How to construct a properly diversified portfolio

The financial crisis has highlighted the need for a truly diversified portfolio, says Brian Fleming, head of multi-asset risk and structuring at Standard Life Investments.

Financial crises have a painful way of reminding investors that it is not easy to construct a diversified portfolio that offers protection during turbulent market conditions. While no universally agreed measure of diversification exists, we believe portfolio diversification should be considered in two broad parts.

The first part understands the diversification within a particular investment portfolio, with which we are most familiar. The second considers the diversification potential available within the investment universe chosen for that portfolio. Clearly the two are not the same: investment judgement, expected returns and client preferences will restrict our portfolio relative to an unconstrained universe.

However, understanding correlations between assets is critical to both. It is often said that during times of crisis, correlations go to one, which leads to a loss of benefits from diversification.

While correlations do tend to increase, one should take care to recognise that meaningful differences in performance can still be obtained even when correlations are high. Correlations may also be negative and very large between asset classes as they often are between equities and government bonds.

Furthermore, if one has the ability to take short positions then every positively correlated investment can be turned into a negatively correlated one. Taking all correlations and volatilities into account to understand diversification can be quite overwhelming. So is there a more practical way to consider portfolio diversification and diversification potential? Let us begin by examining the FTSE 100 index.

From FTSE 100 to FTSE 5.5

When we think of highly correlated stocks during a crisis we often consider there to be little diversification opportunity between them. The universe of stocks behaves as a single stock. In contrast to this we believe there is greater dispersion in stock returns during times of relative calm i.e. the number of stocks exhibiting different behaviour is higher.

Research has appeared during the past couple of years which offers us a way to measure the level of diversification in terms of the effective number of stocks in the index. When all stocks are perfectly correlated it takes a value of one. When all stocks are perfectly uncorrelated it takes a value equal to the total number of stocks in the index.

The effective number of stocks in the FTSE 100 must therefore lie between one and 100. We then simply define the diversification potential as the maximum achievable effective number of stocks for the index.

In figure one, we show the effective number of stocks in the current market capitalisation-weighted FTSE 100 over time. We can see the number of effective stocks has varied between five and 13. It is interesting to observe a persistent decline in diversification from 2005 to the low in 2008 and that even while stocks rebounded in 2009-2010 and volatility decreased, the diversification remained largely unchanged until the beginning of 2011. The effective number of stocks remains low today, which may be an indication of persistent systemic risk.

Furthermore, the relative importance of the stocks in the analysis does not have to be market capitalisation weighted. It is intuitive that an equally-weighted index of stocks is better balanced. We present the results of an equally-weighted index in figure two. While we can see that the overall trend is similar to the market-cap weighted results, the effective number of stocks is significantly higher in general with a correspondingly dramatic fall from around forty in 2006 to fifteen in 2008.

Figure two additionally shows the maximum effective number of stocks achievable for the FTSE 100, which we term the diversification potential of the FTSE 100. We can see this produces an effective number of stocks that is typically around ten greater than the equally weighted index. In practice we have found this maximum can also almost be achieved by an index which is equally weighted in terms of the risk contribution from each stock.

Finally, we examine the diversification in a typical balanced portfolio where the asset allocation is shown in the table to the right. If we term each line an asset class then, excluding cash, we have a total of seven asset classes. However, we know they are not perfectly uncorrelated so we examine the effective number of asset classes. This is shown in figure three.

We see that from a high of around two and a half, the effective number of asset classes declined to around one and a half at the height of the crisis, which is significantly lower than the maximum possible seven. The diversification potential is also plotted taking its highest value of around four and a half at the start of the chosen time period. Similar to the FTSE results, delivering this diversification potential requires a better balance of risk contributions from the various asset classes.

From potential to portfolio

We believe the diversification potential of a particular investment universe should be used to estimate, in a statistical way, the maximum number of independent opportunities available. It is a more complete and intuitive measure than monitoring, for example, average correlation.

For risk and portfolio managers alike such measures offer a way of observing in real time how diversification potential could be deteriorating even when returns and volatility could be moving in a favourable direction. In general for all investors it may be an efficient way to track diversification as an indicator of systemic risk. Research into related measures indicates the possibility that such measures could offer profitable trading signals.

For those constructing portfolios from a chosen investment universe, investment restrictions and expected returns will limit how much of the diversification potential can be delivered on. The achievable diversification will always be less than the potential. Understanding the impact of constraints on the ability of a portfolio manager to deliver robust performance and maintain a diversified portfolio during different market regimes should be a key consideration.

The effective number of asset classes in a typical balanced portfolio is low due to the high correlation between the risky asset classes. This means there are limited benefits from diversification. However, asset allocations in balanced portfolios are largely static, so addressing this by simply reducing exposure to risky assets impacts long-term expected returns. We believe the solution to this particular problem comes in two parts.

The first part is to allow a broader global investment universe with greater granularity to increase the diversification potential. This can be achieved by allowing managers to exploit views on, for example, exchange rates, asset classes, sectors, yield curves and stocks across different geographies.

The second part is to allow unconstrained dynamic asset allocation, which offers access to the full diversification potential of the chosen investment universe. It also allows the removal of risks that are not expected to be rewarding.

It is only within this framework that we believe investors can achieve a more continuously diversified portfolio which does not compromise on return.

Figure one: The effective number of stocks in the FTSE 100 index based on current constituents and fixed current market capitAlisation weightings

_{Source: Factset and Datastream}

Figure two: The effective number of stocks in the FTSE 100 Index based on current constituents and fixed equal weightings

_{Source: Factset and Datastream}

Figure three: The Effective number of Asset classes and diversification potential for a typical UK balanced portfolio

_{Source: Bloomberg}