This is a big idea because the risk premium pervades modern economics like the luminiferous aether pervaded 19th century physics. It's everywhere and explains everything (eg, why did markets fluctuate yesterday? The risk premium was moving!); it is also impossible to measure. One thing it certainly is not, however, is mere volatility. High beta stocks, and high volatility stocks, have lower than average returns. All financial researchers know if risk is priced, it is a covariance with a factor that proxies our 'marginal utility of wealth', often thought to be something like the S&P500 index. It is not 'total volatility', 'total non-diversifiable volatility', or a covariance with anything, well, intuitive--we've tried everything intuitive. The theory does not work in horse racing, lotteries, junk bonds, private-equity, temporal volatility, options, within equities, options on equities, the yield curve > 3 years, among other investments.
While no one has identified this elusive factor, it's an academic snipe hunt that has been going on for 50 years, and yet academics still believe it exists the same way any true believer knows the truth regardless of evidence. The triumph of theory over data is a powerful thing.
Yet I noticed that over at Journal of Finance editor Campbell Harvey's website, he has the standard two-dimensional plots with risk on the x-axis, return on the y-axis, such as the one below.
Now, Campbell Harvey is a clever guy (editor of the Journal of Finance), and does a lot of solid research. Yet to conflate risk with 'standard deviation' in this presentation highlights how the mind confabulates.
The psychologist Jonathan Haidt has this great study on presenting disgusting scenarios to students, like a story about a brother and sister who decide to have sex (with full protection), and who then decide it was a fun special moment. He then asks people, 'was that wrong?' Modern students generally say they don't have a problem with people doing things that don't hurt others, and in this hypothetical, no one was hurt. Yet most everyone finds it objectionable. So when pressed as to why they don't like it, they first offer reasons like 'they will have defective children', even though the risk of pregnancy was assumed zero, or 'it's illegal', when that point is moot because this takes place in France, where it is legal.
Although we like to think of ourselves having beliefs based on painstaking rational deliberation consistent with our enlightened liberal views, Haidt sees the process as just the reverse. We judge and then we reason. Reason is the press secretary of the emotions, the ex post facto spin doctor of beliefs we've arrived at through a largely intuitive process. Basically, our brains don't like it, and we first reach for the obvious reasons (eg, having Prince Edward-like spawn), and when these are shown deficient, move on to others. We don't like saying, 'because I believe it to be so!' when defending our beliefs.
Harvey knows that standard deviation is not even a proxy for risk, yet when presented with a simple graph that superficially works, he uses it as proof. He cherry picks asset classes where this works, and ignores the ones where it does not. For an experienced finance academic this risk-return nexus is burned into his neurons like our aversion to the smell of toe jam, they know it's true, regardless of what the data say. It's an answer that works for his naive MBA students, and so his rationalizing homunculus got the better of him.
Cam Harvey responds in comments:
... Do I believe in a positive relation between expected risk and expected return? Yes. Is is difficult to measure risk? Definitely. It is even difficult to measure expected returns.
Finally, let me comment on your idea that "risk, however measured, is not positively related to returns." Finance theory says nothing about this. Our theory relates risk to "expected returns" not ex-post returns. To be clear, "risk" should also be expected. I emphasize this in my class. I accept your critique of my graph which should have been labeled "Average Historical Returns" vs. "Standard Deviation of Returns."
14 comments:
Could you elaborate on why standard deviation is a poor measure of "risk?"
Ed, risk is not volatility, it is likelihood and severity of loss over the investor's time horizon, where the horizon is when he will likely need to liquidate the assets.
Eric, Thanks for mentioning some of my class notes. Indeed, that graph of "risk" vs. return was robo- produced by Ibbotson Associates' software.
I totally agree with you that standard deviation is not a complete measure of risk - indeed, much of my research focuses on exactly that point.
I think of risk as anything you don't really like (if you are long the asset).
In addition, risk must be forward looking - not some average of what happened in the past.
Some examples:
*you don't generally like expected volatility
*people want to avoid negative skewness (big downside movement)
*you don't like uncertainty (your inability to measure volatility, skewness)
There are many other "factors" like illiquidity that may also be classified as risk.
David's point is important too. Time horizon is critical. You might not care if your portfolio is illiquid in the short term if you have a longer term investment horizon.
Of course, all of these apply to your portfolio - not an individual asset.
I don't think you can throw out all we have learned post-Markowitz.
