An Investor has access to a set of N securities (where N is large). Each of them has an annual return variance of 0.25 and the correlation between every pair of the N assets is 0.5. The investor wants to build an equally weighted portfolio of a subset of these N assets that has a return variance of 0.15 or smaller. What is the smallest number of assets that his portfolio should contain?
Q: You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the…
A: Particulars Asset A…
Q: Suppose the risk-free rate is 5.1 percent and the market portfolio has an expected return of 11.8…
A: Standard deviation of market portfolio and portfolio Z is calculated. Then covariance and beta of…
Q: beta and expected return
A: : Beta refers to the measurement of stock movement in relation to the overall market. A beta greater…
Q: An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of…
A: The question is based on the concept of Minimum variance portfolio. A minimum variance portfolio is…
Q: a. What is the expected return of each asset? b. What is the variance and the standard deviation c.…
A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…
Q: Harry and Frank have been comparing their investment portfolios for several years. Harry claims that…
A: The variance and the standard deviation are the important indicators and tools for the variability…
Q: Consider a T-bill with a rate of return of 5% and the following risky securities: Security A: E(r)…
A: Given information : Stock A : Expected return = 15% , variance = 0.04 Stock B : Expected return =…
Q: You are evaluating various investment opportunities currently available and you have calculated…
A: Since you have asked a question with multiple subparts, we will solve the first three sub-parts for…
Q: What is the standard deviation of the following portfolio if the coefficient of the correlation…
A: Given Information:Variance A is 10% Weight of portfolio A is 0.30 Variance B is 20% Weight of…
Q: The market index return is 1.3% and its standard deviation is 17%. The risk free rate is 3%.…
A: Sharp Ratio = ( Return of Portfolio - Risk free rate)/ Portfolio Standard deviation…
Q: Consider a T-bill with a rate of return of 5 percent and the following risky securities. From which…
A: Risk Seekers: Risk seekers willing to pay for taking risk for getting more profits.…
Q: A portfolio has an average return of 14.4 percent, a standard deviation of 18.5 percent, and a beta…
A: The Sharpe ratio: The Sharpe ratio is one of the most commonly used measures to assess the…
Q: If the market portfolio has a required return of 0.12 and a standard deviation of 0.40, and the…
A: Security market line (SML): The security market line (SML) is the graphic depiction of the Capital…
Q: You have invested in a portfolio of two stocks. Stock A is expected to produce a 7% return next…
A: Sine you have posted question with multiple sub-parts, we will solve first three sub-parts for you.…
Q: An analyst has modeled the stock of Crisp Trucking using a two-factor APTmodel. The risk-free rate…
A: Factor 1: Risk premium r1p =Expected return of factor 1 - Risk free rate Risk premium r1p = (12% -…
Q: Consider a portfolio exhibiting an expected return of 6% in an economy where the riskless interest…
A: Given, Expected return = 6% Risk less interest rate = 1% Expected return on market portfolio = 10%…
Q: A portfolio manager creates the following portfolio: Security Security Weight Expected Standard…
A: Standard deviation of portfolio is dependent on the weight of each security in the in the portfolio…
Q: You are considering investing $1,000 in a T-bill that pays 0.06 and a risky portfolio, P,…
A: To solve the question we first need to determine the expected return of the risky portfolio then…
Q: Adam wants to determine the required return on a stock portfolio with a beta coefficient of 0.5.…
A: Required rate of return = risk free rate + beta * (market return - risk free rate)
Q: vests W0=$10000W0=$10000 on a stock. The monthly return RR follows a normal distribution with mean…
A: Value at risk is related to amount of investment that is at the risk.
Q: If the market portfolio has a required return of 0.12 and a standard deviation of 0.40, and the…
A: SML is an abbreviation used for security market line. It represent the market equilibrium and its…
Q: If standard deviation of security A is 27% and security B is 18%, the correlation coefficient…
A: Standard deviation of security A (sdA) = 27% Standard deviation of security B (sdB) = 18%…
Q: The probability distributions of expected returns for stocks XMX and BMX are as follows: Probability…
A: Let Pn = Probability of each state Xn = Return of XMX in each state Bn = Return of BMX in each state…
Q: Assume that the average variance of return for an individual security is 50 and that the average…
A: Average variance of individual security is 50 Average covariance is 10
Q: Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard…
A: “Hi There, thanks for posting the question. But as per Q&A guidelines, we must answer the first…
Q: Consider a treasury bill with a rate of return of 5% and the following risky securities: Security A:…
A: A ratio that provides information regarding the return of a security to the investor in comparison…
Q: Suppose you create a portfolio with two securities: Security Security Weight (%) Security…
A: Portfolio means a bunch of assets or investments. To maximize the profits, investors invest their…
Q: You have a portfolio of investment which consists of Stock A with a return of A% and Stock B with a…
A: According to the Law of Sum of variances, variances of two stock can be added but that of standard…
Q: Suppose you invest 60% of your portfolio in exxon mobil and 40% in coca cola. The expected dollar…
A: Portfolio is the result of several assets put together in order to have balanced return. In…
Q: What is the Sharpe ratio (S) of your risky portfolio and your client’s overall portfolio? , assume…
A: Sharpe Ratio = (Return on portfolio - Risk free Rate ) / (Standard Deviation of portfolio)
Q: An investor invests 60% of his wealth in a risky asset which has an expected return of 15% and a…
A: Solution- Expected Return on…
Q: You are considering investing $1,000 in a T-bill that pays a rate of return of 0.06 and a risky…
A: Rate of return means the interest rate which is earned by an investor or which a potential investor…
Q: You are constructing a simple portfolio using two stocks A and B. Both have the same expected return…
A:
Q: What is the standard deviation of this portfolio?
