Assignment #1: Virginia Capital Portfolio Optimization
Stock | Mean of Return | Standard Deviation |
IBM | 1.27% | 9.38% |
1) The below table shows the mean of IBM’s Stock to be 1.27% and the standard deviation to be 9.38%.
Stock | Mean | Standard Deviation |
Complete Portfolio of Weighted S&P, Lehman, and MSCI | 0.67% | 2.75% |
The table above shows the mean and standard deviation of a portfolio with S&P 500, Lehman Brothers, and MSCI World Index when they are all equally weighted.
An argument that can be made for the client to sell IBM stock and diversify is about the risk involved. The standard deviation of IBM’s stock is sitting at about 9.34%, which is ...view middle of the document...
This is most likely due to the target standard deviation being lower than any of the standard deviations of the stock.
A few additional assets could be added to reach the targets suggested. For one, you could acquire some T-Bills from the government, which virtually have a standard deviation of zero. This would make it possible to try and achieve a 2% standard deviation for the portfolio. You could also have a larger variety of stock that would reduce the amount of risk due to diversification. The strategy of short-selling would have to commence to reach the target standard deviation of 20%, which the negative weight of 33.22% indicates in the table. Short-selling allows an investor to sell a number of stock that they don’t own in order to invest the money they gain from selling the non-owned stock into something else, like another stock. However, you will need to buy the same amount of stock you sold at some point, making the percentage negative.
Adding a larger variety of risky stock will include a higher rate of return, but with increased risk if you are not effectively diversified. If well diversified your return will be less, but you have less risk. With adding the T-Bills, risk will decrease but so will return. Short-selling could make an increase in return because of the possibility of the stock you sold decreased in value. So when you have to buy the same number of stock back it is cheaper to buy and therefore you gained a profit. However, risk would increase because if the stock you sold while short-selling increases in value, than you may need to pay more when buying the stock back that was borrowed.
If we were not interested in short-selling any stock, then an added constraint should be made. Telling the solver to not allow a negative percentage would eliminate the short-sale. When we do this though, we would not be able to reach the target standard deviation of 20% because no combination of the portfolio standard deviation can go that high.
**Note that the portfolio return for the target standard deviation of 2% was not added because with the available stocks, this was not feasible per Excel solver**
Judging by the above graph, there is a compelling argument to diversify instead of just staying with the IBM stock. There is a large amount of average standard deviation compared to the amount of average return for the IBM stock. In contrast, the average return with the combined portfolio of the three stocks is still risky, but the return is much higher. For example, the return for the combined stock at a standard deviation of 10% is at about 8%, compared to IBM’s...