Data Solver Solution:

When trying to solve the Sharpe ratio using the data solver tool, the Sharpe ratio would not be changed significantly as the shorting of GM stock amount is not as huge as it should require to change the Sharpe ratio.

Q – 1A

Answer – 1A

With respect to the high standard deviation the GM returns are lower as compared with the other two companies stock. As a result the GM stock should be included in the portfolio when going for the long that would impact the Sharpe ratio and it would result in reducing the Sharpe ratio.

For maximization of Sharpe ratio, the best option is to go short on GM stock and buy more of GE stock. It is because of the reason that, GE’s stock has a higher return to the given lower level of risk.

The positive correlation between the three assets can only be obtained if the shorting is allowed within the portfolio that would increase the Sharpe ratio as well.

Q – 1B

Answer – 1B

The negative correlation between the GE stock and GM stock resulted in the increase of Sharpe ratio. This negative correlation also reduces the overall risk of the portfolio and that resulted in increasing the Sharpe ratio.

Q – 1C

Answer – 1C

The Sharpe ratio is reduced and the weight of MRK stock would increase in the portfolio that would also incorporate towards increase the return of the MRK stock. This increase in the MRK returns is higher as compared to the GE’s stock returns with regards to the same risk associated with both securities.

Q – 2A

Answer – 2A

If shorting is not allowed than the investor would not include the GM stock in his portfolio and it is due to the fact that it will generate lower returns with the given higher level of risk associated with the portfolio. The Sharpe ratio would not be changed with respect to the base case scenario.

Q – 2B

Answer – 2B

Even thought the correlation between the GE security and GM security in a portfolio would increase to 0.8 it would not increase the Sharpe ratio. It is due to the fact that, investors would not consider to include the GM security in his portfolio and if investors would go for shorting.

Q – 2C

Answer – 2C

In the case of negative correlation that is high between the GE security and GM security, it could be used effectively for the purpose of reducing the risks for a portfolio. Therefore, the Sharpe ratio would reduce due to the diversification that would also reduce the risk of the portfolio.

Q – 3

Answer – 3

With the given constraints, the Sharpe ratio be reduced and it is because of the fact that investors are not allowed to invest in any of the securities more than 50%. The investors are bound to invest in those securities where return is lower and risk associated with it is also lower. This would affect the Sharpe ratio to be falling below.

Q – 4

Answer – 4

The reduction in the risk free rate would increase the Sharpe ratio and it is because investors would prefer to invest in those portfolios where the returns are higher than the expected returns and it would lead the Sharpe ratio to increase further.

Q – 5

Answer – 5

With respect to the low standard deviation the INTC returns are higher as compared with the other two companies stock. As a result the INTC stock should be included in the portfolio when going for the short that would impact the Sharpe ratio and it would result in an increase in the Sharpe ratio.

In order to maximize the Sharpe ratio, the three assets that would be included in an optimal portfolio are INTC, MRK, and GE. These securities are only allowed when the shorting is allowed. In the case of shorting is not allowed than the GM, MRK, and GE securities would make an optimal portfolio where the Sharpe ratio would be higher...............

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The main objectives of this case are: (1) to familiarize students with the simple version of Markowitz optimal asset allocation model, (2) the development of students' intuition on the optimal asset allocation as a concrete contribution to the model (for example, the expected return, standard deviation, correlation) of the change in the value and (3) to develop students' intuition regarding restrictions that alternative investors may face (such as a short circuit limitations) and their effect on the optimal portfolio.

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by Giorgos Allayannis Source: Darden School of Business 4 pages. Publication Date: August 13, 2001. Prod. #: UV0506-PDF-ENG