Find a portfolio with payoff at time T equal to if 0 ≤ S(T) ≤ 10, if 10 ≤S(T) ≤ 30, if 30 ≤S(T). VT 2ST + 30, -3ST+80, ST-40, Here, ST denotes the price of the underlying asset at time T. You can hold cash, the asset, calls, and puts.

Bhagi

Portfolio  Suppose      rA ~ N (0.05, 0.01), rB ~ N (0.1, 0.04) with pA,B = 0.2 where rA and rB are CCR’s.  a) Suppose you construct a portfolio with 50% for A and 50% for B. Find the variance of the portfolio CCR. b) Find the portfolio expected gross return. c) Find the expected portfolio CCR.

Assume that using the Security Market Line(SML) the required rate of return(RA)on stock A is found to be halfof the required return (RB) on stock B. The risk-free rate (Rf) is one-fourthof the required return on A. Return on market portfolio is denoted by RM. Find the ratioof betaof A(A) tobeta of B(B). Thank you for your help.

Asset W has an expected return of 13.4 percent and a beta of 1.6. If the risk-free rate is 5.0 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Do not round intermediate calculations and enter your expected return answers as a percent rounded to 2 decimal places, e.g., 32.16. Round your beta answers to 3 decimal places, e.g., 32.161.)   Asset W has an expected return of 13.4 percent and a beta of 1.6. If the risk-free rate is 5.0 percent, complete the following table for portfolios of Asset W and a risk-free asset. (Do not round intermediate calculations and enter your expected return answers as a percent rounded to 2 decimal places, e.g., 32.16. Round your beta answers to 3 decimal places, e.g., 32.161.)

Find the weights of the two pure factor portfolios constructed from the following three securities: r1 = .06 + 2F¡ + 2F, r2 = .05 + 3F, + IF, r3 = .04 + 3F, + OF, Then write out the factor equations for the two pure factor portfolios, and determine their risk premiums. Assume a risk-free rate that is implied by the factor equations and no arbitrage.

The portfolio with the highest Sharpe Ratio is I. The minimum-variance point on the efficient frontier II. The tangency point of the capital market line and the efficient frontier III. The maximum-return point on the efficient frontier  IV. The line with the steepest slope that connects the risk-free rate to the efficient frontier Select one: a. II and IV only b. I and IV only c. III and IV only d. Only IV e. I and II only

Consider the following graph.   According to Markowitz’ portfolio theory, which point on the graph represents optimal portfolio?       C     A     B     D

Assume a security follows a geometric Brownian motion with volatility parameter = 0.2. Assume the initial price of the security is 21 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price 19 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price.

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.