Asset allocation decision that are based on a mean - variance framework requires

Question

Asset allocation decision that are based on a mean - variance framework requires the assumption that returns from these assets are normally distributed. However, traditional asset classes and alternative investments (such as Hedge Funds, Private Equities, and Venture Capital funds) are shown to have non-normal return distribution. How should an investor decide the level of alternative investment in their portfolios?

1.Explain what is the mean variance framework?

2.Explain what is meant by normal and non - normal distribution?

3.Explain the impact of using non- normally distributed assets in the MV framework?

4.Give two suggestions to overcome this issue.

Explanation / Answer

1. Mean Variance Framework essentially involves making investment decisions based on the mean and variance of the projects i.e. for a given expected return, project with low variance will be chosen over the one with high variance. Likewise for a given level of variance, project with high return will be chosen as against the project with lower returns. This framework ensures an efficient investment choices.

2. Normal distribution can be simply understood as a symmetrical probability distribution wherein the mean = 0. It indicates that the probability of occuring for data near mean is higher than that of the data away from the mean. This can be made out from the bell shaped graph that it has. For normally distributed data, mean = median = mode. Non normal distribution is characterised by asymmetrical structure of probability distribution and it is caused either because of multiplicity of data sets included in one or due to outliers in data, etc. Non normal distributions makes investing decisions a little more complicated and therefore need to be adjusted.

3. Mean and standard deviation are highly affected by extreme values in the data and as we understand that data outliers may be one cause of non normal data. Thus non normal distributions affect the MV framework by altering the mean and variance values such that they lead to inappropriate investment decisions.

4.The first suggestion would to identify the reason behind the non normality and make changes to the data so as to eliminate those reasons and make the data normally distributed i.e. transform the data. Another suggestion would be to use tools that do no function on the assumption of normality of distribution. One sample sign test, Mood's median test, Kruskal Wallis test, Levene's test etc are few tools that be used for any type of distribution.

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