6. Equilibrium pricing: Let the subscripts: j = 0 denote the risk-free asset, j = 1,...,n the setof 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; ≤ SMfor any j. What is the significance of this condition when interpreted in thecontext of the capital market line? (5)Assume that B = 0.8, μM = 0.1 and r = 0.05. Using the CAPM, determinethe expected return from holding one unit of asset j for oneperiod. (2)Given your answer to c.), what could you conclude (from the perspective ofthe security market line) if a market survey indicated that the forecasted one-period return on asset j was 8 percent? Describe and motivate the rationaltrading response that is consistent with your conclusion. (4)

c. Expected Return using CAPM (Example):Given:Beta (B) = 0.8 (replace B with βj for the specific…

Answered: 6. Equilibrium pricing: Let the…

Corporate Fin Focused Approach

5th Edition

ISBN:9781285660516

Author:EHRHARDT

Publisher:EHRHARDT

Chapter6: Risk And Return

Section: Chapter Questions

Problem 1Q

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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.
Rm-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
Think about whether a risk-free asset should earn a risk-premium beyond the risk-free rate. Thinking about that should give you an idea of the beta for a risk-free asset. Or, look again at the CAPM equation: E(Ri)=Rf+βi[E(RM)−Rf] Given this equation, what beta sets the E(R) of the risk free asset equal to the risk-free rate? A) zero B) 0.5 C) 1.0 D) its random
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.
Consider the following two scenarios whereby the cost-of-carry model is violated. You are required to select appropriate missing words and fill in question 1. a. long b. spot c. over priced d. short arbitrage e. under priced f. long arbitrage g. futures h. short Question 1 a. If ft >S0 (1 + rf - d)^t, then the( ) is ( )relative to ( ) or equivalently, the quoted futures price is higher than what it should be. Thus, the correct arbitrage strategy should be: ( ) the futures contract and ( )the spot market. This strategy is also known as ( ). b. If ft <S0 (1 + rf - d)^t, then the( ) is ( )relative to ( ) or equivalently, the quoted futures price is lower than what it should be. Thus, the correct arbitrage strategy should be: ( ) the futures contract and ( )the spot market. This strategy is also known as ( ).
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)
A forward contract has an underlying asset which, in Cox-RossRubenstein notation, has S=22,u=1.2 and d=0.9. This forward contract matures in one time step and the return over this time step is R=1.02. Assuming the forward price is calculated rationally, what is the value of the forward at node (1,1)? (Give your answer as a positive number.)
Consider the following linear regression model: (R₁-r)= a; + b(RMkt - rf) + e; The b; in the regression: O measures the deviation from the best fitting line and is zero on aver- measures the sensitivity of the security to market risk. measures the diversifiable risk in returns.
Derive the Karush-Kuhn-Tucker conditions for this Bid-price policy program (also shown in the image for clarity),min J˜µT(x)s.t. µ ≥ 0with variable µ ∈ ℝ^m. In particular, show that an optimal solution µ* to this program must satisfy the constraints in the image below:
* Consider the following portfolio II: long one call with exercise price E₁, long one put with exercise price E2, short one call with exercise price E, and short one put with exercise price E1+E2 E. Consider the case E₁ < E < E2 where E < 2 ⚫ (a) Write down the pay-off function A(S) for the portfolio II. • • (b) What is the value of the pay-off function when S < E₁? (c) What is the value of the pay-off function when E < S < E₂?
If I have that the standard estimator of the volatility parameter is 0.2491, how can I estimate the drift parameter, mu, for some price paths assuming the price paths can be modeled by a risk-neutral geometric Brownian motion and the interest rate is 0? (I need to consider how the drift parameter is related to the volatility in a risk-neutral setting.)
You are given the following two equations:SML: E(Ri) = Rf + (E(RM) − Rf )βi (1)CML: E(Rp) = Rf +E(RM) − RfσMσp (2)You also have the following information: E(RM) = .15, Rf = .06, σM = .15. Answerthe following questions, assuming that the capital asset pricing model is correct:(a) Which equation would you use to determine the expected return on an individualsecurity with a standard deviation of returns σ = .5 and a β = 2? Given theparameters above, what is the expected return for that security?(b) Which equation would you use to determine the expected return on a portfolioknowing that it is an efficient portfolio (consisting of the market portfolio Mcombined with the risk-free rate)? If you were told that the standard deviationof returns on that efficient portfolio is equal to σM and you were given the aboveparameters, what is the expected return on that portfolio?(c) Can you determine the β of the portfolio in (b)?(d) Given your answers above, expand on what type of risky assets…

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