An asset can be very volatile but you might like it because it is a good hedge for your portfolio. As a result, the expected return could be very low even though the asset has huge volatility.
I have not read your book. However, I was puzzled by some of your examples.
A lottery is a great example of preference for skewness risk. People like positive skew and dislike negative skew. A lottery has positive skew. Hence, the expected return is very low (people willing to pay a high price to get some positive skew). In the lottery case, the expected return is negative.
Do I believe in a positive relation between expected risk and expected return? Yes. Is is difficult to measure risk? Definitely. It is even difficult to measure expected returns.
Finally, let me comment on your idea that "risk, however measured, is not positively related to returns." Finance theory says nothing about this. Our theory relates risk to "expected returns" not ex-post returns. To be clear, "risk" should also be expected. I emphasize this in my class. I accept your critique of my graph which should have been labeled "Average Historical Returns" vs. "Standard Deviation of Returns."
Dr Campbell,
Forgive my naivete, but of what conceivable practical (non-academic) use is a theory that describes the relationship between two unmeasurable quantities?
Anonymous,
here is another way of asking the question. how would you assign value to a project undertaken today that pays in the future? Finance says you will form an expected return by estimating the probability of future payment and the current discount rate. its hard to measure the expected values you can up with and things change over time, but the reasoning with which you approximated the problem is CAPM, MPT etc.
Cam: thanks for being a good sport.
'Expected returns' is correct,so I corrected this. If risk-return relationship exists, however, I think we have enough data that it would show up in our sample of the real world. Otherwise, 'expected returns' have no empirical meaning.
I mean, it could be every investor thinks they will get higher-than-average returns just as they all think they are better drivers. But that's not an interesting expected return, rather, what's our best statistical guess, and here, delusional investors are irrelevant.
As per skew, I read several papers here, and found the results rather weak. Volatile stocks, and lotteries, have positive skew. Is that why they have low (even negative) returns? What about forming portfolios on volatile stocks, which then due to time-varying correlations, have negative skew? Isn't there arbitrage? What about the low return to negative skew junk bonds that covary strongly with the business cycle? What about the low return to stocks that have a lot of financial distress, and thus conditional negative skew?
Anon. There are plenty of theories in hard sciences like physics where we cannot accurately measure the hypothesized phenomena. In social sciences, it is even more difficult. The bottom line: do you think you should be rewarded for taking extra risk? I think so. Hence, the theory has a sound intuitive basis.
Eric,
Thanks for the response.
On expected returns. You are right that you can learn something from history to develop a long-run expected return. However, the problem is that stocks are so volatile that the confidence band in the expected return is really wide - even with 200 years of data.
Most care about shorter term expected returns. My research shows distinct time-variation in these expected returns. The expected returns are counter cyclical. At the peak of the business cycle, they are very low (when market high) and at the trough of the business cycle they are higher. Again, we are plagued by wide confidence intervals.
Your other questions:
Eric: "Volatile stocks, and lotteries, have positive skew. Is that why they have low (even negative) returns?"
Cam: Yes. Think of it another way. Fire insurance. You pay a premium (like a negative expected return). However, if the house burns down, you get a big positive payoff. The expected return on the lottery ticket is on the order of -55%. There are probably other behavior things going on too.
Eric: "What about forming portfolios on volatile stocks, which then due to time-varying correlations, have negative skew? Isn't there arbitrage?"
Cam: No. This is not arbitrage. Arbitrage means returns with no risk. Skew is risk. A famous example of of this is many the Money Market (or Short-Duration) funds (pre-crisis) that were offering "alpha". They were investing in Treasury bills and other short term paper but also writing some options. The premium they were getting for writing those options helped them "beat" the market. They marketed it as "alpha". But no. This was just some extra risk in terms of negative skew that they were taking. Bad event happens and big negative returns were realized.
Eric: "What about the low return to negative skew junk bonds that covary strongly with the business cycle? What about the low return to stocks that have a lot of financial distress, and thus conditional negative skew?"
Cam: Again, let's be careful about returns and expected returns. Take the stock example. A stock can be distressed. If you look at the historical returns, it has a historical negative skew (because price likely went down rapidly). However, given the price is low, the expected (conditional) skew could be positive.
Another skew example I like is the Internet bubble. Who in their right mind would pay 100x earnings for some of these stocks? Yes, some of this was a real bubble. But some of it was skew. People were buying these stocks like lottery tickets. They were willing to accept that the expected return were negative. However, there was a chance at investing in the next Microsoft (positive skew). Google was one of those stocks.