A: Information Provided: Correlation = -0.10 Standard Deviation of Stock A = 3.0 Standard Deviation of…
Q: Stock A has a variance of 0.25 and stock B has a variance of 0.16. The correlation coefficient…
A: A statistical measure that represents the spread among the return of the investment is term as the…
Q: Consider two types of assets: market portfolio (M) and stock A. The expected return is 8% and…
A: Given: Market rate = 8% Risk free rate = 2% Standard deviation of market portfolio = 15% Standard…
Q: Compute the weights in a portfolio
A: Portfolio return is the return expected from the portfolio. The expected return is the weighted…
Q: An investor puts 60% of her assets in a risky portfolio with an expected return of 15% and variance…
A: The expected return is the amount of profit or loss an investor can anticipate receiving on an…
Q: Consider a risky portfolio, A, with an expected rate of return of 0.16 and a standard deviation of…
A: Given: Expected return is 0.16 Standard deviation is 0.25
Q: An investor can design a risky portfolie based on two stocks A and B. Stock A has an expected retun…
A: Portfolio variance is a measurement of risk, that tells about real returns of stocks in a portfolio…
Q: Estimate the mean and variance of this portfolio, as well as its standard deviation.
A: Mean return of the portfolio = Weight of Mercedes * Mean return of Mercedes + Weight of BMW * Mean…
Q: Your portfolio has a beta of 1.73, a standard deviation of 29 percent, and an expected return of…
A: Treynor ratio = Portfolio Return - Risk Free ReturnPortfolio Beta
Q: Assume that the Capital Asset Pricing Model holds. The market portfolio has an expected return of…
A: IF Capital Asset Pricing Model (CAPM) hold good, Expected Return on Stock = Risk-Free rate + (…
Q: Suppose the risk-free rate is 4.2 percent and the market portfolio has an expected return of 10.9…
A: Capital asset pricing model is the most efficient model to calculate the expected rate of return of…
Step by step
Solved in 4 steps
- A person is interested in constructing a portfolio. Two stocks are being considered. Letx = percent return for an investment in stock 1, and y = percent return for an investment instock 2. The expected return and variance for stock 1 are e(x) = 8.45% and Var(x) = 25.The expected return and variance for stock 2 are e(y) = 3.20% and Var(y) = 1. Thecovariance between the returns is sxy = −3.a. what is the standard deviation for an investment in stock 1 and for an investment instock 2? Using the standard deviation as a measure of risk, which of these stocks isthe riskier investment?An investor wants to determine the safest way to structure a portfolio from several investments, whose annual returns under different scenarios are as follows: Returns Scenario A B. D Probability 1. 0.11 -0.09 0.10 0.07 0.10 -0.11 0.12 0.14 0.06 0.10 3 0.09 0.15 0.11 0.08 0.10 4 0.25 0.18 0.33 0.07 0.30 0.18 0.16 0.1 0.06 0.40 9. Suppose the investor ignores the scenarios have different probabilities. If he has determined his risk aversion value is 0.75, what percentage of his portfolio should be invested in A? percent 2.9. Suppose you plan to form your overall investment portfolio in two steps: STEP 1: Choose a portfolio of stocks with a zero position in the risk-free asset. STEP 2: Allocate your money between the portfolio from Step 1 and the risk-free asset. Suppose you can borrow and lend as much as you want at the risk-free rate in Step 2. Let Erp be the expected return of the Step 1 portfolio. Let Var(rp) be the variance of the return of the Step 1 portfolio. Let rf be the risk-free rate. How will you form the Step 1 Portfolio? Set the Step 1 portfolio to maximize Erp SettheStep1portfoliotominimizeVar(rp) Set the Step 1 portfolio to maximize Erp - Var(rp) Set the Step 1 portfolio to maximize the ratio Erp/Var(rp) Set the Step 1 portfolio to maximize the ratio (Erp- rf)/Var(rp) None of the above.
