Effects of Diversification of Assets on Mean and Variance

Abstract

Diversification is a means of minimizing risk and maximizing returns by investing in a variety of assets of the portfolio. This paper is written to determine the effects of diversification of three types of Assets; uncorrelated, perfectly correlated and perfectly negatively correlated assets on mean and variance. To go about this, useful data were collected for uncorrelated, perfectly correlated and perfectly negatively correlated assets. These data were computed for two assets, three assets and four assets model to know the effects of diversification of the three types of assets on mean and variance. It is observed that diversification of these three types of assets yield the same mean (returns). It is also noticed that Mean increases with the increasing number of diversification. And variance (risk) increases with mean for uncorrelated, perfectly correlated assets. But, for perfectly negatively correlated assets the variance decreases with its increasing mean. This implies that diversifying into perfectly negatively correlated assets (risky and riskless assets) together maximize mean (return) and minimize or cancel variance (risk).

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 131 – 134