Markov’s Trilemma Case Solution

BUFN740 Case 1 Markov’s Trilemma

1. (a) Basic case:

[pic 1]

Basic formulas:

1. Expected return of portfolio (E[]):[pic 2]

[pic 3]

1. Expected standard deviation (): [pic 4][pic 5]
2. Sharpe ratio:

[pic 6]

(b) Correlation of GM & GE changes to 0.8:

[pic 7]

Conclusion: if correlation of GE & GM changes to 0.8 instead of 0.26, using solver we could see that the weight of GM is decreasing much and the weight of GE is increasing a lot. In addition, the Sharpe ratio of the new portfolio is 1.96.

Explanation: Because the correlation of GE & GM changes to 0.8, which means that these two stocks have too much relations and may be have similar future tendency. Thus, these two stocks cannot diversify the portfolio and reduce the risk if purchase both. So, we should buy much more of the one with higher expected return and lower standard deviation. Therefore, as depicted in the table, GE show a better potential to generate money, so we increase the amount invested in GE and reduce the amount in GM.

(c) Correlation of GM & GE changes to -0.8:

[pic 8]

Conclusion: if correlation of GE & GM changes to -0.8 instead of 0.26, using solver we could see that the weight of both GM and GE is increasing and the weight of MRK is decreasing a lot. In addition, the Sharpe ratio of the new portfolio is 3.09.

Explanation: Because the correlation of GE & GM changes to -0.8, which means that these two stocks have less relations and may be have largely different future tendency. Thus, these two stocks can well diversify the portfolio and reduce the overall risk if purchase both. So, we should buy much more of these two stocks to become diversified and reduced risk. Therefore, the amount in MRK will decrease correspondingly.

(d) For GE, the expected return changes to 30%, and the standard deviation changes to 30%:

[pic 9]

Conclusion: if GE’s expected return for the upcoming year and standard deviation both change to 30%, the weight of GE decrease to 28% and the weight of MRK increase to 64.3%. In addition, the new portfolio’s Sharpe ratio is 1.23.

Explanation: if GE’s expected return for the upcoming year and the standard deviation change to 30%, then the best performing stock of these three will be MRK, with the highest expected return and a relatively low standard deviation. Therefore, for investors, investing more in MRK will increase the overall expected return. So the weight of MRK increase a lot.