Consider 1-factor model and assume that the price of a certain fixed income security P(y) for y=9% 9.05% and 8.95% is given by P(0.09)=$5,000; P(0.0905)=$4,980; P(0.0895)=$5,030. Find the estimate for DVO1, Duration, and Convexity of this security. Keep at least 4 decimal digits while performing your calculations.

Consider 1-factor model and assume that the price of a certain fixed income security P(y) for y=9% 9.05% and 8.95% is given by P(0.09)=$5,000; P(0.0905)=$4,980; P(0.0895)=$5,030. Find the estimate for DVO1, Duration, and Convexity of this security. Keep at least 4 decimal digits while performing your calculations.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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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
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.
Assume that security returns are generated by the single-index model,Ri = αi + βiRM + eiwhere Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 0.7 7 % 20 % B 0.9 9 6 C 1.1 11 15 a. If σM = 16%, 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.)
Consider a two-factor Arbitrage Pricing Theory (APT) model, T; = a; + b1,ifı + b2.i f2 + €i, with the following information Asset i Asset 1 0.07 0.50 0.25 Asset 2 0.15 1.10 0.75 Asset 3 0.20 b1,3 Hi b1i b2i 1.0 and the risk-free rate rp is 0.025. (a) Find the value of b13 to preclude arbitrage opportunity. (b) is an Asset 4 with 4 = 0.13, b14 = 0.8, and b2.4 = 0.4. Explain how you would exploit an arbitrage opportunity if there
Suppose the nominal rate of return is 0.085 and the risk-free rate is 0.010. What is the risk premium? Instruction: Round to two decimal places. E.g., if your answer is 0.0106465 or 1.06465%, you should type ONLY the number .01, neither 0.0106465, 0.0106, nor 1.065. Otherwise, Blackboard will treat it as a wrong answer.
Assume that there are two factors that price assets. Risk free rate is 4%. Factor 1 has anexpected return of 8% and factor 2 has an expected return of 10%. Calculate the expectedreturn for each asset with the following sensitivities using the Arbitrage Pricing Theory (APT). (a) β1 = 1.2, β2 = 0.9; (b) β1 = 1.5, β2 = −0.60;
Suppose the CAPM is true. Consider two assets, X and Y, and the market M. Suppose cov(X,M) = .3, cov(Y,M) = .5. %3D (a) Is the expected return higher on X or Y? (b) Suppose var(M) = 1.5, what are the betas of X and Y? (c) Suppose the expected market return is 20% and the risk free rate is 5%, what is the expected returns of X and Y?. (d) Given your analysis in (a)-(c), what type of investor would prefer asset X to asset Y?
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.)
Assume CAPM holds. Consider a portfolio that consist of a risk-free asset and two risky assets A and B such that they are in equal supply in the market. This implies that the market portfolio M = 0.5A +0.5B. Given that µM = 11%, σA = 20%,σB = 40%,ρAB = 0.75 and the risk-free rate is 2%. Compute: a) The beta factor for each security. b) The values for µA and µB and verify these quantities via the SML.
We consider a one-step binomial tree in which the parameters are u = 1.2, d = 0.8, r = 0.12, T = 0.25, fu = 3, fa = 0. Evaluate the followings: (1) Calculate the probability p of an up movement in a risk-neutral world. (2) Compute the current price f.
The beta of the risk-free asset is: 0.5 1.0 -1.0 2.0
The risk-free rate and the expected market rate of return and 0.056 and 0.125. Using the CAPM model, the expected rate of return of a security, that you are interested in, has a beta of 1.25 would be equal to Calculate the expected rate of return

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