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Sunday, 22 March 2009

Alpha and Beta - Beware Gift Bearing Greeks

A Land of Giants and Dwarves

Anyone involved in the stockmarket for any length of time will eventually come up against the concepts of Alpha and Beta. The terms are freely bandied about as though they can explain the mysteries of the investing universe without, unfortunately, any corresponding explanation of actually what they are.

The best way to think of Alpha and Beta is to imagine a world populated by an inordinate number of very tall and very short people. Everywhere you go you’re either tripping over them or being stood on and squished. As usual the securities industry has latched onto a useful tool and started to use it in an automated, mindless and value destroying way. Of course, the value being destroyed isn’t theirs, it’s ours.

If the CAPM Fits

Alpha and Beta arise out of something called the Capital Asset Pricing Model (CAPM) that was developed back in the sixties and which is used to figure out risk adjusted asset values. Put as simply as possible – the CAPM attempts to adjust the value of an asset, such as a stock, for how inherently risky it is. The more risky it is the more you need to discount its current price to figure out what it’s really worth.

Alpha is a measure of the risk-adjusted return on a portfolio, such as a fund, in comparison with the return on a risk free asset. Assuming that cash in a bank account is the risk-free asset in question (which may, of course, not be so risk-free if it’s stashed in Zimbabwe, Iceland or, the way things are going, the UK) then Alpha measures, over a period of time, how much more (or less) than cash the fund has returned. More usually the risk free asset is the average return on a target stockmarket index. So, in effect, the alpha of a fund is how much more or less than an index it’s returned.

Beta and Volatility

On its own the Alpha doesn’t really tell you a lot. Generally it’s possible to generate excess returns – or losses – by taking on excess risk. So a high Alpha positive to the market might simply be telling you that the fund manager has been gambling and winning. This is where Beta comes in. Beta is a measure of the risk taken by the fund manager in generating their returns. All things being equal – Alpha being “all things” in this case – we should prefer a lower Beta.

In fact Beta is actually measuring the volatility of the assets in question – the amount by which their value varies. Roughly (very roughly), a stock that varies in price between $2 and $3 and averages $2.50 has a lower Beta than a stock that varies in price between $1 and $4 and also averages $2.50.

Technically, Beta is showing the correlation between the portfolio and the wider market. Correlation is simply a measure of how closely the portfolio and market move together so Beta is showing whether the portfolio has higher or lower volatility than the market, while Alpha is measuring whether the portfolio is outperforming or underperforming the market.

The Markets are not Normal

Now in and of themselves the CAPM, Alpha and Beta are useful and interesting things. However, this being the stockmarket, once you give the securities industry a tool they’ll start to use it as much as possible, without regard for whether or not it’s appropriate. And there’s a problem with CAPM (actually there are lots of problems, but we’ll only worry about one of them) which is that it makes an assumption about the way that returns on the market are distributed.

In essence it expects that returns are distributed normally.

That’s a normal distribution over there. This particular one is for the average height of American men. Basically there are a lot of men around the middle value (the “mean”) and the further away you go from the centre the less people there are at the ends of the distribution.

The Tall and Short of It

The CAPM assumes that stockmarket returns are distributed normally over long periods of time. Unfortunately this isn’t – quite – true. Out at the edges of the distribution where we would expect only a few examples of very bad returns or very good returns we find many more than we’d predict (technically the distribution is known as leptokurtic or "fat tailed"). It’s like wandering into a shopping centre and being surprised that there are lots of very tall and very short people wandering about looking cross because the shops don’t stock their sizes.

What this means, in essence, is that the stockmarket goes mad out at the edges far more than the CAPM expects and this means that the models don’t work, some of the time. For hiding under the covers of the CAPM is the Efficient Market Hypothesis, assuming that every investor is coolly and rationally investing all the time instead of wandering around in a confused daze taking their cues from everyone else and hoping for the best.

The markets can behave normally for long periods of time but when they go wrong it can be spectacular. Long Term Capital Management (LTCM) a hedge fund run by Nobel laureates found this out to their cost in 1998 when their normally distributed model collapsed when they were unable to sell assets at any price due to the collapse in the Russian bond market. Only concerted government intervention prevented a massive financial crisis.

As a rule of thumb there are no models that work all the time.

When Beta Goes Bad

This doesn’t mean that Alpha and Beta don’t have a part to play in investors’ analyses, but it does mean that you get some really odd things happening if you rely on them solely. Take a company that’s trading at a discount to its net assets which for some reason suddenly drops further in price. In value investing terms, all other things being equal, that makes it a better investment and less risky, with a greater margin of safety. In CAPM terms, according to Beta, it just got more risky.

Go figure.

Alpha and Beta do give us clues as to how to proceed either as a passive investor or as an active investor. As a passive investor we want to, over long periods of time, maximise our Alpha while removing Beta as much as possible. If Alpha is the expected market return and we invest in an index tracker, tracking that market, we want it to have an Alpha as close to that market as possible and a Beta as close to 1 as possible (which means the index tracker has the same volatility as the index).

The Efficient Frontier

Fundamental index trackers, which track the market on other than market capitalisation, might be expected to offer a higher Alpha but at the cost of more volatility in Beta terms. Generally whether you can accept this would be dependent on your investing horizon. CAPM provides some guidance in this area by allowing the construction of mixed asset portfolios.

The idea is that there is an ideal market portfolio consisting of a higher risk portfolio of assets – shares, possibly – combined with a lower risk portfolio – cash, possibly – which gives the optimal rate of return. The possible combinations of low and high risk assets provide a value for what’s known as the Efficient Frontier – the very edge of returns achievable at minimum risk.

The Efficient Frontier leads us into mixed portfolios of assets – cash, bonds, property, shares, etc – which can be varied to achieve more or less guaranteed levels of return relative to the market – Alpha and Beta – over long enough periods of time. We’ll look more at this elsewhere, when considering passive investing strategies.

When Markets Go Mad, Rely on Old Saws

For active value investors, Alpha and Beta really give very little guide to what you should be investing in. The inadequacy of the CAPM when the markets go mad mean that it doesn’t help at the edges of the investing universe, although it does show quite clearly that the markets tend to revert to the mean. Mean reversion indicates a simple strategy – invest when the markets go mad at the low end and get out when they do so at the upper end.

So guess what? Buy low, sell high.

Related Posts: Newton's Financial Crisis, Fundamental Indexing Can't Save Your From Aliens, Don't Give Index Trackers The Bird, Regression to the Mean: Of Nazis and Investment Analysts, Contrarianism, The Death of Homo economicus

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