markov's case
Markov’s Trilemma
First we try to find the optimal portfolio for our original set up.
Weighting
Asset
GM
-0.8%
MRK
34.8%
GE
66.0%
100.0%
Risk-free rate
7%
Expected Return
41.3%
Expected standard deviation
21.4%
Sharpe Ratio 1.60
1. Then we try the following actions and try to understand their consequences:
a. Suppose that GM has decided to become a diversified conglomerate, much like GE, so that its correlation with GE will be 0.80 instead of 0.26.
Weighting
GM
-61.4%
MRK
21.1%
GE
140.2%
100.0%
Risk-free rate
5%
Expected Return
53.2%
Expected standard deviation
23.6%
Sharpe Ratio 1.96
The weight of GM, MRK, and GE change to -61.4%, 21.1%, and 140.2% and Sharpe Ratio change to 1.96. We have higher weight on GE and lower on GM because GM has decided to become much like GE but its Sharp Ratio is much lower then GE, so we chose invest more on GE and short sell more on GM.
b. Now suppose the GM has decide to focus on automobiles and move away from anything that GE is doing, so the correlation between GE and GM is excepted to be as low as -0.8.
Weighting
GM
40.9%
MRK
-13.2%
GE
72.3%
100.0%
Risk-free rate
7%
Expected Return
32.9%
Expected standard deviation
8.4%
Sharpe Ratio 3.09
The weight of GM, MRK, and GE change to 40.9%, -13.2% and 72.3% and Sharpe Ratio change to 3.09. Now there is a very strong negative correlation between GM and GE, invest to them will benefit us from diversification.
c. Suppose that GE’s expect return for the upcoming year is 30% and its standard deviation is expected to be 30%. This new information change our weights to 7.8%, 64.2% and 27.9% on GM, MRK, and GE, and Sharpe Ratio become 1.23.
2. Assume again that the correlation between GE and GM is 0.26. What happens to the weight and portfolio Sharp Ratio when shorting is not allowed.
Weighting
gm
0.0%
mrk
34.6%
ge
65.4%
100.0%
Risk-free rate
7%
First we try to find the optimal portfolio for our original set up.
Weighting
Asset
GM
-0.8%
MRK
34.8%
GE
66.0%
100.0%
Risk-free rate
7%
Expected Return
41.3%
Expected standard deviation
21.4%
Sharpe Ratio 1.60
1. Then we try the following actions and try to understand their consequences:
a. Suppose that GM has decided to become a diversified conglomerate, much like GE, so that its correlation with GE will be 0.80 instead of 0.26.
Weighting
GM
-61.4%
MRK
21.1%
GE
140.2%
100.0%
Risk-free rate
5%
Expected Return
53.2%
Expected standard deviation
23.6%
Sharpe Ratio 1.96
The weight of GM, MRK, and GE change to -61.4%, 21.1%, and 140.2% and Sharpe Ratio change to 1.96. We have higher weight on GE and lower on GM because GM has decided to become much like GE but its Sharp Ratio is much lower then GE, so we chose invest more on GE and short sell more on GM.
b. Now suppose the GM has decide to focus on automobiles and move away from anything that GE is doing, so the correlation between GE and GM is excepted to be as low as -0.8.
Weighting
GM
40.9%
MRK
-13.2%
GE
72.3%
100.0%
Risk-free rate
7%
Expected Return
32.9%
Expected standard deviation
8.4%
Sharpe Ratio 3.09
The weight of GM, MRK, and GE change to 40.9%, -13.2% and 72.3% and Sharpe Ratio change to 3.09. Now there is a very strong negative correlation between GM and GE, invest to them will benefit us from diversification.
c. Suppose that GE’s expect return for the upcoming year is 30% and its standard deviation is expected to be 30%. This new information change our weights to 7.8%, 64.2% and 27.9% on GM, MRK, and GE, and Sharpe Ratio become 1.23.
2. Assume again that the correlation between GE and GM is 0.26. What happens to the weight and portfolio Sharp Ratio when shorting is not allowed.
Weighting
gm
0.0%
mrk
34.6%
ge
65.4%
100.0%
Risk-free rate
7%