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- 2. Suppose that you have a riskfree asset and N risky assets for investment. The rate of return on the riskfree asset is r,, while the (Nx1) vector of the rate of return on the N risky assets is r, which is multivariate normal, i.e., r N(u, E). Your utility function for a portfolio that consists of the riskfree asset and the N risky asset is u(r,)=r,-=o, 2 Suppose that the sum of investment proportions on the riskfree and risky assets is one. Answer the following question. A. What is your optimal investment proportion in the risky assets? How is your investment on the riskfree asset affected by different values of 2? B. Suppose that there is only one risky asset i. Show the effects of the Sharpe ratio (4,/0, ) on the investment proportion in the risky asset.3.1 Show that for any portfolio w = equal to (wi,..., wn) the Beta of the portfolio is Bw = wiB1 + + wn Bn, !! ... where B; for i = 1,...,n are Betas of individual assets.4. Valuation of a Derivative Consider a derivative on a stock with the time to expiration T and the following payoff: 0 K₁ 0 if ST K₁. What is the present value of the derivative? Provide an analytic expression of the price using N(), the cumulative probability distribution function of a standard normal random variable.
- As diversification increases, the firm-specific risk of a portfolio approaches A. 1. B. infinity. C. 0. D. (n – 1) × n.The slope of the Security Market Line equals to ____, and the slope of Capital Allocation Line equals to____. Select one: A. Beta; Sharpe Ratio B. Market Risk Premium; Sharpe Ratio C. Risk free rate; Volatility D. Market Risk Premium; Volatility6. Equilibrium pricing: Let the subscripts: j = 0 denote the risk-free asset, j = 1,...,n the set of available risky securities, and M the market portfolio. For the questions that follow, assume that CAPM provides an accurate description of reality. a. b. C. d. State the CAPM equation. (1) Use the CAPM equation to show that the following condition is true s; ≤ SM for any j. What is the significance of this condition when interpreted in the context of the capital market line? (5) Assume that B = 0.8, μM = 0.1 and r = 0.05. Using the CAPM, determine the expected return from holding one unit of asset j for one period. (2) Given your answer to c.), what could you conclude (from the perspective of the security market line) if a market survey indicated that the forecasted one- period return on asset j was 8 percent? Describe and motivate the rational trading response that is consistent with your conclusion. (4)
- Refer to the graph below, what is the beta of portfolio X under CAPM? E(r) A 0.14 0.10 0.06 N Beta of portfolio X = place) M X o(r) (to the nearest 1 decimalchoose which one ? 3.Assume CAPM holds. What is the correlation between an efficient portfolio and the market portfolio?a.1b.-1c.0d.Not enough informationRm-R is read as: O a. The return offered by the market over and above the risk-free rate O b. Market risk premium- Oc. Excess return on the market C. Od. All options are correct
- 1. Suppose there are three complex securities and three different states as follows: Security So S₁(1) S₁ (2) S₁ (3) 1.2 3 0 0 1.8 4 2 0 1.2 2 1 1 2 10 4 A B C D (a) Find the arbitrage-free price of asset D. (b) What is the risk-free return compatible with these asset prices?1. Fill the parts in the above table that are shaded in yellow. 2.Using the data generated in the previous question (Question 1) a. Plot the Security Market Line (SML) b. Superimpose the CAPM’s required return on the SML c.Indicate which investments will plot on, above and below the SML? d.n is the number of periods of an investment, PV is the starting value, FVn is the future value n periods ahead, and ^ means 'to the power of'. What is the correct formula for calculating return? a)(PV/FVn)^n - 1 b)(FVn/PV)^n c)1 - (FVn/PV)^n d)(FVn/PV)^n - 1