# Is CAPM a failure?

CAPM says that in order to generate high returns I need to take more systemic risk. But the ex-post results do not seem to validate this theory.

There is a ETF SPHB - PowerShares S&P 500 High Beta ETF (SPHB). If I compare this to plain SPY, I believed that at least on average if not every day I should be rewarded for taking extra risk.

Results since 2011-06-01:

                     SPHB    SPY


Annual average return 12.6% 14.64%

Cumulative return 47.6% 68.08%

Annual Volatility 21.06% 11.78%

As you can see apart from volatility line where SPHB proves true to its promise of more risk, I do not see that I got awarded by more return. In fact I got completely clobbered by putting my money in SPHB.

So what am I missing. Is CAPM and all this efficient frontier thing a complete hogwash ?

Thanks.

Coder.

• Is there anything else we could do for you? Otherwise it would be great if you could accept one of the answers - Thank you :-) – vonjd Mar 9 '15 at 14:01
• You computed annual volatility, but what if you compute the beta from the covariance of the SPHB with the market (SPY etc.). What is the beta? – highBandWidth Feb 9 '16 at 19:15
• Right now according to my analysis it is coming out to be 1.62. Like they say "Your mileage may wary." I think a quote that suits aptly to most things in finance. – George Coder Apr 23 '16 at 16:31

I think the answer to this question must be yes, it is flawed indeed. The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. Yet empirically measures of risk like volatility and beta do not generate a positive correlation with average returns in most asset classes.

The best exposition I have seen so far is this exhaustive survey (150 pages) of 20 different asset classes:
Risk and Return in General: Theory and Evidence by Eric G. Falkenstein

The abstract:

Empirically, standard, intuitive measures of risk like volatility and beta do not generate a positive correlation with average returns in most asset classes. It is possible that risk, however defined, is not positively related to return as an equilibrium in asset markets. This paper presents a survey of data across 20 different asset classes, and presents a model highlighting the assumptions consistent with no risk premium. The key is that when agents are concerned about relative wealth, risk taking is then deviating from the consensus or market portfolio. In this environment, all risk becomes like idiosyncratic risk in the standard model, avoidable so unpriced.

• I was reading the paper you mentioned, until it said something about Jessica Alba and George Cloony.. Yeah Right !! – George Coder Feb 17 '15 at 2:10
• Thank you @GeorgeCoder If my answers was helpful please upvote and perhaps even accept it. I have noticed that you haven't cast a single vote since you joined. Feedback is very valuable for the community - Thank you :-) – vonjd Feb 17 '15 at 18:01
• If all risk is idiosyncratic risk, then the covariance Cov($r_i$,$r_M$) should be high and beta should be low. Is this true for the high volatility stocks? – highBandWidth Feb 9 '16 at 19:16
• @vonjd I guess you missed the sarcasm in my comment. – George Coder Apr 23 '16 at 16:34
• @GeorgeCoder: So do you have something to say that can be taken seriously? – vonjd Apr 23 '16 at 18:32

I would not necessarily call it a failure. CAPM explained ~70% of returns (on average) so this may quite be one of the 30% that could not be explained (see link). However, an improved approach or extension of the CAPM would be the the Famma-French factor model which explains roughly 90% of returns (see link). Again, the Famma-French is an extension of CAPM so you see that it is not a complete failure.

In academics, Roll's critique of the CAPM is discussed a lot, for a start see Wikipedia page of Roll's critique. It is more of a principled "theoretical" critique of the CAPM than an empirical one.

It says basically that the CAPM cannot be tested because

• every mean-variance efficient portfolio satisfies the CAPM
• the market portfolio is unobservable

The CAPM is by no means a failure. While not a normative theory like MPT, but a positive one describing a capital market equilibrium under conditions of risk, the CAPM, if applied carefully, still provides a reasonable basis for methods to value uncertain cash flows, e.g. in capital budgeting. Further, it is at the core of models for derivatives pricing - in particular in cases where perfect continuous replication is not possible.

The failure consists rather in "testing" the CAPM with realized returns.

The CAPM is not meant to forecast that a high beta fund will perform better than a low-beta fund on average in the long term. Neither is it supposed to explain the past performance of these funds.

The CAPM describes relationships between expectations.

It is amazing that still so much effort has been spent on trying to test it with data about returns in the past.

Imagine you want to test what people are expecting today about the performance of GE vs. the Dow over the coming twelve months. So do you call PMs and ask? Do an online survey? Go through all pulished research you can find to try to see a consensus view? Do you analyze current mutual fund and portfolio holdings?

All these seem justifiable methods to assess expectations.

But instead your "test design" is to go on a holiday, come back in a year, and check what the Dow and GE have actually done...???

In principle, and simple terms, the famous Fama-French study tested if historical betas measured with realized returns in the past can explain differences between realized returns in the more recent past... While this was a thorough and valid test of historical relationships between realized returns, this test and all that followed, had and have nothing to do with expectations.

Again, the CAPM describes relationships between expectations. There is no link to realized returns. On the contrary. The CAPM describes a market in equilibrium, at a point in time. In equilibrium, there is no trading. At equilibrium prices, supply and demand are balanced. The CAPM is the Capital Asset PRICING Model. Not the Capital Asset Return Generation Model. There is no explanation at all in the CAPM for anything having any kind of realized return.

Sharpe seems to be a very diplomatic guy. He was relatively outspoken, though, about the distinction between the CAPM and models for the "return-generating process" in his speech when he got the Rijksbank prize for economics in memory of Alfred Nobel, which is downloadable at the Rijksbank web site (the speech, not the prize...).

A few years ago, Markowitz wrote a text called "The "Great Confusion" concerning MPT" - arguing against the common view that mean variance portfolio selection would require normally-distributed returns. One may or may not find arguments to disagree with Markowitz, but if that misunderstanding is as great as the title suggests - it still is dwarfed by the CAPM confusion.

Capital market theory relies on 3 assumptions, Rationality, risk aversion and that returns are normally distributed. In reality returns are not normally distributed, we see an L distribution. What does that means? means that variance (the measure of risk) does not converge to a single number. what does that means, it means that secondary measures (covariance, beta etc etc) are all flawed (beta is a function of covariance which itself relies on the variance which it self does not converge... a circular nonsense. The fact that this simple model tries to boil everything down to a linear model is foolish by itself. Capm is a valid try at modelizing the markets but it fails mathematically everywhere.