Portfolio Effect on Risk and Return

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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 CONTENT

Title Page……………………………………………………1 Content…………………………………………………...…2 Problem…………………………………………………...3-4 Answers…………………………………………………..5-7

Problem:

The 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 discouraging 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 of 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
d. 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....
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