Recall that the risk-neutral probability of an asset corresponds to the probability for which the expected return on the asset equals the risk-free rate. Consider a special case where the current asset value is So = 100, and the annual risk-free rate is r = 0%. The asset does not pay dividends. Additionally, consider a simple distribution in which the asset price goes up by $10 with probability p and drops by $10 with probability 1 - p. Based on this information, what is the risk-neutral probability?

Recall that the risk-neutral probability of an asset corresponds to the probability for which the expected return on the asset equals the risk-free rate. Consider a special case where the current asset value is So = 100, and the annual risk-free rate is r = 0%. The asset does not pay dividends. Additionally, consider a simple distribution in which the asset price goes up by $10 with probability p and drops by $10 with probability 1 - p. Based on this information, what is the risk-neutral probability?

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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Suppose that there is an upward shift in the expected rate of return on the risky asset, from 15% to 17%. If all other parameters remain unchanged, what will be the slope of the CAL for y≤ 1 and y> 1?
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
Asset X has an expected return of 10% and volatility of 10% . If its Sharpe Ratio is 0.60, what is the risk-free rate?
Suppose the risk-free rate is 5%. The expected return and standard deviation of a risky asset are 10% and 20%, respectively. a. What is the slope of the capital allocation line (CAL) constructed using the risk-free asset and the risky asset? A. 0.30 B. 0.15 C. 0.25 D. 0.20 b. If an investor has a risk aversion coefficient of A=2, what is the optimal fraction of the money that she invests in the risky asset? A. 62.5% B. 42.5% C. 30% D. 20% c. If an investor invest 25% of her money in the risky asset, which is the investor’s risk aversion coefficient? a. 5 b. 1 c. 3 d. 4
Assume that the risk-free rate, RF, is currently 9% and that the market return, rm, is currently 16%. a. Calculate the market risk premium. b. Given the previous data, calculate the required return on asset A having a beta of 0.4 and asset B having a beta of 1.8.
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)
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.
We 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?
Consider an asset with a beta of 1.2, a risk-free rate of 4.3%, and a market return of 12%. What is the reward-to-risk ratio in equilibrium? What is the expected return on the asset?
The CAPM states that the expected (required) return on an asset is : E(Ri)=Rf+βi[E(RM)−Rf] where the term in square brackets is the risk-premium earned by the market portfolio. Therefore, the beta of the market portfolio (βM) must be equal to __________ . A) zero B) 0.5 C) 1.0 D) an unknown estimate
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? There is an arbitrage opportunity because RS(0) > S(1, 1). There is an arbitrage opportunity because > 1. There is no arbitrage opportunity because 0 < < 1. There is an arbitrage opportunity because R < d.
4

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