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Investment Analysis & Portfolio Management The table contains the annual rates of return for 2 specific assets and also the market as a whole (like the S&P 500 Index) Year Asset A Asset B Market 1 -11% 18% 15% 2 9% 12% -6% 3 20% -5% 12% 4 -7% -13% -11% 5 17% 24% 16% 1) Expected Returns Asset A Asset B Market 2) Std. Dev. of Returns Asset A Asset B Market 3) Calculate the Coefficient of Variation (CV) for each of the three Asset A Asset B Market 4) Asset A & B Asset A & Market Asset B & Market 5) Calculate the expected returns from the following portfolios: Use the following formula to calculate the portfolio standard deviation Rate of Return Calculate the expected returns for Asset A, Asset B and the Market (hint: use Average function in Excel) Calculate the standard deviation of returns, ϭ, for each asset (hint:use STDEVP function) Coefficient of Variation Calculate the correlation of returns , ρ, between Asset A and Asset B; Asset A and the Market as a whole; and Asset B and the Market as a whole (hint: use CORREL function) Correlation of Returns ϭP =√ ((wAσA) 2 +(wBϭB) 2 +(2 wA wB ϭA ϭB ρ(A,B)) =(((wA*ϭA)^2) +((wB *ϭB )^2)+(2 *wA* wB *ϭA *ϭB *ρ(A,B))^0.5 % Asset A % Asset B 0% 100% 20% 80% 40% 60% 60% 40% 80% 20% 100% 0% 6) 7) Beta Asset A & Market Asset B & Market Where wA and wB are the % of assets in Asset A and B respectively ϭA and ϭB are the respective standard deviations of return and ρ(A,B)).is the correlation of returns between asset A and B Using Portfolio Expected Returns on the Y axis and Portfolio Standard Deviation in the X axis, draw the efficient frontier for possible portfolio combinations of Asset A and B. (include 100% A and 100% B as two possibilities). (Hint: Use the Excel Chart Wizard and select the XY(scatter) plot option) Calculate Beta for Asset A relative to the Market and Asset B relative to the Market (Hint: use SLOPE function or βi = (Ϭi x ρi,M) / ϬM ) Portfolio Mix Portfolio Expected Return Portfolio Std Dev. 0% 20% 40% 60% 80% 100% 120% 0% 20% 40% 60% 80% 100% 120% Expected Portfolio Return Portfolio Risk (Std. Dev) Portfolio Risk vs. Return 8) 2% 12% Required Return Asset A Asset B 9) Investment Beta Proportion of Portfolio Beta x Proportion Mutual Fund A 0.9 0.0% Mutual Fund B 1.4 0.0% Total $120,000 Weighted Average = 10) 3% 6% Beta Required Return 0.8 1.2 11) Stock Investment Beta A $400,000 1.5 B 600,000 -0.5 C 1,000,000 1.25 D 2,000,000 0.75 Total Portfolio $4,000,000 Assume that for next year the Risk Free Rate is expected to be 3% and that the overall market will realize a return of 12%. Using the CAPM / SML methodology, calculate the required returns for Asset A and Asset B. Risk Free Rate = Expected Market Return = An individual has portfolio totalling $120,000. 60% in invested in a mutual fund with a beta of 0.9 and 40% invested in another mutual fund with a beta of 1.4. If these are the only two investments in her portfolio, what is the Assume that the risk free rate is 3% and that the market risk premium is 6%. What is the required return on a stock with a beta of 1.0 and on a stock with a beta of 0.8? Risk Free Rate = Market Risk Premium = Suppose you manage the $4 million portfolio that consists of four stocks with the following investments: 6% 14% Stock Investment Beta Required Return Portfolio Share A $400,000 1.5 B 600,000 -0.5 C 1,000,000 1.25 D 2,000,000 0.75 Total Portfolio $4,000,000 Weighted Average = 12) Number of Securitie s Value Beta 20 2,000,000 1.1 1 100,000 0.9 1 100,000 1.4 13) Expected Market Return = If the market’s expected rate of return is 14% and the risk-free rate is 6%, what is the portfolio’s required rate return? Risk Free Rate = You are a consultant to a large manufacturing company tht is considering a project with the followiing net after tax cash flows: New Portfolio Prior Porfolio Security Sold Residual Porfolio New Security Purchased You have a $2 million portfolio consisting of $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.1. You are considering selling $100,000 worth of one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4 what will be the portfolio’s new beta after these transactions? Year Cash flow 0 (net investment) -40 1 through 10 11 N = 10 rRF = 3% rM = 14% β= 1.60 a) What is the Net Present Value (NPV) for the project? b) What is the highest possible Beta estimate for the project before its NPV would become negative? The project's Beta is 1.6. Assuming that the risk free rate (rRF) is 3% and the expected market return (rM) from other available investments is 14%:

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