By James Montier
Is C(apital) A(sset) P(ricing) M(odel) C(ompletely)
R(edundant) A(sset) P(ricing)?
The capital asset pricing model (CAPM) is insidious. It creeps into almost every discussion on finance. For instance, every time you mention alpha and beta you are tacitly invoking the CAPM, because the very separation of alpha and beta stems from the CAPM model.
A brief history of time
Let's take a step back and examine a brief history of the origins of CAPM. It all started way back in the 1950s when Harry Markowitz was working on his PhD. Markowitz created a wonderful tool which allows investors to calculate the weights to give each stock (given expected return, expected risk, and the correlation) in order to achieve the portfolio with the greatest return for a given level of risk. Effectively investors using the Markowitz's methods will have mean-variance efficient portfolios that is to say; they will minimize the variance of portfolio return, given expected return, and maximize expected return given the variance.
Markowitz gave the world a powerful tool that is much used and loved by quants everywhere. However, from there on in, the finance academics proceeded down a slippery slope. Somewhere around the mid-1950s Modigliani and Miller came up with the idea of dividend and capital structure irrelevance. They assumed that markets were efficient (before the efficient market hypothesis was even invented), and argued investors didn't care whether earnings were retained by the firm or distributed as income (this will be important in a little while).
In the early 1960s the final two parts of efficient markets school dawned into the unsuspecting world. The first of these was CAPM from Sharpe, Litner and Treynor. In the wonderful world of CAPM all investors use Markowitz optimization. It then follows that a single factor will distinguish between stocks. This all encompassing single factor is, of course, beta.
The second was the summation of all ideas, the birth of the efficient market hypothesis itself from Eugene Fama (another PhD thesis). I don't want to rant on about market efficiency as my views on this topic are well known.
CAPM in practice
It is worth noting that all these developments were theoretical. It could have been very different. In a parallel world, David Hirshleifer describes:
A school of sociologists at the University of Chicago proposing the Deficient Markets Hypothesis: that prices inaccurately reflect all information. A brilliant Stanford psychologist, call him Bill Blunte, invents the Deranged Anticipation and Perception Model (DAPM), in which proxies for market misevaluation is used to predict security returns. Imagine the euphoria when researchers discovered that these mispricing proxies (such book/market, earnings/price, and past returns), and mood indicators such as amount of sunlight, turned out to be strong predictors of future returns. At this point, it would seem that the deficient markets hypothesis was the best-confirmed theory in social sciences. To be sure, dissatisfied practitioners would have complained that it is harder to actually make money than ivory tower theorists claim. One can even imagine some academic heretics documenting rapid short-term stock market responses to new arrival in event studies, and arguing that security return predictability results from rational premia for bearing risk. Would the old guard surrender easily? Not when they could appeal to intertemporal versions of the DAPM, in which mispricing is only correct slowly. In such a setting, short window event studies cannot uncover the market's inefficient response to new information. More generally, given the strong theoretical underpinnings of market inefficiency, the rebels would have an uphill fight.
If only we lived in such a parallel reality! In general our industry seems to have a bad habit of accepting theory as fact. As an empirical skeptic my interest lies in whether CAPM works. The evidence from the offset has been pretty appalling. Study after study found that beta wasn't a good measure of risk.
For instance the chart below is taken from Fama and French's 2004 review of CAPM. Each December from 1923 to 2003 they estimate a beta for every stock on the NYSE, AMEX and NASDAQ using 2-5 years of prior monthly returns. Ten portfolios are then formed based on beta, and the returns tracked over the next 12 months.
The chart below plots the average return for each decile against its average beta. The straight line shows the predictions from the CAPM. The model's predictions are clearly violated. CAPM woefully under predicts the returns to low beta stocks, and massively overestimates the returns to high beta stocks. Over the long run there has been essentially no relationship between beta and return.
Of course this suggests that investors might be well advised to consider a strategic tilt towards low beta and against high beta ? a strategy first suggested by Fisher Black in 1993.
Nor is this simply another proxy for value. The table below (taken from some recent work by Vuolteenaho) shows the beta arbitrage strategy holds across book to price (B/P) categories. For instance, within the growth universe (low B/P) there is an average 5% differential from being long low beta, and short high beta.
