Portfolio Effect on Risk and Return

ERC INSTITUTE Name : Kimberly Limanto Student ID : 1004434 Course Name: SADBA Title Of The Course : Investment and Fund Management Date of Submission : 15 November 2012 Instructor Name : Mr. Johnson Yang TABLE OF CONTENTThe Financial advisor’s investment case: Inferior investment alternatives Although investing requires the individual to bear risk, the risk can be controlled through the construction of diversified portfolios and by excluding any portfolio that offers an inferior return for a given amount of risk. While this concept seems obvious, one of your clients, Laura Spegele, is considering purchasing a stock she will bear. To convince her that the acquisition is not desirable, you want to demonstrate the trade-off between risk and return.While it is impractical to show the trade-off for all possible combinations, you believe that illustrating several combinations of risk and return and applying the same analysis to the specific investment should be persuasive in discour aging the purchase. Currently, US Treasury bills offer 7%. Three possible stocks and their beta are as follows:- SecuritiesExpected ReturnBeta Stock A9%0. 6 Stock B 11%1. 3 Stock C 14%1. 5 Required I. What will be the expected return and beta for each of the following ? portfolios? a.Portfolio 1 through 4 : all of the funds are invested solely in one asset ? (the corresponding three stocks or the Treasury bill) b. Portfolio 5: one quarter of the funds are invested in each alternative c. Portfolio 6: one half of the funds are invested in stock A and the other half in stock C. d. Portfolio 7: One third of the funds are invested in each stock. II. Are any of the portfolios inefficient? III. Is there any combination of the Treasury bill and Stock C that is superior to portfolio 6 (i. e. half the funds in Stock A and half in Stock C)? IV.Since your client’s suggested stock has an anticipated return of 12% and a beta of 1. 4 does that information argue for or against the purchase o f the ? stock? V. Why is it important to consider purchasing an asset as part of a portfolio ? and not as an independent act? Answers: I. Expected Return and Beta of each portfolio. a. All of the funds are invested solely in one asset. * Portfolio 1 : 100% in investment T-Bill E(R) = 7% E (beta) = 0. 0 * Portfolio 2 : 100% investment in Stock A E(R) = 9% E (beta) = 0. 6 * Portfolio 3 : 100% investment in Stock B E(R) = 11%E (beta) = 1. 3 * Portfolio 4 : 100% investment in Stock C E(R) = 14% E (beta) = 1. 5 b. Portfolio 5 : 25% investment in each security E(R) = (0. 25*0. 07) + (0. 25*0. 09) + (0. 25*0. 11) + (0. 25*0. 14) = 0. 0175 + 0. 0225 + 0. 0275 + 0. 035 = 0. 1025 = 10. 25% E (beta) = (0. 25*0. 0) + (0. 25*0. 6) + (0. 25*1. 3) + (0. 25*1. 5) = 0 + 0. 15 + 0. 325 + 0. 375 = 0. 85 c. Portfolio 6 : 50% investment in Stock A, 50% investment in Stock B E(R) = (0. 5*0. 09) + (0. 5*0. 14) = 0. 045 + 0. 07 = 0. 115 = 11. 5% E (beta) = (0. 5*0. 6) + (0. 5*1. 5) = 0. 3 + 0. 75 = 1. 05 . Portfolio 7 : one-third investment in each security E(R) = (0. 33*0. 09) + (033*0. 11) + (0. 33*0. 14) = 0. 03 + 0. 036 + 0. 046 = 0. 1122 = 11. 22% E (beta) = (0. 33*0. 6) + (0. 33*1. 3) + (0. 33*1. 5) = 1. 12 Each Portfolio returns and beta 100% in T-bill| 7%| 0. 0| 100% in stock A| 9%| 0. 6| 100% in stock B| 11%| 1. 3| 100% in stock C| 14%| 1. 5| 25% in each| 10. 25%| 0. 85| 50% in A and C| 11. 5%| 1. 05| 1/3 in each stock| 11. 22%| 1. 12| II. Inefficient portfolio is a portfolio where the expected risk is higher than the expected return in their comparison.In this case, portfolio 3 where the investment is 100% invested in stock B is the most inefficient because its expected return is 11% and its beta is 1. 3 while in portfolio 6 the expected return is slightly higher, which is 11. 5%, but the beta is lower, which is 1. 05. Therefore from this, we can conclude that portfolio 3, or when she invest 100% in stock B, is the most inefficient portfolio. III. The portfolio which combin es 50% investment in stock A and 50% investment in stock C generates an expected return of 11. 5% and beta of 1. 05.The combination on investment between T-Bill and stock C that will be superior to the previous portfolio is: E (beta) = 1. 05 = [X% * 0. 0] + [Y% * 1. 5] = 1. 05 = 0 + [Y% * 1. 5] = 1. 05 Y% = 1. 5/1. 05 Y% = 0. 7 = 70% X% = 100% – 70% = 30% E(R) = (0. 3*0. 07) + (0. 7*0. 14) = 0. 021 + 0. 098 = 0. 119 = 11. 9% The portfolio which combines 30% or less investment in T-Bill and 70% or more investment in stock C will e superior to portfolio 6 which combine 50% investment in stock A and 50% investment in stock C. IV. The portfolio that the client suggested which has 12% expected return and 1. beta is inferior compared to any other portfolio. To prove that this portfolio is inferior to another portfolio, we can try to calculate by : Beta of 1. 4 is a combine of 93% investment in stock C and 7% investment in T-bill. Calculation: (0. 07*0. 0) + (0. 93*1. 5) = 1. 4 This portfolio will generate an expected return of: (0. 07*0. 07) + (0. 93*0. 14) = 0. 0049 + 0. 1302 = 0. 1351 = 13. 51% This calculation prove that a beta of 1. 4 suppose to give 13. 51% expected return. Therefore, the client's suggested portfolio is inferior compared to any other portfolio.V. Purchasing an asset as a part of a portfolio is a much clever way than just purchasing one single asset. It is because by purchasing several assets, the investor can either have higher return with the same risk, or same return but with a lower risk. Therefore, purchasing more than one asset will give benefits to the investor. Also, by purchasing in more than one asset, the investor can be more â€Å"safe†. What safe means is when the other asset collapse, or its value decline, there are still other assets that can cover the losses.