- A particular firm’s portfolio is composed of two assets, which we will call" A" and "B." Let X denote the annual rate of return from asset A, and let Y denote the annual rate of return from asset B. Suppose that E(X) = 0.15, E(Y) = 0.20, SD (X) = 0.05, SD (Y) = 0.06, and CORR (X, Y) = 0.30. Use a spreadsheet to perform the following analysis. (a) What is the expected return of investing 50% of the portfolio in asset A and 50% of the portfolio in asset B? What is the variance of this return? (b) Replace CORR (X, Y) = 0.30 by CORR (X, Y) = 0.60, 0, -0.30, and -0.60 and answer the questions in part (a). What is the impact of correlation on the expected returns and its variance? Explain why this is so. (c) Suppose that the fraction of the portfolio that is invested in asset B is f, and so the fraction of the portfolio that is invested in asset A is (1 – f). Let f vary from f = 0.0 to f = 1.0 in increments of 5% (that is, f = 0.0, 0.05, 0.10, 0.15, ...), and compute the mean and the…We consider a market with N risky assets. The following table shows the information of some portfolios constructed by these risky assets. Expected return Portfolio 1 (W₁) Portfolio 2 (W₂) Portfolio 3 (W3) Portfolio 4 (W4) 0.0321 0.0607 0.1263 0.1322 Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 Standard deviation of the return The correlation coefficient of returns of these portfolios are given in the following table: Portfolio 1 Portfolio 2 Portfolio 3 Portfolio 4 0.731672 1 0.731672 1 0.62553 0.002018 -0.02533 0.662908 0.093207 0.088882 0.217899 0.212048 0.002018 0.62553 1 0.915149 You are also given that two of these portfolios are efficient. -0.02533 0.662908 0.915149 1 Question (a) Using the above information, determine the global minimum variance portfolio. Express your answer in terms of W₁, W2, W3 and W₁.The following portfolios are being considered for investment. During the period under consideration, RFR = 0.07.Portfolio Return Beta σiA 0.15 1.0 0.05B 0.20 1.5 0.10C 0.10 0.6 0.03D 0.17 1.1 0.06Market 0.13 1.0 0.04 a. Compute the Sharpe measure for each portfolio and the market portfolio. b. Compute the Treynor measure for each portfolio and the market portfolio. c. Rank the portfolios using each measure, explaining the cause for any differences you find in the rankings.
- f. Assume a Portfolio of two assets A and B whose standard deviations of their returns are 8.6% and 10.8% respectively, while their correlation coefficient of returns is Pas = - 0.61. You are given the right to do portfolio optimization without restrictions. What proportions would you choose and why?Portfolio Suppose rA ~ N (0.05, 0.01), rB ~ N (0.1, 0.04) with pA,B = 0.2 where rA and rB are CCR’s. a) Suppose you construct a portfolio with 50% for A and 50% for B. Find the variance of the portfolio CCR. b) Find the portfolio expected gross return. c) Find the expected portfolio CCR.Consider the following performance data for a portfolio manager: Benchmark Portfolio Index Portfolio Weight Weight Return Return Stocks 0.65 0.7 0.11 0.12 Bonds 0.3 0.25 0.07 0.08 Cash 0.05 0.05 0.03 0.025 a.Calculate the percentage return that can be attributed to the asset allocation decision. b.Calculate the percentage return that can be attributed to the security selection decision.
- (Portfolio VaR) Suppose there are two investments A and B. Either investment A or B has a 4.5% chance of a loss of $15 million, a 2% chance of a loss of $2 million, and a 93.5% change of a profit of $2 million. The outcomes of these two investments are independent of each other.Suppose that there exist two securities (A and B) with annual expected returns equal to ra = 3% and rg = 5% and standard deviations equal to o4 = 7% and oB = 10% respectively. The correlation coefficient between the returns of these securities is p = -0.5. What is the expected return and the standard deviation of an equally weighted portfolio consisting of the securities A and B? Describe every step of your calculations in detail. What is the expected return and the standard deviation of a portfolio consisting of the securities A and B, if the relevant weights are chosen to minimize the risk of the portfolio? Present the minimisation problem and describe every step of your calculations in detail. How could an investor maximize diversification benefits? Critically discuss and explain in detail.c. Suppose the risk-free rate is 4.2 percent and the market portfolio has an expected return of 10.9 percent. The market portfolio has a variance of .0382. Portfolio Z has a correlation coefficient with the market of .28 and a variance of .3285. According to the capital asset pricing model, what is the expected return on Portfolio Z?