There is one period. Assume a representative agent with utility function U(ct) = αc_t − βc^2_tassume the following: α = 100, β = 1, and δ = 0.97. Consumption at t = 0 is C0 = 24. At t = 1 one of two states θ1 and θ2 eventuate with probability π1 = 0.5, and π2 = 0.5,respectively. There are two complex securities s^1 and s^2.s^1 has a payoff of 23 in θ1 and 27 in θ2.s^2 has a payoff of 20 in θ1 and 32 in θ2.What is the stochastic discount factor mt+1? hint: Recall mt+1 =δU′(ct+1)/U′(ct)

The beta of a risk-free security is _____ and the beta of the overall market is _____: a. 0; 1. b. 0; 0. c. 1; 0. d. 1; 1.

The beta of the risk free security is: a) 0 b) > 0 but < 1 c) 1 d) > 1

Two sets of security X and Y have the following characteristics. Security X Probability Return Securty Y Probability  Return 0.1 30% 0.5 -20% 0.2 20% 0.25 10% 0.4 10% 0.30 20% 0.2 05% 0.30 30% 0.1 -10% 0.10 40% Required. Calculate the expected return for each Security. Calculate the standard deviation for each security.

There are two assets 1 and 2, with returns X and Y correspondingly. Return X is a random variable with mean 1 and variance 1; return Y is a random variable with mean 1 and variance 3. We know that the expectation of X*Y is equal to 0. Find the share of asset 1 in the risk-minimizing portfolio.

Assume that security returns are generated by the single-index model,   Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data:   Security βi E(Ri) σ(ei) A 1.4 14 % 23 % B 1.6 16   14   C 1.8 18   17       a. If σM = 22%, calculate the variance of returns of securities A, B, and C.   b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)

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.

Can you have an investment with DCFRR > MARR, but NPV $0 (calculating NPV with iTyM=MARR)? Can you have an investment with DCFRR < MARR, and NPV < $0 (calculating NPV with iTyM=MARR)?

You are given the following possible returns for Security J. Given this information, determine the coefficient of variation for Security J State Probability G 1 30% 10% 25% 18% 14% 24% 27% 2 3 4 O 0.3907 O 0.3847 O 0.3721 O 0.4040 00.3597 31%

Consider a one-period model with N = {1,2,3} and two risky assets S1, S2 whose with current prices are 71 = 42 and 12 = 23 respectively. At time one, the price of S1 is believed to be either 44, 43, or 40 while the price of S2 is believed to be either 27, 22, or 20. Suppose that the risk-free interest rate is 3%. What is the unique risk-neutral probability measure Q in this situation? Select one: О а. Q(1) — 0.35, Q(2) — 0.27, Q(3) — 0.38 O b. Q(1) = 0.63, Q(2) = 0.34, Q(3) = 0.03 Ос. Q(1) — 0.25, Q(2) — 0.62, Q(3) — 0.13 O d. Q(1) = 0.35, Q(2) = 0.62, Q(3) = 0.03