Skew like expected returns, is hard to measure. Volatility and kurtosis are much easier to measure.
I forgot to promote my own blog. Hope you don't mind.
Blog http://dukeresearchadvantage.com/author/charvey/
Twitter http://twitter.com/camharvey
Cam: I see that in Campbell, Hilscher and Szilagyi (2005) that the higher distress portfolios do have higher positive skew, so I guess it doesn't all go away in aggregation. Your paper with Siddique excluded firms w/o 60 months of data, about 40% of the sample. That's a lot. Reading Conrad, Dittmar, and Ghysels (2008ish), I see the skew factor is sufficiently messy to see a lot of things (ie, its correlated with vol, and kurt, and can be considered in aggregate, or total, depending on the author). Ang, Chen, and Xing (2002) emphasize downside beta, negative coskewness, positive related to all firms be the highly volatile stocks, where the return was negative. Further, value and small companies that have higher than average returns (who knows what their expected returns are!), have positive skew.
So, skew is hard to isolate, ambiguously defined, and results are rather tenuous (I think your paper with Siddique found only that it did as well as the FF-3factor model).
If people hate, say, covariance with the S&P, yet love conditional positive skew, the theory becomes a lot like Freudian analysis, it's hard to not get the answer (expected return) your id wants.
I would be persuade the theory worked if a single intuitive SDF--not different for every asset class--could explain the negative beta/volatility&average return correlation we see over time, in call options, leverage between public firms (no Miller Modigliani effect on returns), the low returns to B-rated bonds and their equities. Also, the null relation between any metric of risk and futures returns, private businesses, currencies, world country returns (update your 1995 paper, and look at geometric returns--nothing), past the mid point in the yield curve. As an explanation for the data we see, risk is basically for explanation, not prediction.
Does investing in Greece, at this point, imply a higher expected return? Well, it feels riskier than most people relative to Swiss bonds, but I think it would fall into the class of bonds that historically, has not significantly outperformed BBB rated bonds (ie, B). I would bet it underperforms nonetheless, because too many people are hoping for a lottery return if Greece goes back to its old glory (ie, 330 B.C.).
Anyway, my theory why risk is not related to expected returns in general is here. (I acknowledge that at super high risk, people tend to like to buy lotto tickets in various forms, but these are deluded; also, there is a small risk premium as one goes from a medium of exchange like Fed Funds and US Treas to slightly less risky stuff, but that's in the book, not that post). My videos on this subject, which has a unique survey of empirical work for MBAs, is here.
Eric: I have to get back to my day job but a few last comments.
Finance is a very young field. The first empirical asset pricing study was published in 1972.
It is true that people are searching for the model that makes sense -- and works. The models that we have right now are relatively crude.
Covariance (conditional, changing through time) is hard to estimate. The factors by which it is measured against also have to be defined.
On skew, I agree that the same issues arise as with covariance.
I agree with you that we need the single SDF to explain all asset classes. We do not have that.
Does that mean that we abandon the ship? No. To me, the gap in our understanding makes the field of finance extra interesting. There is a lot of progress to be made and that is exciting. I am hopeful more and more insights will arise from the research.
Eric,
I just finished reading "Panic" by Redleaf & Vigilante. I liked it; you might too.
This book also lambasts the idea that risk leads to greater reward. They make the obvious point that being better [i.e. smarter, faster, etc.] leads to greater reward, NOT risk per se!
Regards,
Michael
Cam stated:
"People were buying these stocks like lottery tickets. They were willing to accept that the expected return were negative."
1) Most money in the US is run by institutions. If professional managers (like myself) have become such relativists that expected negative returns are now acceptable, that's a sorry state of affairs.
2) Re. individual investors during that bubble: I know many who quit their day jobs to trade. They didn't do so because of the skew. They thought it was a *reliable* source of income.
I discussed the bubble in realtime with many people. None of them acknowledged the expected negative return. Your assertion above is simply wrong. Instead, as Eric notes, they were simply deluded.
"The bottom line: do you think you should be rewarded for taking extra risk? I think so. Hence, the theory has a sound intuitive basis."
But Eric's point is that you're not rewarded for taking on extra risk in the real world. And his point is consistent with anecdotes you read about successful entrepreneurs who don't seek out inherently risky areas but instead seek out areas where they think they have an obvious edge and try to minimize their risk.
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