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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Suppose the demand functions for two products are q1 = f(p1, p2) and q2 = g(p1, p2) wherep1, p2, q1, and q2 are the prices (in dollars) and quantities for products 1 and 2. Consider thefour partial derivatives∂q1/∂p1,∂q1/∂p2,∂q2/∂p1and ∂q2/∂p2,State the sign of each of these partial derivatives if:(a) the products are complementary goods(b) the products are substitute goods.
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
Question 1. Suppose t ≤ T1 ≤ T2 ≤ T3, where t is the current time, and ∆ > 0. Recall that Z(T1, T2) is the price at time T1 of a ZCB with maturity T2 and F(T1, T2, T3) is the forward price at time T1 for a forward contract with maturity T2 on a ZCB with maturity T3. a) For each of the pairs of A and B in the table, choose the most appropriate relationship out of ≥, ≤, = , ?, where ? means the relationship is indeterminate. Give brief reasoning. A ≥, ≤, = , ? B (i) Z(t, T1) 1 (ii) Z(T1, T1) 1 (iii) Z(t, T2) Z(t, T3) (iv) Z(T1, T2) Z(T1, T3) (v) Z(T1, T3) Z(T2, T3) (vi) Z(T1, T1 + ∆) Z(T2, T2 + ∆) (vii) F(t, T1, T2) F(t, T1, T3) (viii) F(t, T1, T3) F(t, T2, T3) (ix) limT→∞ Z(t, T) 0 Hint: Remember that at current time t, F(t, ·, ·) is known but Z(T, ·) is a random variable. b) What can you say about interest rates between T1 and T2 if i) Z(t, T1) = Z(t, T2)? ii) Z(t, T1) > 0 and Z(t, T2) = 0?
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:
The NPV profile: O A. shows the payback period the point at which NPV is positive. O B. shows the internal rate of return the point at which NPV is zero. OC. shows the NPV over a range of discount rates. O D. B and C are correct.
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.)

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