Decomposing diversification - A three part analysis

An interesting perspective on the benefit of diversification focuses on decomposing the gains into three parts. As presented by Morgan Stanley Research, this is a framework that will be useful for any investor. It is just a recasting of the mean-variance frontier with a focus only on the volatility benefits.  Looking at the decomposition of volatility reduction is just another way of looking at the volatility of a portfolio with different weights between two assets while accounting for the impact of correlation. It is especially helpful for discussions concerning the value-added of hedge funds.

Let's take the simplest example of a combination of stocks and bonds. Assume that you have an all equity portfolio and you would like to add bonds. As you add bonds to the mix and switch out of equities, the volatility of the portfolio will decline until you reach the point where the portfolio will have the volatility of bonds. This would be the 100% bond portfolio. Those two extremes anchor the volatility in the portfolio. The volatility of the portfolio will be a combination of the volatility of the two assets and their correlation. 

The decline in volatility from forming a portfolio of stock and bonds versus holding 100% equities can be divided into three parts. One is the change in the volatility based on the addition of the new assets assuming that the two assets are perfectly correlation. The decline in the volatility of the portfolio could be called the volatility compression. You can get diversification, that is lower portfolio volatility, by just substituting with assets that have lower volatility. The reduction is  proportional to the amount of held. 

There is a second effect which is the amount of risk reduction that is caused by de-correlation or the lack of correlation between the two assets. A more uncorrelated asset will lead to greater or enhanced diversification relative to just buying the less volatile asset. For most assets, this will be the extent of risk reduction. However, there can be a third effect which is the impact or the added diversification from buying an asset which is negatively correlated with the portfolio. This is the hedging effect because negative correlation will actually offset some of the existing volatility. These are the assets that are especially valuable for diversification.

Bonds can generate all three effects when added to the portfolio. Bonds are less volatile than equities. There is a de-correlation effect and the added effect of it being a hedge versus equities. Hedge funds have not done as good a job as bonds for diversification because they have not been able to generate the hedge effect. Hedge funds are less volatile than equities, and have lower correlation but except for managed futures and short-selling funds, the correlation is usually between 0 and .5, at best.  

The hedge effect is volatile and may not continue with bonds, but right now it is what has made bonds a special asset. Investors have to look for the special managers or assets that can have a hedge effect on a portfolio.