Portflio Case

Summary:

In example #1, our recommendation for a risk adverse investor would be to go with the GMV when short sales are allowed which would yield a 9.6% return with the lowest risk of 2.3%. If the investor is willing to take a little more risk he/she could go with the Roxoff security which would earn him/her 15% return with a risk of 3.41%.

In example #2 we see that by adding a riskless lending and borrowing rate of 2% we manage to optimize the portfolio by bringing the standard deviation or risk to 0% with a combination of the five assets. On the other the return always decreases to a 2%.

In example #3, we are looking to see the risk/return effects when two more investment opportunities arise. We know that the historical way of investing the money gives us a 1.016% return with a 2.634% level of risk. By examining several options our conclusion is that the best solution is to distribute between the S%P 500 and the High Yield Bond with weights of 53.36% and 46.640% respectively.

Example #4 simply makes us use a rate of .415% of riskless lending and borrowing which yields an expected return of 2.154% and a level of risk of 4.849%

Once again, in example #5 we continue to use a .415% riskles lending and borrowing this time adding a correlation factor of 0.4 constant. After plugging in these numbers, our expected return is of 2.323% with a level of risk of 4.852%.

In example #6, numbers such as correlation and riskless borrowing and lending change to provide us with an expected return of 5.851% with a standard deviation of 3.811%

In the book problem #4, the results of the GMV yield a 18.871%with a 3.289% level of risk when short sales are allowed.

Example 1

What are the investment weights, expected return, and total risk, of the least risky (Global Minimum Variance or GMV), when short sales are allowed and when short sales are not allowed?

Short Sales are allowed (Fig1 & 2)

All assets in relation to efficient frontier (Fig 3)

The graphs above are showing that in order to get the least risky portfolio when short sales are allowed the weights of each asset should be as follows:

* Dori Motor 70.696%

* Roxoff Corp. 40.410%

* Widget Tech -24.117%

* Beavis Enter 17.817%

* Shoki -4.806%

Assuming the weights already mentioned, the expected return and the standard deviation (which tell us about the risk of the portfolio) are

* Expected Return = 9.660%

* Risk (standard deviation) = 2.353%

Compare the efficient counterpart of Roxoff (fig 4 & 5):

Roxoff expected return and standard deviation are

* Expected Return = 15.086%

* Standard Deviation = 3.411%

Custom Portfolio A weight in all assets of 20% (fig 6):

This graph shows the custom portfolio which distributes its weight in 5 equal percentages which gives each asset a 20% weight.

Short Selling not allowed: (Assumed default limits) (Fig 7)

* Expected Return = 10.318%

* Standard Deviation= 3.084%

Example 2

Consider the data given in Example 1. What are the expected return, standard deviation and investment weights of the optimal tangent portfolio of the five risky assets is riskless lending and borrowing are available at a rate of 2% when short sales are allowed?

Short Sales Allowed (Fig8 & 9):

According to the graph based on the optimal tangent portfolio the results for this problem is

* Expected Return= 2.0%

* Standard Deviation= 0.0%

* In which we can notice that there is no risk involved.

What are the investment weights of the optimal tangent portfolio of the five risky assets?

1. 46.473%

2. 45.338%

3. -34.966%

4. 36.680%