Correlation and diversification

Central to many asset allocation models is modern portfolio theory. This was developed by Harry Markowitz in an article entitled Portfolio Selection, which was published in the 1952 Journal of Finance. Modern portfolio theory says it is not sufficient to look at the expected risk and return of one particular stock.

Each stock has its own standard deviation from the mean, which modern portfolio theory describes as risk. The risk in a portfolio of a diverse range of stocks will be less than the risk of holding just one single stock as long as the stocks are not truly correlated. This is because if one stock falls in value this should be offset by another lowly correlated stock in the portfolio rising in value. Markowitz added that investment is not just about selecting stocks, but choosing the right combination of stocks across which you need to diversify your portfolio.

Modern portfolio theory identifies two components of risk. Systematic risk, such as interest rates, recessions and wars, are market risks that cannot be diversified away. Unsystematic risk is specific to individual stocks and can be diversified away, as you increase the number of stocks in your portfolio.

Taking this one step forward, modern portfolio theory says it is possible to construct a portfolio offering a lower risk for a given level of investment return. Risk-adjusted returns can be plotted on a graph to show the ideal portfolio, by applying modern portfolio theory to sectors or markets, rather than specific stocks. Any portfolio that lies on the upper part of the curve is efficient, as it gives the maximum expected return for a given level of risk. A rational investor will only ever hold a portfolio that lies somewhere on the so-called efficient frontier. The maximum level of risk that the investor is prepared to take determines the position of the portfolio on the frontier.

The lower the correlation coefficient, the better the diversification. If there is no correlation between the returns of two sectors and the correlation coefficient is equal to zero, you can divide your portfolio between each and reduce risk by almost one-third. As the correlation coefficients between the returns in each sector increases, the gains from diversification fall. If there is perfect correlation in returns and the correlation coefficient equals one, there is no gain from diversification. Correlation coefficient is explained as follows:

• Positive correlation describes a relationship where an increase in one variable is associated with an increase in another.
• Negative correlation describes a relationship where an increase in one variable is associated with a decrease in another.
• Perfect correlation describes a relationship where a change in one variable is exactly matched by a change in another.

To enhance diversification, as outlined by modern portfolio theory, you should spread your risk across asset classes. Holding asset classes such as bonds, property and alternative investments, as well as equities should reduce volatility across your portfolio. However, extreme market movements in recent years have indicated that historically uncorrelated assets can become correlated in some circumstances. Whilst diversification continues to provide benefits, it is not a failsafe solution.

As described by modern portfolio theory, dividing a portfolio between different asset classes should lower the level of risk taken, when compared to holding just one sector. This is because the returns of one sector can rise at the same time as those of another sector fall. This movement of returns should dampen the overall volatility of the portfolio.

Some people only invest in UK equities and fixed interest. Rather than reducing risk, however, being fully or largely invested in UK quoted assets can increase portfolio risk.

Even within one asset class, diversification helps to reduce risk. Take equities as an example. Research by Professor Paul Marsh of the London Business School supports the argument that long-term investors do benefit from international diversification. He analysed the risk reduction that would have been achieved by a dollar-based investor during the 20th century. He did this by using standard deviation, which is a measure of volatility. The higher the standard deviation then the greater the level of volatility. Professor Marsh's analysis shows that the standard deviation for a single country portfolio was 29.1 percent in the 20th century but this declined to 17.3 percent for an equally weighted 16-country portfolio. This represents a 41 percent reduction in the level of volatility for the portfolio.

The reduction in volatility, however, was lower during the period from 1996 to 2000. The standard deviation fell from 20 percent for a typical one-county investment during this shorter period to 14.6 percent for an equally weighted 16-county portfolio. This is a 27 percent volatility reduction.

Over the very long and short term, it can benefit you to invest overseas. For example, between 1900 and 2004, the UK stock market delivered an annualised return of 5.4 percent. This was lower than Australia (7.6 percent), Sweden (7.6 percent), South Africa (7.0 percent), the US (6.6 percent) and Canada (6.1 percent).

There is evidence that the benefits of diversifying across international stock markets are reducing, however. As suggested by Professor Marsh's research, this is based on the fact that stock markets around the world are becoming more highly correlated. This means if the UK market rises or falls in value, it is more likely that others, particularly developed markets, will do the same.

For example, Professor Marsh shows in research carried out with colleagues Elroy Dimson and Mike Staunton at the London Business School that correlation increased between 1900 and 2000. The correlation between the UK and world stock markets in real dollar returns between 1900 and 2000 was an average 0.70.

Other studies have also pointed towards greater correlation, particularly over the past 30 years. But it should be stressed that the degree of correlation changes over time and varies depending on the relationship between countries and stock markets. It is possible that markets will become less correlated again in the future.

Nevertheless, increased correlation between markets poses significant challenges to international diversification. The driving force behind this trend has been globalisation. This reflects the increasingly interconnected world we live in today. The financial and economic integration of different regions through trade and financial flows increases the correlation between their financial markets and economies.

Since the 1990s, the pace of global and economic integration has accelerated rapidly. This has led to national firms becoming multinational corporations. As companies expand across the world, it is becoming less and less important in which country a firm is headquartered, or where its shares are listed.

With a greater percentage of business being conducted internationally by these companies, they are being exposed to similar risks faced by overseas corporations.

But the potential of increased correlation should not necessarily deter you from investing internationally. There can still be merits in diversification overseas, both by geography and in particular by sectors. Fund managers argue that, even if correlations are rising, international diversification offers opportunities to profit from stock picking. By selecting the best performing stocks from each market, investors can enhance returns. Of course, this strategy is notoriously difficult to achieve in practice.

Sectors are an important reason for looking for diversification. Increasingly, a few sectors dominate the individual stock markets.

You can benefit from different levels of sector exposure in other markets. Technology comprises a far larger proportion of the US stock market, for example, than of the UK. Investing overseas enables you to access sectors that have little if any presence in the UK. It also allows you to invest in well known global companies like Microsoft and Apple that are not listed in the UK.

One argument used in favour of remaining invested in the UK has been the higher yield available from shares listed on the FTSE index. Traditionally, most overseas markets have had little dividend income available. But this appears to be changing. There have been particularly pronounced rises in yield in Europe, Japan and Asia.