Consider two perfectly negatively correlated risky securities A and B (the correlation = –1). A has an expected rate of return of 10% and a standard deviation of 15%. B has an expected rate of return of 13% and a standard deviation of 25%.The risk-free portfolio that can be formed with the two securities will earn a _____ rate of return

Consider two perfectly negatively correlated risky securities A and B (the correlation = –1). A has an expected rate of return of 10% and a standard deviation of 15%. B has an expected rate of return of 13% and a standard deviation of 25%.The risk-free portfolio that can be formed with the two securities will earn a _____ rate of return

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Use the following two tables to answer questions a. - e. a. Which of the above securities cannot lie on the efficient frontier? b. Why might you nonetheless include it in your portfolio? c. What is the expected return for a portfolio comprised of 40% security B and 60% security C? d. What is the standard deviation for a portfolio comprised of 40% security B and 60% security C? e. Suppose a risk-free asset with a yield of 3% exists, but only for lending. Would the highly risk-averse investor's optimal portfolio be likely to contain asset C? Why or why not?
There are two investments projects A and B each involving an initial investment of $2,000. The possible payoffs of investments A are $1,000, $2,000 and $3,000 with respective probabilities 0.20, 0.40, and 0.40, while the possible payoffs of investment B are $1,600, $2,000, and $2,750 with respective probabilities 0.25, 0.35, and 0.40. Calculate the expected value and the standard deviation of the payoff for each of the two investments.
Suppose that spot and futures prices of the underlying asset when hedge is initiated are $3.10 and $2.50 respectively, and when hedge is closed out are $2.90 and $2.80 respectively. 1. What is the meaning of above numbers? 2. What is the basis risk when hedge is initiated? 3. What is the basis risk when hedge is closed out? 4. Is it a perfect hedge? 5. What will be the effective price received (paid) for the hedging asset? (S₂ + F₁-F₂
(a) The monthly returns on two securities A and B are both known to be normally distributed, with the following parameters: Security Expected monthly Return, E(Ri) Standard Deviations of monthly Return, SD(Ri)A 3% 4%B 2% 3% Correlation between monthly returns: corr(RA, RB) = rAB = 0.3 An investor intends to create an equally-weighted portfolio by investing equal amounts in securities A and B at the start of each month. (i) What is the probability that the monthly return on security A is negative? (ii) What are the expected monthly return and the standard deviation of the monthly return on the equally-weighted portfolio? (iii) What is the probability that the monthly return on the equally-weighted portfolio is negative? (b) Six prize…
b) You decide to buy 10,000 shares of each company. If the covariance between ABC and XYZ is 0, what is the expected return and standard deviation of your portfolio over the next year? 1
Assume that security returns are generated by the single-index model, Ri = αi + βiRM + ei where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data: Security βi E(Ri) σ(ei) A 1.4 14 % 23 % B 1.6 16 14 C 1.8 18 17 a. If σM = 22%, 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 an economy with two states of nature and one time period. An option pays $3 in state 1 and $0 in state 2, and is being traded for the price of $1. A forward contract pays $3 in state 1 and -$2 in state 2. Using this information, compute the risk-free rate and the risk-neutral probabilities for each state of nature.
Mike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the load
52. Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the secondhaving μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated,with ρ = −0.8.a. If you could only invest in one security, which one would you choose, andwhy?b. Suppose you invest 50% of your money in each of the two. What is yourexpected return and what is your risk?c. If you invest 80% of your money in security 1 and 20% in security 2, whatis your expected return and your risk?d. Denote the expected return and its standard deviation as functions of π byμ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as πvaries from 0 to 1. Plot this curve.e. Repeat b–d if the correlation is ρ = 0.1
Consider two assets (X and Y) with mX = 10%, mY = 10%, σX2=.16, σY2=.25, and Cov(X,Y) = -.125. What is the expected return and variance of the portfolio having 70% invested in X and 30% invested in Y? Compare the risk and return of this portfolio with the risks and returns associated with investing everything in either X or Y. a) What is p(XY)? b) What is the expected return of the portfolio (m.7X+.3Y)? c) What is the standard deviation of the portfolio (s.7X+.3Y)? d) How does the standard deviation of the portfolio (s.7X+.3Y) compare to the standard deviations of assets X and Y? Show all work and formulas used in EXCEL
4.) Consider an M/M/2 system with an arrival rate of 9 per minute and a service rate of 8 per minute. What is the probability a newly arriving customer will have to wait? Take your answer to three decimal places.
Given the following payoff table with the profits ($m), a firm might expect alternative investments (A, B, C) under different levels of interest rate (attached) (a) Which alternative should the firm choose under the maximax criterion? (b) Which option should the firm choose under the maximin criterion? (c) Which option should the firm choose under the LaPlace criterion? (d) Which option should the firm choose with the Hurwicz criterion with α = 0.2? (e) Using a minimax regret approach, what alternative should the firm choose? (f) Economists have assigned probabilities of 0.35, 0.3, and 0.35 to the possible interest levels 1, 2, and 3 respectively. Using expected monetary values, what option should be chosen and what is that optimal expected value? (g) What is the most that the firm should be willing to pay for additional information? Use Expected Regret (h) Use the alternative method to verify EVPI