Within the value universe (high B/P), a long low beta, short high beta created an average difference of 8.3% p.a. over the sample. So both growth investors and value investors can both exploit a strategic tilt against beta.
A recent paper from the ever fascinating Jeremy Grantham of GMO reveals that amongst the largest 600 stocks in the US, since 1963 those with the lowest beta have the highest return, and those with the highest beta have the lowest return ? the complete inverse of the CAPM predictions. Yet more evidence against the CAPM.
Nor is this purely a US problem. With the aid of the Rui Antunes of our Quant team we tested the performance of beta with the European environment. The chart below shows that low beta on average has outperformed high beta! Yet another direct contradiction of the CAPM.
Another of CAPM's predictions states the cap-weighted market index is efficient (in mean-variance terms). With everyone agreeing on the distributions of returns and all investors seeing the same opportunities, they all end up holding the same portfolio, which by construction must be the value-weighted market portfolio.
There is a large amount of evidence to suggest that CAPM is wrong in this regard as well. For instance, in a recent issue of the Journal of Portfolio Management Clarke, de Silva and Thorley showed that a minimum variance portfolio generated higher returns with lower risk than the market index.
Rob Arnott and his colleagues at Research Affiliates have shown that fundamentally weighted indices (based on earnings and dividends, for example) can generate higher return and lower risk than a cap-weighted index. Remember that the fundamentally weighted index is still a passive index (in as much as it has a set of transparent rules which are implemented in a formulaic fashion).
The chart below shows the return per unit of risk on selected Fundamental Indices vs. the MSCI benchmark. It clearly shows the cap-weighted indices are not mean variance efficient. On average the Fundamental Indices shown below outperformed MSCI cap weighted equivalents by an average 278bps p.a. between 1984 and 2004. They delivered this outperformance with lower risk than the MSCI equivalents, the Fundamental Indices had a volatility that was an average 53bps lower than the MSCI measure. Something is very wrong with the CAPM.
Of course, those who believe in CAPM (and it is a matter of blind faith given the evidence) either argue that CAPM can't really be tested (thanks for a really useless theory guys) or that a more advanced version known as ICAPM (intertemporal) holds. Unfortunately the factors of the ICAPM are left undefined, so once again we are left with a hollow theory. Neither of these CAPM defenses is of much use to a practioner.
Ben Graham once argued that "Beta is a more or less useful measure of past price fluctuations of common stocks. What bothers me is that authorities now equate the beta idea with the concept of risk. Price variability, yes; risk no. Real investment risk is measured not by the percent that a stock may decline in price in relation to the general market in a given period, but by the danger of a loss of quality and earning power through economic changes or deterioration in management".
Why does CAPM fail?
The evidence is clear - CAPM doesn't work. This now begs the question as to why. Like all good economists when I was first taught the CAPM I was told to judge it by its empirical success rather than its assumptions. However, given the evidence above, perhaps a glance at its assumptions might just be worthwhile.
CAPM assumes:
- No transaction costs (no commission, no bid-ask spread)
- Investors can take any position (long or short) in any stock in any size without affecting the market price
- No taxes (so investors are indifferent between dividends and capital gains)
- Investors are risk averse
- Investors share a common time horizon
- Investors view stocks only in mean-variance space (so they all use Markowitz's optimization model)
- Investors control risk through diversification
- All assets, including human capital, can be bought and sold freely in the market
- Investors can lend and borrow at the risk free rate
The idea that everybody uses Markowitz optimization is also massively wide of the mark. Even its own creator Harry Markowitz when asked how he allocated assets said "My intention was to minimize my future regret. So I split my contributions 50-50 between bonds and equities". George Aklerof (another Nobel Prize winner) said he kept a significant proportion of his wealth in money market funds; his defense was refreshingly honest "I know it is utterly stupid". So even the brightest of the bright don't seem to follow the requirements of CAPM.
Nor is it likely that a few 'rational' market participants can move the market towards the CAPM solution. The assumption which must be strictly true is that we all use Markowitz optimization.
Additionally, institutional money managers don't think in terms of variance as a description of risk. Never yet have I met a long only investor who cares about up-side standard deviation, this gets lumped into return.
Our industry is obsessed with tracking error as its measure of risk not the variance of returns. The two are very different beasts. Tracking error measures variability in the difference between the returns of fund manager's portfolio and the returns of the stock index. Low beta stocks and high beta stocks don't have any meaning when the investment set is drawn in terms of tracking error.
