# Are there ways to measure the risk aversion of a representative investor, based on publicly available market data?

Are there ways to measure the risk aversion of a representative investor, based on publicly available market data? Public available data could include asset price, volume, and flow data, and may be aggregated according to some criterion (asset class and contract type being the most obvious). Pointers to any existing literature are greatly appreciated.

• By risk aversion do you mean the economics version -U''/U'? Or is there a more practical version? If you're looking for the econ version, then there's a lot of work on this. Unfortunately none of it is very promising (probably for the reasons Dirk lists). Most find that investors demand returns that are too high given risk aversion estimates and the stability of wealth and consumption (called the equity premium puzzle). Let me know if I'm way off base, but this may give you some leads/ideas: academicwebpages.com/preview/mehra/pdf/… Feb 9, 2011 at 2:52
• @richardh Thanks for pointing to th original article by Prescott and Mehra. I didn't know it had a derivation of risk aversion from asset class returns. Feb 9, 2011 at 12:21
• NP. I just remembered Richard Thaler has a take on this same problem and figures out how to make it work with a different utility function (loss aversion, which I think some consider irrational). It might have a more practical approach. www.google.com/search?sourceid=chrome&ie=UTF-8&q=q%3D (I have the pdf if necessary) Feb 9, 2011 at 14:07

By definition, the average investor holds the market portfolio. Risk aversion can be measured as the slope (i.e. ratio of expected returns to volatility) on the efficient frontier. Therefore, the risk aversion of the average investor assuming the S&P500 is the proxy for the market portfolio is the expected returns of the S&P 500 divided by the volatility of the portfolio.

Suppose that you have a model of returns, and a representative agent whose form of utility function you have specified right off the bat. This RA can be constructed, under conditions, from a population that is defined to have heterogeneous utility objectives. This is the problem of aggregation, and it's treated in every good asset pricing theory text (e.g. Skiadas' Asset Pricing Theory or Duffie's Dynamic Asset Pricing Theory). @Dirk is unfortunately wrong: virtually all financial models (even B&S!) assume an RA; and the CAPM and market portfolio have nothing to do with the existence or not, in theory or in "reality", of an RA in asset pricing.

If you want to estimate or otherwise assess risk aversion, you have to have such a model explicitly spelled out. Otherwise you will have to estimate a distribution of risk aversion coefficients, that is virtually impossible - unless you have data on the initial positions of every player in the market! You also need a measure of consumption growth - as creative as possible.

Now @Tal Fishman's answer is accurate. Lucas's (1978) "Asset Prices in an Exchange Economy" model, when applied to equity premium data predicts a coefficient of risk aversion for the utility function of the RA that is exorbitantly high - and hence "unreasonable". This is the equity premium puzzle -- there is also a dual puzzle in the relevant literature, called "risk-free puzzle".

Economists have tried to resolve it. Currently, the consensus in the literature seems to accumulate on the solution proposed by Rietz, and put forward by Barro and his student, Ian Martin in a series of very interesting papers. In sum, a model that is consistent with market anticipation of "rare disasters" in consumption growth can produce reasonable (i.e. low to the point of being manageable) coefficients of risk aversion in such an RA asset pricing model.

This is the canonical theory. A Taleb kind of approach, commonly known as "decision theoretic" (cf.@richardh's comment above) can extend standard expected utility constructions in theoretical asset pricing into having different forms of utility objectives, probability assessments of future events, or what have you. Doing empirics with these models is very often impossible.

As a practical solution to all this, one would suggest to estimate the changes in risk aversion of whatever model you predefine, and not its absolute level. But you certainly need an RA model, whose use is put to work every time you compute the beta of a stock or a market portfolio.

Short answer yes! It's called VIX. When it goes up, investors are afraid. When it goes down, investors are complacent.

There are multiple components to this but in a very general sense one has to look at two things: The "credit" spread and the "cost of insurance" The former tells you how much excess return the representative investor is demanding to be compensated for the risk of counterparty default. The later tells you how much an investor is willing to pay to defease a risk over a given interval. Insurance can come in the form of credit default swaps, option premium or in some cases the contango.

