An asset has values S(0) = 10 and S(1, 1) = 9 with up factor u = 1.1 and the return over one time-step is R = 1.04. Which of the following is true?
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- If someone computes for the MARR using AW Method and AW becomes positive at a certain fixed interest i ≥ 0and same n ≠ 0 periods, then A. PW is always larger than FW and AWB. PW is always larger than FWC. AW is always smaller than PW and FWD. AW is always larger than PWA 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.)In the asset price model, verify that E[S(t)] = Soeht E[S(t)²] = S²e(²µ+o²)t Var[S(t)] = Se²ut (eo²t - 1)
- 3. A market consists of two risky assets and no risk-free asset. Let R₁ and R2 denote the return on each of the risky assets. Using market data the following have been estimated: E[R₁] = 0.10, E[R₂] = 0.15, o2 = Var (R₁) = 0.1², o2 = Var(R₂) = 0.2² and p1,2 = -1/ where p1,2 denotes the correlation coefficient for R₁ and R₂. (i) Given that an investor is targeting a total expected return of = 0.125 on a portfolio, what is the minimum variance that can be achieved? (ii) Determine the global minimum variance portfolio and the expected return and variance of return on this portfolio.3. A market consists of two risky assets and no risk-free asset. Let R₁ and R₂ denote the return on each of the risky assets. Using market data the following have been estimated: E[R₁] = 0.10, E[R₂] = 0.15, o² = Var(R₁) = 0.1², o² = Var(R₂) = 0.2² and p1,2 = -1/2 where P1,2 denotes the correlation coefficient for R₁ and R₂. (i) Given that an investor is targeting a total expected return of portfolio, what is the minimum variance that can be achieved? = 0.125 on a (ii) Determine the global minimum variance portfolio and the expected return and variance of return on this portfolio. (iii) Using your answers to parts (i) and (ii) make a rough sketch of the minimum- variance set in - o2 space. You should indicate the efficient frontier and the global minimum variance portfolio. (iv) Without further calculation, explain how you would expect the variance of return calculated in (ii) to change if the two risky assets were independent.Please calculate CAPM of Asset J with the following information: where, kj = required return on asset j, Rf = risk-free rate of return, (6%) bj = beta coefficient for asset j, (1.75) %3D Rm = market return. (10%) The equation for CAPM is kj = Rf + [bj x (Rm - Rf)] kj = Solve for required return on asset j (kj is CAPM) Please be detailed when answering and show all work, thank you.
- 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.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 randomWe believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0 A B β 1.2 0.8 E(r) 0.1 0.08 (1) What is the rate of return of the risk-free asset? (2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market? (3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?
- Suppose two asset returns are described by a 1-factor model = 2% + 0.6f + ej r2= 2% + 0.6f+ e2 where the volatility of fis 30% and the volatility of e and ez is 20%. What is the covariance of r and r2? (Nearest 0.0001)Hydro Ottawa has two options for upgrading a natural gas power station to meet new government standards. Option 1: Hydro Ottawa will make the upgrades themselves. This is expected to cost $12,700 at the end of each month for 12 years. At the end of the operation (in 12 years) Hydro Ottawa expects to sell all equipment needed for the upgrade for $122,000. Option 2: Pay experienced contractors. This will cost $28,000 up front and $13,900 monthly (at the end of every month) for 15 years. Assume all interest is 3.72% compounded monthly. Round the answers to NPV (Option 1), and NPV (Option 2) to the nearest dollar. Round all other answers to two decimal places where applicable. 1) Find the net present value of option 1: P/Y = C/Y = N = I/Y = PV = PMT= FV = Payments (Cost) GA % Sale of equipment (Residual) GA GA LA %The correct formula to calculate the future value (FV) of a present value (PV) when simple interest is used is? Note: N would be number of periods and i would be the interest rate. A. FV = PV X (1+i)^N, where^ represents power B. FV = PV X (1+i)^-N, where^ represents power O C. FV = PV/((1+i) X N) D. FV = PV x (1 + (N x i)) Reset Selection Mark for Review What's This? The correct formula to calculate the future value (FV) of a present value (PV) when simple interest is used is? Note: N would be number of periods and i would be the interest rate. A. FV = PV X (1+i)^N, where^ represents power OB. FV = PV X (1+i)^-N, where^ represents power C. FV = PV /((1+i) x N) D. FV = PV x (1 + (N X i)) Reset Selection Mark for Review What's This?