Fins2624 Portfolio Management For Deviation Assessment Answers

Answer:

Modification of Expectation-Variance Model

Mean Absolute Deviation Method

In order to overcome the limitations of the expectation and variance (Standard Deviation) being the return of risk measures, another method can be used. This is the Mean Absolute Deviation (MAD) method. The following expression gives the measure of the MAD.

Here,  is denoted as the return of  asset,  is denoted as the expected value of the return of assets and N is denoted as the total number of returns.

There are some attractive features for the measure of MAD. This include portfolio optimization, which can be done by skipping the calculation of the covariance matrix, and follow an algorithm, which is much easier to solve. This reduces the time of computation and the optimal portfolios are computed with improved methods. It can also be said that Mean Absolute Deviation is gives a more stable measure considering time which was not given by the standard deviation. Unlike the variance measure, MAD is less affected by the presence of any outliers and assumption about the shape of the distribution is not required to compute this measure. This model also holds the positive characteristics of the expectation-variance model. Mean Absolute deviation is also an appropriate measure to apply in situations where the number of assets (N) is more than the total time-period (T).

It can also be said that with the high use of computers and advancements of the facilities provided by it, the significance of the computation has decreased. Further, the mean absolute deviation method is excluded where the covariance matrix is important in calculation and omitting the calculation will lead to a greater risk of estimation.

Minimax Method

Another method, that can be used to overcome the limitations of the expectation-variance method is the minimax method. This method is simple linear programming method solution. In this method, the minimum risk is used as the measure of risk and not the variance.

The portfolio of Minimax rule can be explained as minimizing the maximum loss acquired. It can be stated alternatively as maximizing the minimum gain. Minimax rule also represents the maximum loss that has been determined from previous data. The minimax rule can be solved following the given algorithm.

Subject to the constraints:

Here,  is denoted as the return of  asset in  time period,  is denoted as the mean return on  asset,  is the allocation of the portfolio to the   security,  is the minimum portfolio return.  is subject to the constraint that the mean return on the portfolio is higher than the lower level which is given by E. Another constraint can be said to be the sum of the allocations given to the portfolios are less than the total number of allocations, which is denoted by F.