Answering this question is impossible without making many significant assumptions regarding risk preferences, utility functions, a model of returns, etc.

One way to measure the risk aversion of the representative investor is to compare the market's expected return to expected volatility. When applied to the allocation decision between equity and fixed income, this is known as the equity risk premium. The equity premium puzzle, first pointed out by Mehra and Prescott (1985), holds that this difference is too large to be explained by most reasonable models of investor risk preference.

Damodaran details a number of ways in which equity risk premium is commonly measured. For example, combining the implied equity risk premium with implied volatility from the VIX, one can directly obtain a measure of the market's current risk aversion.

Cochrane (2011) discusses the variation among and commonality between risk premia in different asset classes.

Going out on another limb here: No.

First off, there is no representative investor. If we were all the same, the CAPM and the market portfolio would hold. So that part is unobservable.

Second, that is why the sell-side strategists are to happy to create things like misery indices (bad example as it's more macro-based in its sum of inflation plus unemployment), or vix plus credit spreads, or things like AAII sentiment, or speculators/hedgers rations, or put/call ratios, or ... You get the drift.

All that said, I'd love to be proven wrong and see estimates of one such beast.

• With regards to the first point, there is a representative investor, and that doesn't mean we are all the same... books.google.com/… Second point. That is why I am actually asking the question. I am trying to understand if sell-side strategists are bullshitting, or at least if there is some empirical methodology to come with a measure of risk aversion. Feb 9, 2011 at 12:13
• Because some papers stipulate an abstract concept ("representative invenstor") that is useful in an economic model does not make it observable---so still no way to estimate this as you had asked. Secondly, per EMH :), if this was as easy to pull together as you seem to imagine ... some sell-sider (or academic economist) would have done so. So I stand behind my No you can't. Feb 9, 2011 at 14:00
• Sell-side people talk about changes is risk aversion and risk appetite all the time. I should ask them but I am a bit shy. Apr 10, 2011 at 14:34
• @DirkEddelbuettel : an army of academic economists have tried to pull it together, since the early 1960s. These are not "some papers": it's the current edifice of asset pricing theory. Putting forward an EMH argument to contradict this is like asking why there were no cars in the middle ages since donkey transportation is an inferior technology. Theory is theory until proven otherwise. Sep 28, 2011 at 9:47
• Right, a 40 year old paper is proof that all is well with the world (and the EMH). Where have been the last two decades? Or, for that matter, in 2007/2008. Moreoever, your critique entirely misses the point that we still have operational answer to the OP's initial question: What would be the risk aversion of the representative investor be (assumed he existed) ? You also misunderstood my previous comment: I am not looking for MathEcon proofs, I am looking for operational predictions from your beloved theory which can withstand at least somewhat economtrically sound tests. There are none. Sep 28, 2011 at 15:15

I second @DirkEddelbuettel here. Measuring aggregate risk aversion implies abstracting away and making an explicitly artificial theoretical construct. There does not 'exist' a representative investor. What we have are investors, traders, with varying risk aversions, utility functions with differing parameters (if not functional forms). The distribution of risk aversion coefficients which @Dimitris says is virtually impossible, is obviously closer to reality, complex yes, but more plausible. Masanao Aoki's work is on lines such as these [ econ.ucla.edu/faculty/regular/Aoki.html ], though not directly at the level of specificity in finance.

Even as far as estimating the utility function of one investor is concerned, that is non-trivial, even as from a more recent text on the field [ http://amzn.com/0521748682 ]. I am not sure how coming up with a summary statistic for a few million investors is any easier.

Also, it might so happen that there are periods when a greater number of investors converge in their utility functions, and at other times, there is greater dispersion. i.e. if there is a distribution of the utility function parameters over the set of investors, the moments are constantly fluctuating in a non-trivial way. Also, the existence of a representative investor, I think, implies that we are concerned only with inter-temporal decision making, and hence investing/trading - whereas, the reality of trading is a mix of inter-temporal decision making coupled with heterogeneity of investor/traders.