A maximizing investor with preferences u(u, ơ) = 0.2µ – 0.50^2 will allocate a portfolio worth 4000 between a risk free asset with a return of 4 percent and the market asset with a return of 20 percent and risk of 4 percent. How many dollars should be invested in the market asset?
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- A company is considering implementing a project that generates a guaranteed income of 1000 from next year and every year thereafter, while the project has an investment cost of 10,000 today. In addition, there is a one-off maintenance cost of 20 000 in exactly 10 years time. Assume that the risk-free interest rate is 3 percent. Is the project profitable to implement?Q2 - Returns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7Stock X 4% -2% 5% -1% 10% 7% 12%Stock Y -3% 7% 4% 2% 2% 8% -3% Consider a portfolio of 10% stock X and 90% stock Y. What is the mean of portfolio returns? Please specify your answer in decimal terms and round your answer to the nearest thousandth (e.g., enter 12.3 percent as 0.123).An entrepreneur recently learned about a new hotel business that requires an initial investment of $12M and annual cash flow of $2M in perpetuity. The appropriate discount rate is 20%. Now, consider a pretty similar scenario: an Initial investment $12M. Now, in good state, $6M annual cash flows. In a bad state, -$2M annual cash flows. Furthermore, assume that the entrepreneur wants to own at most, 1 hotel (no option to expand). - But things change when we consider the abandonment option. At date 1, the entrepreneur will know which forecast has come true. If the world is in the good state, he will keep the project alive. If bad state, he will abandon the hotel after period 1. - Now, what is the NPV of the project? - What is the value of the option to abandon?
- suppose that you invest $100 today in a risk-free investment and let the 4 percent annual intrest rate compound. Rounded to the full dollars, what will be the value of your investment 4 years from now?A project has an initial cost of $26,000, a discount rate of 11.7 percent, a life of 5 years, and an NPV of $11,216. Given this, you know that the project is expected to earn a return: A equal to 11.7 percent of $26,000 plus an additional $11,216. B of $11,216 in total. C equal to 11.7 percent of $37,216 (= $26,000 + 11,216). D of 11.7 percent of $11,216. E of $26,000 minus $11,216.Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w.
- Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.1) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?2) Find A as a function of w.Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?In a financial market a stock is traded with a current price of 50. Next period the price of the stock can either go up with 30 per cent or go down with 25 per cent. Risk-free debt is available with an interest rate of 8 per cent. Also traded are European options on the stock with an exercise price of 45 and a time to maturity of 1, i.e. they mature next period. Find prices of Arrow-Debreu securities.
- The table below shows information for 3 stocks. Security Beta Risk-free rate Expected market return Stock 1 1.9 0.02 0.09 Stock 2 1.2 0.035 0.09 Stock 3 0.2 0.015 0.09 The risk-free rates are different because they were measured in different years. Calculate the expected (or required) return for each stock, using the Capital Asset Pricing Model (CAPM). What is the required return for stock 1? What is the required return for stock 2? What is the required return for stock 3?As a manager of your company, you are considering to go for a project, with an initial outlay of $200,000. The project has a life of three years and yields (year-end) cash inflows of $ 100,000 in year-1, $150,000 in year-2 and $200,000 in year 3. What is the net present value of the project if the interest rate is 10 percent? Show your steps. Should you recommend to go for the project? Explain in details.You observe the E[IBM] = 8%, E[AAPL] = 12%, B(AAPL)=B(IBM)+2/3, Risk-free rate is 4%. What is the expected return on the market portfolio assuming the CAPM is true.