An even spread of balanced risk

Harry Markowitz wrote in as early as 1952 that merely spreading an investment sum between as large a number of equities as possible does not in itself constitute a diversified portfolio. The winner of the 1990 Nobel Prize for economics wrote in a then groundbreaking article, entitled Portfolio Selection: “A portfolio of 60 different railway securities, for example, would not be as well-diversified as the same size portfolio with some railroad, some public utility, mining, various types of manufacturing, etc. The reason is that it is generally more likely for firms within the same industry to do poorly at the same time than [it is] for firms in dissimilar industries.”

Distribution

The process of asset allocation boils down to a portfolio manager deciding how to distribute assets among a variety of asset classes. The first stage in every asset allocation process is to subdivide the investment universe into the asset classes, each of which bear their own particular risks. As a rule, the equity universe is split into asset classes by both country and sector.

The importance of the industries Dr Markowitz mentioned more than 50 years ago has of course changed. However, his conclusion that a risk-averse investor should spread his investments over a variety of asset classes remains just as relevant today.

According to Dr Markowitz, who is rightly regarded as founder of modern portfolio theory, a trade-off between risk and return exists and investors are well-advised to take into account the covariances between different asset classes when making investment decisions.

At the beginning of the 1950s, only a very few investors spread the risk beyond their own borders. In the era of globalisation with increasingly integrated goods and financial markets, investors now wonder to what extent any previous advantage of international diversification will gradually disappear.

Transparency

In light of this, one approach to asset allocation is to divide up the equity universe according the price/book ratio or other valuation ratios into growth and value stocks. Equally, it can be split based on the market capitalisation into large and small caps.

Each of these approaches can make the inherent portfolio risk more transparent, because equities of the same fundamental asset class – just as Dr Markowitz recognised – very often perform particularly well or badly during the same period.

The importance of underlying asset classes can be proven empirically, although economists have not yet formulated a well-articulated theory to adequately explain the existence of the value/growth and large/small capitalisation factors.

Factor models

In practice, institutional investors employ factor models to quantify the overall portfolio risk. The advantage of factor models is that they take into account the covariances between the individual asset classes when calculating the current portfolio risk. Factor models are often used to estimate the standard deviation, tracking error and value at risk of a portfolio.

Standard deviation shows the investor to what extent the returns deviate from the mean. The greater the deviation from the mean, the higher the portfolio risk. Tracking error is calculated as the standard deviation of the differences between the portfolio returns and the benchmark returns, thereby measuring how widely the portfolio returns deviate from the benchmark.

Value at risk (VaR) quantifies the potential loss which, at a predetermined probability and over a set time frame, may not be exceeded provided that the composition of the portfolio remains the same. For example, a “daily VaR” of –2 per cent at 99 per cent confidence means that on only one of every 100 days will a loss be expected to exceed the –2 per cent mark.

Investment managers also employ factor models to analyse the sensitivity of their portfolios to changes in individual factors or asset classes. The contribution to risk of an asset class shows an investor to what extent a given country or underlying asset class contributes to the total portfolio risk. The marginal contribution to risk expresses how much the portfolio risk changes when a certain risk position (eg, a sector weighting) is increased by one per cent by reducing the cash component.

A factor model is well-specified when a small number of factors reliably explain the returns generated by a portfolio. Using statistical key figures such as R-Square, portfolio managers can confirm the quality of their factor models. Unlike purely statistical models, factor models are based on solid economic fundamentals: equities of the same asset class mostly react in a similar manner to exogenous economic changes.

For example, at the moment highly export-dependent German automobile equities are all suffering from the strong euro, while all the Chinese raw materials equities are benefiting from high economic growth and the massive influx of investment capital into the country.

Reality check

However, investors should be forewarned: every economic model is based on a number of assumptions that in real life cannot be completely fulfilled. We are convinced that factor models can play a very valuable role in quantifying total risk and in identifying the sources of that risk. But just like valuation models, which show the portfolio manager how equities are valued, risk models are always flawed.

Because the returns, variances and covariances of a portfolio over the course of time are not sufficiently stable, mechanically-driven portfolio optimisation is less than ideal.

In simple terms: just as the speedometer accurately shows how fast the car is travelling, factor models can show the portfolio manager’s current risk exposure. But this does not ever mean the speedometer can steer the vehicle or that portfolio management can be left to a factor model. As soon as the traffic or the economics change, then neither dashboard nor factor models are a reliable guide.

Jan Viebig, senior portfolio manager, DWS Investments