Two stocks are available. The corresponding expectedrates of return are r¯1 and r¯2; the corresponding variances and covariances areσ12, σ22, and σ12. What percentages of total investment should be invested ineach of the two stocks to minimize the total variance of the rate of return ofthe resulting portfolio? What is the mean rate of return of this portfolio?

Two stocks are available. The corresponding expectedrates of return are r¯1 and r¯2; the corresponding variances and covariances areσ12, σ22, and σ12. What percentages of total investment should be invested ineach of the two stocks to minimize the total variance of the rate of return ofthe resulting portfolio? What is the mean rate of return of this portfolio?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Q5 - Summary statistics for returns on two stocks X and Y are listed below. Mean VarianceStock X 2.85% 0.005000Stock Y 5.91% 0.006000 The covariance of returns on stocks X and Y is 0.002800. Consider a portfolio of 30% stock X and 70% stock Y. What is the variance of portfolio returns?Please round your answer to six decimal places. Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.
Exercise 9.2 (start-up and venture capitalist exit strategy). There are three periods, t = 0, 1, 2. The rate of interest in the economy is equal to 0, and ev- eryone is risk neutral. A start-up entrepreneur with initial cash A and protected by limited liability wants to invest in a ﬁxed-size project. The cost of invest- ment, incurred at date 0, is I > A. The project yields, at date 2, R > 0 with probability p and 0 with prob- ability 1 − p. The probability of success is p = pH if the entrepreneur works and p = pL = pH − ∆p (∆p > 0) if the entrepreneur shirks. The entrepre- neur’s eﬀort decision is made at date 0. Left unmon- itored, the entrepreneur obtains private beneﬁt B if she shirks and 0 otherwise. If monitored (at date 0), the private beneﬁt from shirking is reduced to b B. There is a competitive industry of venture capi- talists (monitors). A venture capitalist (general part- ner) has no fund to…
You live in an area that has a possibility of incurring a massive earthquake, so you are considering buyingearthquake insurance on your home at an annual cost of $180. The probability of an earthquake damagingyour home during one year is 0.001. If this happens, you estimate that the cost of the damage (fully coveredby earthquake insurance) will be $160,000. Your total assets (including your home) are worth $250,000.
Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w.
Hugo has a concave ubility function of U(W)=√W. His only asset is shares in an Internet start-up company. Tomorrow he will learn the stock's value. He belleves that it is worth $225 with probability 80% and $256 with probability 20%. What is his expected utsty? What risk premium would he pay to avoid bearing this risk? The stock's expected utility (EU) is EU = (Enter a numeric response using a real number rounded to two decimal places.) han fro
a) (3) Consider two investments X and Y, where X pays $0 and $10 with equal probability and Y pays 0 with probability 0.75 and $20 with probability 0.25. What investment would an investor choose if her utility function is u(x) = x? u(x) = x u(x) = 1-e 10 () (i) (ii)
An investor has utility function U = 10 + 5P – 0.02P2. What is the expected utility of the following investment option? Probability Payoff (P) 0.4 10 0.3 20 0.2 30 0.1 40
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky funds are as follows: Expected Return Standard Deviation Stock fund (S) 20% 30% Bond fund (B) 12 15 The correlation between the fund returns is 0.10. a-1. What are the investment proportions in the minimum - variance portfolio of the two risky funds. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Portfolio invested in the stock Portfolio invested in the bond a-2. What are the expected value and standard deviation of the minimum variance portfolio rate of return? (Do not round intermediate calculations. Enter your answers as percentage rounded to 2 decimals.) Expected return % Standard deviation %
Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.1) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?2) Find A as a function of w.
You plan to invest $1,000 in a corporate bond fund or in a common stock fund. The following table represents the annual return (per $1,000) of each of these investments under various economic conditions and the probability that each of those economic conditions will occur. Compute the expected return for the corporate bond and for the common stock fund. Show your calculations on excel for expected returns. Compute the standard deviation for the corporate bond fund and for the common stock fund. Would you invest in the corporate bond fund or the common stock fund? Explain. If choose to invest in the common stock fund and in (c), what do you think about the possibility of losing $999 of every $1,000 invested if there is depression. Explain.
You are at a casino and there are three slot machines you can use to bet on. You must have a return of .5% of higher on what you are betting. Below is the expected returns for each slot machine under various scenarios. What combination of machines do you play to maximize your average return? Decision Variables Data Slot 1 100.0% Monday Tuesday Wednesda Average Slot 2 0.0% Slot #1 8% 4% 5% 5.667% Slot 3 0.0% Slot #2 2% -3% 3% 0.667% Slot #3 6% -2% 4% 2.667% Objective 5.7% Constraints 0.08 >= 0.5% 0.04 >= 0.5% 0.05 >= 0.5% 100.0% .: 100%
You are considering investing in one of two projects, which have the following returns and probabilities of occurrence: (a) Compute the mean return for each project.(b) Compute the variance of return for each project.(c) Which project would you prefer, and why?