To tracking error obsessed investors the risk free asset isn't an interest rate, but rather the market index. If you buy the market then you are guaranteed to have zero tracking error (perhaps a reason why mutual fund cash levels seem to have been a structural decline).
CAPM today and implications
Most universities still teach CAPM as the core asset pricing model (possibly teaching APT alongside). Fama and French (op cit) wrote "The attraction of CAPM is that it offers powerful and intuitively pleasing predictions about how to measure risk and the relation between expected return and risk. Unfortunately, the empirical record of the model is poor ? poor enough to invalidate the way it is used in applications." Remember this comes from the high priests of market efficiency.
Analysts regularly calculate betas as an input into their cost of capital analysis. Yet the evidence suggests that beta is a really, really bad measure of risk, no wonder analysts struggle to forecast share prices!
An entire industry appears to have arisen obsessed alpha and beta. Portable alpha is one of the hot topics if the number of conferences being organized on the subject is any guide. Indeed the chart below shows the number of times portable alpha is mentioned in any 12 months. Even a cursory glance at the chart reveals an enormous growth in discussion on the subject.
However every time you mention alpha and beta remember that this stems from CAPM. Without CAPM alpha and beta have no meaning. Of course, you might choose to compare your performance against a cap-weighted arbitrary index if you really wish, but it hasn't got anything to do with the business of investing.
The work from Rob Arnott mentioned above clearly shows the blurred line that exists between these concepts. The fact that Fundamental Indices outperform cap-weighted indices, yet are passive, shows how truly difficult it is to separate alpha from beta.
Portable alpha strategies may not make as much sense as their exponents would like to have us believe. For instance, let us assume that that someone wants to make the alpha of a manager whose universe is the Russell 1000 and graft in onto the beta from the S&P500. Given these are both large?cap domestic indices the overlap between the two could well be significant. The investor ends up being both potentially long and short exactly the same stock ? a highly inefficient outcome as the cost of shorting is completely wasted.
Now the proponents of portable alpha will turn around and say obviously the strategy works best when the alpha and the beta are uncorrelated i.e. you are tacking a Japanese equity manager's alpha onto a S&P500 beta. However, if the investor is already long Japanese equities within their overall portfolio, they are likely to have Japanese beta, hence they end up suffering the same problem outlined above they are both long and short the same thing. Only when the alpha is uncorrelated to all the elements of the existing portfolio can portable alpha strategies make any sense.
My colleague Sebastian Lancetti suggested another example to me. It is often argued that hedge funds are alpha engines, however, the so called attack of the clones suggests that they are in large part beta betters (a point I have explored before, see Global Equity Strategy, 11 August 2004 for details). If their performance can be replicated with a six factor model, as it is claimed by the clone providers, then there isn't too much alpha here.
Alpha is also a somewhat ephemeral concept. A fund's alpha changes massively depending upon the benchmark it is being measured against. In a recent study, Chan et al found that the alphas delivered on a variety of large cap growth funds ranged from 0.28% to 4.03% depending upon the benchmark. For large cap value managers, the range was -0.64% to 1.09%.
The terms alpha and beta may be convenient shorthand for investors to express notions of value added by fund managers, and market volatility, but they run the risk of actually hampering the real job of investment ? to generate total returns.
A simple check for all investors should be "Would I do this if this were my own money", if the answer is no, then it shouldn't be done with a client's money either. Would you care about the tracking error of your own portfolio? I suggest the answer is no. In a world without CAPM the concept of beta adjusted return won't exist. In as much as this is a fairly standard measure of risk adjustment then it measures nothing at all, and potentially significantly distorts our view of performance.
Perhaps the obsession with alpha and beta comes from our desire to measure everything. This obsession with performance measurement isn't new. Whilst researching another paper (on Keynes and Ben Graham) I came across a paper written by Bob Kirby in the 1970s. Kirby was a leading fund manager at Capital group where he ran the Capital Guardian Fund. He opined:
Performance measurement is one of those basically good ideas that somehow got totally out of control. In many, many cases, the intense application of performance measurement techniques has actually served to impede the purpose it is supposed to serve ? namely, the achievement of a satisfactory rate of return on invested capital. Among the really negative side effects of the performance measurement movement as it has evolved over the past ten years are: