Risk premiums for equity: the puzzle and the bezzle

Another note to myself post: an idea I thought I’d blog quickly rather than trying to work through in detail.

One of the big unsolved problems in economics is to explain the risk premium for equity, that is, the fact that the historical average rate of return to equity investment (shares) is much higher (about 6 percentage points) than the average rate of interest on high grade (government or genuinely AAA corporate) bonds, whereas the standard economic model of these things (the consumption-based capital asset pricing model or CCAPM) suggests that the premium should be no more than 0.5 percentage points. The basic idea is that the reason for the premium is that the market portfolio of equity represents a claim on aggregate consumption, so the risk premium must arise from the variability of the growth rate of aggregate consumption and this is small (the growth rate ranges from about 4 per cent in a boom to -3 per cent in a moderately severe recession).

One possible explanation for the puzzle is that equity investment has its own special risks in addition to the riskiness of aggregate consumption. But not any kind of risk will do: the risk has to be correlated with fluctuations in aggregate consumption, that is with the business cycle.

Observation of the current crisis phase reminded me of JK Galbraith’s idea of the bezzle. The bezzle is the amount of undetected corporate fraud. As a boom continues, and everyone does well, people realise they can siphon off money and use it to make even more money. If they are threatened with detection, the original amount stolen can be returned to the till, and thye are still ahead. But, in a crisis, this can’t be done and, in any case, outside accountants are all over the books. So, embezzlers are caught and the bezzle shrinks. It stays small in the early stages of recovery when most decisions are being made by the cautious types who survived the crisis. But as the boom continues, hungrier and less-risk averse types come to the fore and the bezzle begins to grow again.

What this means is that recorded profits (and therefore dividends, capital gains and so on) will be higher than true profits in booms, while hidden losses will emerge in recessions, just when investors need their money. This would imply a larger risk premium.

The bezzle seems to work nicely as an explanation (at least partial) for both the equity premium puzzle and the apparent excess volatility of stock prices (a quick Google search suggests that this idea is not entirely new as regards excess volatility – Eden and Jovanovich had a similar idea a long time ago, but didn’t connect it to the equity premium, and they assumed that the problem was good and bad firms rather than a cyclical fluctuation in badness).

18 thoughts on “Risk premiums for equity: the puzzle and the bezzle

  1. I don’t understand why equity returns are any kind of puzzle. The argument seems to rely on a confusion between excess return and a risk premium. If a stock returns 10 percent over cash in a particular year it does not necessarily mean that the risk premium for that stock was 10 percent, yet this is the required assumption to make the case for a puzzle.

  2. Given rational expectations, the average excess return over a suitably long period must equal the expected premium.

  3. I’ve never come across JK Galbraith’s idea of the bezzle. (It gives me an idea as to why some applied Finance texts refer to the NPV, conditional on weighted average cost of capital, as ‘free cash flow’!)

    There may be another partial explanation. Aggregate consumption (national income data) includes income from businesses that are not listed, while equity return data typically pertains only to listed companies. But this is perhaps so obvious that it is already taken care of in the literature.

  4. “Given rational expectations, the average excess return over a suitably long period must equal the expected premium.”

    This is true in a world where investors know the shape of the distribution of future returns, but that is not the world we live in. We have seen one realisation of the possible path of equities over a hundred years or so, that gives us exactly one data point and zero degrees of freedom to calculate the mean. Many other things might have happened and these possibilities informed the valuations investors placed on stocks.

    If you interpret excess return as a risk premium you are saying that investors in each period correctly anticipated future expected returns. You are also implying that if they knew the expected returns were so high they would not change their behaviour. This seems deeply implausible to me. Can you defend it?

  5. Does the C-CAPM still use the simplifying assumption that the risk free investment is exogenous; that is, everyone can invest as much as they like in the risk free investment and its return will not change in response?

  6. Joseph, this is pretty much the explanation of the puzzle offered by Marty Weitzman. I’m not defending the standard model from which the puzzle is derived, just describing it and observing that, among the many solutions that have been offered, solutions based on specific characteristics of equity as an investment look more plausible than they did.

    Will, the puzzle remains if you assume that the return on the risk free rate is endogenous, and in fact the low value of the market risk free rate is another facet of the puzzle.

    Ernestine, the model is one which typically assumes complete market spanning, so that you can buy securities that replicate the return on non-traded assets like equity in unlisted firms. That’s one of the many problems.

