1 the bond fund, then the return on your investment is R = wR₂ + (1-w)Rp. - Suppose that w = 0.53. Compute the mean and standard deviation of R. The mean is. (Round your response to three decimal places.) The standard deviation is. (Round your response to three decimal places.) w, in
- You have been given the following return Information for a mutual fund, the market Index, and the risk-free rate. You also know that the return correlation between the fund and the market is 0.97. Year 2018 2019 2020 2021 2022 Fund -23.0% 25.1 14.3 6.8 -2.34 Market -43.5% 21.4 15.1 8.8 -5.2 Risk-Free 3% 5 2 6 2 What are the Sharpe and Treynor ratios for the fund? Note: Do not round Intermediate calculations. Round your answers to 4 decimal places. Answer is complete but not entirely correct. Sharpe ratio Treynor ratio 0.2589 0.3216You are looking for an investment vehicle that has two characteristics. First, you want an incentive structure for asset managers where they earn more money when you (the investor) earns more money. Second, you want a mostly diversified pool of investments. Which vehicle is your best option? O Hedge fund Closed-end mutual fund Open-end mutual fundYou have been given the following return information for a mutual fund, the market index, and the risk-free rate. You also know that the return correlation between the fund and the market is 0.97. Year 2018 2019 2020 2021 2022 Fund -15.2% 25.1 12.4 6.2 -1.2 Sortino Ratio Market -24.5% 19.5 9.4 7.6 -2.2 Risk-Free 1% 3 2 Fund 4 2 What is the Sortino ratio for the fund and the market? Note: A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers rounded to 4 decimal places. h Market
- 1. There are two mutual funds, A and B with the following information, R₁ 0.08 0.03 0.07 I 0.09 Security The Market The Riskfree Bond Pim (i) (iv) (vi) (viii) where σ; is the standard deviation, and pim is the correlation with the market portfolio. Assume that the CAPM holds, with fund A being efficient. (a) What are the answers to (i)-(v) above without doing any computation? (b) From given information, compute (vi) and (vii) in the table above. (c) If you are using the CAPM as a benchmark, which fund should you buy? [hint: what is the return implied by the CAPM] O 0.20 (iii) 0.12 0.30 Mutual Fund A Mutual Fund B (ii) (v) (vii) 1.2Given a simple world with two assets, a bond fund and a stock fund, clearly detail the steps involved in arriving at the 1) efficient frontier, and 2) market (optimal) portfolio.Of the following investment vehicles, which is the best and which is the worst? Choose from common stocks, mutual funds, ETFs, REITs. Explain why.