Equilibrium asset pricing models - a quickie (a bit technical)
In my traditional daily trawl through FT Alphaville's in addition reading (well worth looking at, registration required however free - it is not at the back of the FT's paywall) I got here across this little gem.
It's worth reading the total article, however I'd similar to to cite a couple of elements:
"Actually I think there has been historically quite a lot of interest in models based on macro factors that would lend themselves relatively naturally to interpretation in terms of equilibrium valuation models. The problem is that they don't tend to work very well empirically... those models just didn't do a good job of explaining a substantial fraction of asset returns... Plus they usually seem to have unobservable or hard-to-observe components. For example, any model of interest rates is going to have to have some place for a market price of interest rate risk.... Even a small error in that estimate is going to produce a huge discrepancy to observed yields."
To be clear we're talking about models of the form P = f (a,b,c....) where P is the 'correct' asset price, and a,b,c are factors like for example the market price of interest rate risk and other such. To make these models work you also need to know the factor loadings; if the model was linear these loadings would just be the coefficients on the various factors in a pricing equation.
If this sounds like mumbo jumbo, bear in mind you probably already know about one such model, which is the CAPM (if you don't know what the CAPM is then it's still going to sound like mumbo jumbo and this post probably isn't for you). In the CAPM the factor is the market return and the loadings is the much maligned beta (covariance with the market). The CAPM equation is specified in excess returns rather than expected values, but it's easy to switch between the two when we note that the correct value is equal to todays price plus the expected return. If we add in the expected speed of reversion to the correct value then we can make the two approaches equivalent.
Now I've spent a fair bit of my own time in the past messing around with these models, and I have a few thoughts and ideas to share. To make this post more tractable I'll refer to a specific examples: where we are trying to estimate the equity risk premium.
Choice of element
There is an unfortunate habit in the literature of these models to choose factors which have nice economic meaning, regardless of whether they are observable. So for example in the equity risk premium world it usually makes more sense to use expected real interest rates. However it's difficult to get inflation expectations for some long horizon. In some countries you can use inflation linked securities, but biases mean it's not easy to extract inflation expectations from them. Survey measures are better, but will rarely go back (for a longer and better discussion of this see Expected Returns ).
It's tempting to fall back on creating your own model to forecast inflation. A reasonable model could consist of an equilibrium (primarily based on a shifting average of inflation), a price of exchange (recent modifications in inflation) and survey and asset fee measures if available. Note but we've just exploded the quantity of coefficients we must estimate. Also if the version is to forecast a long time in the destiny (say twenty years) it'll consume a variety of information records, and waste the final many years well worth.
An ugly class of models is wherein the loadings are designated, and you find the elements. This is done in elements of the bond pricing literature. One of the few great matters about the macro factor fashions is that the factors have a few form of which means. But rather than have intuitive interest price elements just like the stage of rates, and the steepness of the curve, we've a element that is based totally on a unusual function of forward quotes.
Reversion to equilibrium
An obvious point is that these fashions are not any exact in the event that they don't get the equilibrium price correct. As the quote notes a moderate distinction within the equilibrium could make a big difference. For instance the equilibrium PE ratio of stocks (which we are able to extract from the fairness risk premium) under one model might be 20, and with slightly one of a kind assumptions it is probably 15. Give the ordinary range of stock PE ratios this could make a huge difference to performance.
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| Supply: investopedia |
The opposition - kitchen sink
You can think of a macro factor model as a big bunch of variables in a regression; on some of which the coefficients or relative coefficients are specified (like the current real interest rate is the nominal interest rate minus current inflation); and others (the loadings) which we have to estimate.
Given all of the caveats above you may conclude the quality technique is to simply throw all of the observable elements you have into a large kitchen sink regression and let them combat it out. So instead of trying to cobble together an inflation forecasting mini model as above, you simply chuck the underlying observable variables into the regression with the whole thing else.
But the huge benefit of getting a few pre-current shape for your information is it reduces the degrees of freedom, and in case you are proper about the structure will give you a stronger version.
(You may also take a Bayesian view that you suppose your imposed structure is correct, until confirmed statistically false).
The opposition - simple imply reversion
There is an excellent less complicated method, that is to do a easy suggest reversion version on one or more valuation elements. So in shares you'll simply take the records of PE ratios, after which take some type of sluggish shifting common to degree the equilibrium. If the PE dips beneath that equilibrium then you buy; otherwise you sell.
Mild improvements can be made to this by incorporating more sensible variables, as is done in the CAPE model with real earnings, as long as you don't put yourself into a position when you have to start estimating coefficients again.
Mean reversion isn't, generally, sturdy sufficient
These macro models should have an advantage over a kitchen sink approach where the same kind and number of underlying variables are regressed without any structure being imposed. However they're unlikely to beat a relatively simple mean reverting model. Worst still all such mean reverting models only perform well at relatively slow time scales, useless to any active investor.
If as an instance you're forecasting at a horizon of some months, and also you upload a 'momentum' element on your version, you will discover it dominates all of your other predictive variables.
What kind of valuation model works at sensible time scales?* No, not a macro model but a micro, relative value, model with asset specific factors in it. In this case we don't need to worry if the equilibrium is correct or not; it's implicit in the fact that we have no net exposure, only relative value bets.
* though having said that relative momentum is also important in these kinds of models.
Good at telling you where you're... Now not where you're going
I have similar feelings about these kinds of models as I do about "big data" (bear with me). Big data, it strikes me, is very good at modelling the current behaviour of for example spending by loyalty card shoppers*. Each of those shoppers is relatively similar (they all go to the same supermarket for a start), and importantly they are not interacting with each other, nor do their shopping habits change much when for example the US non farm release comes out. Unless their behaviour changes radically, which it tends not to, we can make some reasonable predictions about how they will behave.However huge data and marketplace forecasting is extra difficult. The prices are a result of a huge quantity of pretty heterogenous contributors interacting, and reacting to exogenous information and shocks, in a manner that supermarket consumers hardly do. At exceptional you could overfit to the acute and tell a few interesting memories. Just don't strive the usage of it to change.
Similarly properly specified macro models can tell you some very exciting tales about the past. So it is feasible to disaggregate the fairness threat top class (with out by the way wanting to estimate any coefficients), and conclude that a lot of the excess return of equities in the ultimate 40 years is due to an earthly fall in inflation.
The most effective beneficial prediction I can make out of that is that equity returns are likely to be decrease within the future. That's beneficial, however it slightly qualifies as a forecast and its no use in anyway for any kind of dynamic buying and selling.
Conclusion
It's a laugh playing with macro fashions, and they're intellectually interesting, but they haven't any location within the armory of any investor or trader.