  7. I suggest governments protect listed companies in subtle ways and help them earn higher profits than would be the case from open competition. At a stroke of the pen Coles and Woolies could be prevented from excessive market share, or BHP and Rio Tinto from owning too much coal. There are several plausible reasons; big profitable firms are reliable sources of company tax, they are reliable employers reducing the need for social security, they are good investments for super funds and as public-private partners. Thus pre-bailouts highly profitable companies help governments so in turn governments help them.

  8. If you have a race between a wheelbarrow and a bicycle, you can have any expectation you like, but the bicycle is going to win all of the completed races.

    The bonds have no time diversity and no way to lock in gains, suffer from re-investment risk, and cannot usefully drop into cash. Equities have all kinds of possible diversity and combine potentially unlimited gains with losses limited to 100%.

    Significantly, virtually all of the historical record has occurred in an environment of an inflationist central bank. The actions of the central bank depress nominal interest rates and future discount rates, and adjust real returns downward with significant price inflation. This produces a double whammy for bonds. For equities, most of the time, the reduction in the discount rate increases the net present value of future cash flows far more than the inflation rate reduces real returns.

    Regards, Don

  9. Thanks for the Weitzman pointer – very interesting. I don’t think you can get away with not defending the model from which you draw such strong conclusions, particularly when you use it to make a policy argument as you have in your work with Simon Grant.

  10. Don, this is only true if the race is a marathon. As you can easily check, US bonds have outperformed equity over lengthy periods, despite the better long-term performance of equity. A week or so ago for example, the S&P 500 fell below the level it had reached when Greenspan gave his irrational exuberance speech back in 1996. So an equity investor over that period would have received only the dividend returns, at a rate well below the bond rate


  11. Joseph, we don’t draw policy conclusions from the CCAPM model. We observe that the model fails to explain observed outcomes then consider the implications of various explanations for that failure. So, obviously, we don’t need to defend the standard model – exactly the opposite in fact.

    Weitzman’s argument is one among many possible reasons that CCAPM could fail. Simon Grant and I consider a lot of possibilities, including claims like Don’s that bond investors are simply making a mistake.

  12. There’s a well-documented psychological phenomena where people value potential losses more highly that potential gain.

    The most common experiment showing this involves offering people the choice between receiving a dollar and a 50-50 chance of receiving $3. Most people will choose the dollar.

    I think the risk premium can be explained by an irrational adverse reaction to the greater volatility of equity returns.

  13. John,

    “…A week or so ago for example, the S&P 500 fell below the level it had reached when Greenspan gave his irrational exuberance speech back in 1996. So an equity investor over that period would have received only the dividend returns, at a rate well below the bond rate…”

    It’s not enough to say that bonds have a significant duration of outperformance. You have to consider what the magnitude of that outperformance is. I would be surprised if bonds had a total real return of more than 40% over the 12 years, which would pale in comparison to many far shorter periods of equity outperformance. (only US considered)

    Regards, Don

  14. The post points out we are comparing apples to oranges.

    To measure the correct bond vs equity gains, one has to compare buying equity versus buying corporate bills over the whole term structure, not just long term corporate bonds.

    Gains and losses from the long term yield curve are partially offset by losses and gains from the short end.

  15. Here is another possible partial explanation of the equity puzzle (bezzle?) which might be in the literature because it is obvious:

    The consumption CAPM (CCAPM) belongs to the ‘micro-foundation of macro-economics’ approach (methodology). As such it assumes there is only one physical commodity. This assumption is invalid on empirical grounds.

    PZ: While I have been aware of the equity puzzle as a research topic, I’ve never worked in this area not even casually.

  16. JQ – the reason CAPM throws up funny results is that it is a flawed model.

    Empirical evidence provides no support for CAPM.

    CAPM tells you that the expected return of an equity investment is the risk free rate plus the risk premium for equities times the beta of the particular equity you are buying.

    Er = Rf + b x Rp

    Every study I’ve ever seen shows that empirically there is no relationship between beta and returns. CAPM is just a flawed concept

  17. Andrew at 16, I don’t think “flawed concept” is a meaningful expression. I don’t understand your descripion of the CAPM either. The CAPM ‘tells you’ (if you wish to personify an abstract theoretical model) that under specified conditions there exists a particular relationship between securities prices.

    Further on possible explanations of the equity puzzle (bezzle?). The theoretical model from which the CAPM is derived is that of a private ownership economy with complete (securities) markets. The institutional framework regarding joint ownership of enterprises is very different from the one we have. For example, all returns are assumed to be distributed to shareholders while in our institutional framework it is the Directors who deside on distributions (to themselves and to shareholders). In short agency problems, arising from the legal framework, are not allowed for. A step closer to bezzle?

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s