Is your fund manager worth his fees?

If you regularly read articles about investment including some of the ones in this magazine you'll come across references to analysing stock returns in terms of 'factors' and 'models'.For anyone without a background in finance and economics, these ideas may seem very academic and without much use in real-world investing.

But while the financial theory can be quite technical, the basic principles are relatively straightforward. And getting to grips with them can be a lot more useful than you might expect. They can help you to understand why your investments are getting good results because the manager is an investment genius, or because they are buying into certain types of stocks that are likely to beat the market anyway. So let's take a quick look at the background to the models and what they tell us.

Introducing CAPM

The first widely used model for explaining investment returns was the capital asset pricing model (CAPM), which was independently developed by a number of researchers (Jack Traynor, William Sharpe, John Lintner and Jan Mossin) in the early 1960s. CAPM says that the expected rate of return on a stock depends on the stock's sensitivity to movements in the wider market. This measure of sensitivity is usually referred to as 'beta'.

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A stock that goes up by more than the market when the market is rising and falls by more than the market when the market is falling has a high beta. CAPM says it will have a higher expected return than a stock that is less volatile (ie, one that has a lower beta). That makes a lot of sense: more volatile stocks need to offer a higher rate of return to compensate investors for the greater risk of holding them.

CAPM is engagingly simple and became a cornerstone of modern finance. But there was a problem: data showed that beta certainly didn't explain all the variation in security prices. Importantly, the ways in which it was wrong weren't entirely random: researchers realised that certain types of stocks seemed more likely to do better or worse than CAPM predicted.

This led to the three-factor model, first published by Eugene Fama and Kenneth French in 1993. Fama and French's model adds two additional variables to beta, based on which types of stocks typically seemed to outperform.

The first is the 'size': smaller stocks appear to have higher average returns, so the three-factor model predicts higher returns for these stocks than CAPM would suggest. The second is 'value': stocks whose market capitalisation is low compared to the value of their assets appear to outperform. So lower-valued stocks have higher expected returns than more expensive ones (known as 'growth' stocks) under the three-factor model.

Risk and reward

Fama and French's model works significantly better than CAPM: they found it describes about 90% of stock returns, versus about 70% for CAPM. Of course, once you begin adding more special cases to a model, you risk seeing a pattern whether there's a real relationship or not. However, the three factor model again appears sensible.

Small stocks are generally riskier than larger ones, so it's understandable that investors would demand extra returns to hold them (indeed, some recent work suggests that the small-cap effect is due to the exceptional performance of outliers and the average small-cap underperforms, demonstrating this additional risk).

The value effect is harder to explain, but one possible cause is that these cheap stocks are also riskier, especially in extreme situations: they may be carrying more debt, or have a more difficult operational outlook. So again, investors need to be rewarded for taking the risk.

But size and value aren't the only anomalies people have found. In 1997, Mark Carhart proposed a four-factor model, adding a 'momentum' factor to the existing three. Momentum is the tendency for stocks to continue rising if they are already rising and to continue declining if they are already declining. Under Carhart's model, a stock whose 12-month average return is positive has positive momentum and is associated with higher expected returns than a stock with negative momentum.

Momentum is important because the previous three factors (beta, size and value) can be linked to risk, as we saw. But momentum is harder to explain in terms of risk: instead, it seems to be about investor psychology (investors prefer to buy stocks that are going up). In other words, momentum suggests that markets are inefficient, whereas our first three factors were about efficient markets rewarding investors for taking risks.

Looking for a fifth factor

While Carhart's work is the most recent widely accepted addition to the model, academics and investors are still trying to identify other factors. One popular candidate is 'quality': the idea that profitable businesses with stable earnings and low debt seem to outperform. Another is 'low volatility': many of the least volatile stocks also seem to perform better than existing models predict.

While neither factor is universally accepted yet, there is evidence to support them. Both are a further blow to the idea that markets are efficient, since they imply that some types of safer stocks are persistently earning higher returns.

Understanding these effects can help you analyse why investments performed in a certain way. For example, if a fund manager has beaten the FTSE 350, they may have done so through skill. But they might simply have loaded up on smaller stocks and value stocks, giving them a portfolio that would be expected to beat the index anyway. If so, you would have been able to earn the same kind of returns using low-cost exchange-traded funds (ETFs) based on these factors meaning that there would be no justification for paying the manager's higher fees.