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A Case on Portfolio Risk and Return - UMGC Fin - Case Study Individual 2

Woman in a seafoam green sweater, sits on the couch while on a laptop.

 

This article was originally submitted as an academic paper to UMGC. It has been posted here for educational purposes only. Don't be a dummy. If you found this with Google, then so will turn it in.

The questions for this UMGC/UMUC assignment come fro Halil D. Kaya's paper, A Case on Portfolio Risk and Return, published in the International Research Journal of Applied Finance, Vol. VII Issue - 10, October, 2016. ISSN 2229-6891.


Case Study-Individual 2

State         Probability         A         B        C        D

Recession        15%            (10%)        (3%)        0        2%

Normal        40%            15%        12%        9%        7%

Expansion        45%            20%        15%        12%        8%

Wa=50%,     Wb=20%, Wc=10%, Wd=30%

  1. What is the expected return on this portfolio under each state of economy (i.e. recession, normal, and expansion)?

Recession= 0.50(-10%) +0.20(-3%) +0.10(0) +0.30(2) s= (0.5%)

Normal=      0.50(15%) + 0.20(12%) +0.10(9%) +0.30(7%) = 12.9%

Expansion= 0.50(20%) + 0.20(15%) +0.10(12%) +0.30(8%) = 16.6%

  1. What is the expected overall portfolio return? 

E(Rp)=0.15(-0.5%)+0.40(12.9%)+0.45(16.6%)

E(Rp)= 12.555%

  1. What is the risk (i.e. standard deviation) of this portfolio?

σp = SQRT [0.15(-0.5-12.555)2 + 0.40(12.9-12.555)2 + 0.45(16.6-12.555)2 

= SQRT [25.565 + 0.04761+ 7.363]

=SQRT [32.98]

= 5.74.

  1. What are the expected returns on individual stocks (E(R)A, E(R)B, E(R)C, E(R)D)?

E(R)A = (0.15)(-10%) + (0.40)(15%) + (0.45)(20%) = 13.5%

E(R)B = (0.15)(-3%) + (0.40)(12%) + (0.45)(15%) = 11.1%

E(R)C = (0.15)(0%) + (0.40)(9%) + (0.45)(12%) = 9%

E(R)D = (0.15)(2%) + (0.40)(7%) + (0.45)(8%) = 6.7%


  1. Which stock has the highest expected return? Which one has the highest expected risk?

 Stock A has the highest expected return at 13.5% compared to other stocks with lower expected return. 

 Stock A has the highest expected risk with standard deviation of 13.37. 

Computation of risks for each stock 

σ2A = SQRT [0.15(-0.10 – 13.5)2 + 0.40(0.15 – 13.5)2 + 0.45(0.20 – 13.5)2] = 13.37

σ2B = SQRT [0.15(-0.03 – 11.1)2 + 0.40(0.12 – 11.1)2 + 0.45(0.15 – 11.1)2] = 10.99

σ2C = SQRT [0.15(0 - 9)2 + 0.40(0.09 – 9)2 + 0.45(0.12 – 9)2] = 8.91

σ2D = SQRT [0.15(0.02 – 6.7)2 + 0.40(0.07 – 6.7)2 + 0.45(0.08 – 6.7)2] = 6.63

  1. She wants to use the expected returns on individual stocks (E(R)A, E(R)B, E(R)C, E(R)D) in an equation to find the expected return on this portfolio. How does she do that? Will she find the same expected return here as she finds in #2?

One approach for using the expected return on the individual stocks to get the expected return for the portfolio is to take the individual returns and compute the average.

 The equation would be as follows.

Sum of 13.5% + 11.1% + 9% + 6.7% = 40.3% 

40.3% / 4 = 10.1%

 The expected return obtained here is not equal to the one obtained in question 2 because the individual stocks have diverse standard deviations.


If this was helpful, check out my other homework help articles that include other academic paper examples.




 

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