# The Three Factor Model explained

Modern Portfolio Theory (MPT) is a series of tools which aim to minimise the risk of a portfolio while targetting a required investment return. At its most basic level modern portfolio theory is just the assertion that a portfolio assembled out of dissimilar assets will tend to have a lower level of risk than one made of very similar ones. This is because dissimilar assets can be expected to respond differently to each other in differing market and economic environments and thus not all go down at the same time.

For all the complexity wrapped around it, that is basically the core of MPT. It can of course become very technical once you start to get down to the details though.

The first problem is how exactly you define “risk”. The definition first used by Harry Markowitz in his PhD thesis which kicked off the whole Modern Portfolio Theory movement was the standard deviation of returns, a statistical measure of how far returns typically deviate from their average. Markowitz’ 1952 paper didn’t get much attention at the time it was published, but is now regarded to be one of the classic finance papers. (Markowitz, Harry M. (1952). “Portfolio Selection”. *Journal of Finance* 7 (1): 77-91. ) An online version of Markowitz’ book Portfolio Selection which is based on this work can be read here .

Standard deviation is a reasonable first attempt at defining risk mathematically. It has the advantage of being quite simple to calculate and, if certain assumptions hold true, a reasonably complete description of how risky an asset is provided that history provides a good guide to the future.

Standard deviation, more commonly just called “volatility”, was the risk measure on which much subsequent work in Modern Portfolio Theory was based. Various advances in theoretical understanding of market pricing lead to the hypothesis that rational investors should act on prices in such a way that for a diversified portfolio the expected return should be positively correlated to the amount of compensated risk taken on.

“Compensated” risk is what remains when you diversify away all the risks for which you can’t expect to be paid. All things being equal, dividing your money up among several risky securities is less risky than putting it all into the one security because the risk of being wiped out by a single event are correspondingly reduced.

Compensated risk is a good thing to the extent that investors can usually expect higher returns for taking on that sort of risk, but there is also “uncompensated” risk. Uncompensated risk is the unnecessary risk taken without any reasonably expected reward simply by having a portfolio which isn’t diversified enough.

The idea of compensated risk was tested by one of the earliest pricing models, the Capital Asset Pricing Model, or CAPM. CAPM is simply the idea that expected cashflows should be valued (discounted) using a risk factor called Beta, which is a measure of how risky a security is compared to the average of its asset class, where the risk measure used is volatility, the standard deviation of returns.

CAPM was highly influential for a long time, but began to fall from favour when better data and more powerful computers allowing systematic measurement and comparison of returns as a function of beta found that the expected relationship between beta and returns was much weaker than theory predicted. The problem, it turns out, is that standard deviation and beta aren’t very complete measures of how risky a security is. Researchers began to search for a better way of measuring risk.

Various attempts at creating a superior beta measure failed. More complicated formulae were tried calculating beta in various ways, however none of these met with much success.

The field advanced slowly until the early 1990s, when Professors Eugene Fama and Ken French jointly produced a paper which tied together a number of papers which had come out over the years documenting market behaviours which were contrary to the predictions made by the CAPM.

This paper, “The Cross-Section of Expected Stock Returns” has since become one of the most referenced articles in its field, which was surprising to Fama and French themselves as they point out that much of their work was just tying together threads of work which others had been doing for decades.

This paper used the statistical tool of multi-factor regression to analyse what characteristics of market returns corresponded to statistically significant long term higher or lower returns. The assumption made was that any factors which are linked to *consistent* higher or lower returns would be empirical pointers to dimensions of market risk.

The study identified numerous factors which are associated with returns higher or lower than the general market, however the largest of these were company size and company price vs. company earnings, sales, book value or other metrics of “value”.

Noting that company size and company “value” together predicted the return of a basket of stocks with far higher accuracy than beta and the CAPM, Fama and French devised the “Three Factor Model” of portfolio returns.

The model is fairly simple, it states that the expected return of a portfolio is mainly determined by three factors:

- Stocks tend to beat bonds over the long term by an amount known as the “equity risk premium”, so the amount of stocks vs. bonds in a portfolio is the first factor that will determine the long term expected return.
- Smaller companies tend to outperform larger companies over the long term by an amount known as the “small company premium”, so the size bias of the portfolio is the second factor that will affect the portfolio’s long term expected return.
- Cheap companies tend to outperform more expensive ones over the long term by an amount known as the “value premium”, so the portfolio’s allocation toward cheap (“value”) vs. expensive (“growth”) stocks is the third factor.

Beta was one of the factors tested by Fama and French, but once the effects of size and value were taken into account the beta factor vanished. In other words, company size and value work where beta failed. In the text of this paper Fama and French announced that beta as a risk measure had been made redundant.

If you assume that higher returns are always and everywhere payment for assuming more risk, then the three factors are identifiable as proxies for risks. They are thus also ways to get a higher return, if investors are willing to increase their exposure to these risks in their portfolio.

Stocks really are riskier than bonds. Stockholders are paid a return only after employees and creditors are paid what they are owed, so being last in line means that stockholders assume more risk. This risk factor is uncontroversial.

Small companies tend to be more susceptible to economic downturns than large and this is visible in the volatility of their profits and the rates at which they go bankrupt. The small company factor, once verified by other researchers looking at samples of data outside the one used by Fama and French, was also uncontroversial.

Fama and French caused more of a stir with the value factor, because for a long time investors like Warren Buffett and Ben Graham had been claiming that cheap companies outperform but that this was due to mispricing, not risk. Of course using circular logic one could argue that the companies wouldn’t be cheap unless there was something wrong with them to make them out of favour, and therefore they aren’t mispriced at all. This never really satisfied a lot of investors though, and the concept of a “value risk” has divided researchers ever since with distinct camps of “efficient markets” believers vs. those who believe markets are not efficient, most notably researchers interested in how investor psychology can distort prices, these are the researchers in the field of “behavioural finance“.

There is now, after 16 years of research, an impressive body of work by both the “value premium is a risk premium” theorists and the “value premium is caused by the market consistently making mistakes” theorists. Fama and French initially threw their lot in strongly with the “risk” side, however in the last few years have produced a number of papers supporting the idea that the value premium is at least in part driven by mispricing. The consensus, to the extent that one could be said to exist, is that the value premium is probably a combination of mispricing by the market systematically paying too much for glamourous “growth” companies and too little for dull or out of favour “value” companies, and in part a risk factor attached to a lot of shaky unprofitable companies with doubtful futures which also reside in great numbers among cheap companies.