In order to forecast the future movements of an equity market you need to know several things, but I want to keep this discussion as simple as I can. Perhaps the easiest way to make a forecast is to predict corporate earnings, and then to predict what the Price will be as a multiple of earnings. If I have earnings (E) and the prevailing Price to Earnings (PE) ratio, then I can predict price. I think that may be about as simple as I can make it.
But let’s simplify the problem even further. Let’s assume that we all share the same earnings forecasts. Under this assumption, all we have to do is forecast a PE ratio, and we are done. Let’s make the problem even easier by assuming that the risk-free rate of return is known and fixed over whatever we think the relevant time frame is. If all of this is true, then the only reason that the PE ratio will change is if the Equity Risk Premium (ERP) changes for no apparent reason. Given earnings, the present value of those earnings is a simple number. It is a function of the earnings and the discount rate, and the discount rate is simply the sum of the Risk Free Rate and the Equity Risk Premium. Now, we have simplified an impossibly hard problem to the estimation of a single factor the ERP.
Again, the relevant discount rate is simply the risk-free rate plus something more. We call this “something more” the Equity Risk Premium. If we all agree on expected earnings and the risk free rate, the only reason P/E will change is if this risk premium changes. Once we know that number, the problem is solved. So how do we figure out that number. (I know I am being redundant here. I an just underlining the ridiculous reduction to a single variable.)
Each year a Professor at NYU (Aswath Damodaran) works with colleagues to publish a lengthy paper on estimating the Equity Risk Premium (ERP). This particular work is noteworthy because it is updated annually. Thus, it provides a track record of these estimates over time and discusses how they evolve. The ERP is never known with certainty, but having some estimate is a necessary input to any forecast even if everything else is assumed to be fixed.
There are several ways to get this estimate. First, it can be done based on using surveys of investors. Second, a calculation can be done using historical data. Finally, it can be estimated based on the current prices of equities and options. Let’s look at each of these approaches in turn.
Fernandez, Aguirreamalloa, and L. Corres (2011) compared both the level and standard deviation of ERP estimates provided by analysts, companies, and academics in the United States. (Not sure why anyone would ask the academics, but we appreciate the attention anyway.) The averages based on surveys of the three groups were surprisingly close. The average from the Analysts was 5.0%. The average from the academics was 5.6%, and the average from CFO’s was 5.5%. This is consistent with the ways that such info is typically presented in the Financial news media, where we will hear something like, “the average analyst estimate is 5.5%.” Sounds comforting doesn’t it? However, if we look a bit closer we see that the range of the estimates was from 1.5% to 15%. So which number would you choose? The fact that the average of a collection of digits can be stated to 2 decimal places should not be taken to mean that the experts agree, or that any of them had any idea of what the real value is. Any list of numbers will have an average. The simple fact is that the best informed, highest paid, and experienced experts are all over the map on this simple question.
If we narrow the discussion to analysts based in the US we see a similar average near 5.8%, but the estimates ranged from 3.2 to 10.5%. Think about what this means. One analysts believes that the “average” company in the S&P 500 index has to promise a return of 3.2% above the risk-free rate, while another thinks that it will give at least 10.5%. I am willing to bet that the right answer is somewhere in that range, but if you ask me where, I will state with the greatest confidence and conviction that I can muster, “I have no idea.” On the other hand, each of these analysts will tell you an exact number with equal confidence and conviction. After each of them are shown to be wrong (because all forecast are ultimately incorrect), they will compose a great story to explain the difference, but your money is already gone by then.
An alternate approach is to use historical data to develop an estimate. We can always look at earnings histories and prices, and work backwards to find the ERP that held at that moment in time. We can then average these values in some way to come up with an estimate. There are at least 3 problems with this approach. First, it is backward looking by definition while current prices are based on what we think will happen in the future. Second, the current setting is not an exact match with any prior setting, and the ERP can be different when economic factors or public sentiment differs for any reason. Third, this number is surprisingly sensitive to what period is taken and the sample used.
Most of those who use this approach argue that the risk aversion of the average investor has changed over time. A much wider swath of the US population is invested in the Equity markets today compared to prior generations. Thus, the very definition of the “average investor” is not really stable. A related problem is that the standard deviation in stock returns between 1928 and 2023 is 19.55% (roughly 20%). Recall your first statistics course where you were taught that the standard error in an estimate is the standard deviation divided by the square root of the number of observations. Why is this a problem? Well one can easily argue that the last 25 years are significantly different than the period from 1926 to 1999. If you want to focus on the last 25 years, then you have a standard error of roughly 4%. If you have an estimate of the ERP of 4% with a standard error of 4%, have you really said anything useful? You can’t even say that you have strong statistical evidence that the ERP is different from 0, even though common sense tells you that it has to be.
Here is another approach. At any point in time we could look at that moment’s projected earnings and prices and work backward to estimate the ERP in place at that instant. Intuitively, this feels better because, at least we can say it is based on data and the state of knowledge in place at the time. Of course, this is only useful if the current ERP is a reliable estimate of what it will be in the future. This might make sense if these estimates have small error terms and are stable over time. But, as we have already stated, neither of these claims appears to be true. Finally, let’s not lose sight of the fact that what we really need is not the ERP today, but a forecast of what it will be tomorrow.
Damodaran conducts an interesting exercise. He uses all of these approaches to predict the ERP in the following 5 years. For a predictive model to have power we will have to see correlations between the model inputs and the output of interest. When we look at correlation between model inputs including 1) Current Earnings Yield, 2) Dividend Yield, 3) Current Implied ERP, 4) Historical ERP values, and 5) ERP based on default spreads, we see correlations of 0.136, 0.152, 0.05, -0.107, and 0.286. In other words, the correlations are not very high, and in some cases even negative. In addition none of these correlation coefficients are statistically significant at the 1% level. Oh well.
Ultimately, what’s the point here? Think about what we have laid out. We took a very hard problem – predicting future equity prices – and made VERY, VERY strong assumptions to reduce the problem to one of estimating a single variable (the ERP) that has a long history and is explored by millions of people every day. Even with these unrealistic assumptions to simplify the problem we still end up with an intractable problem just to estimate a single variable.
On top of these difficulties, we also have to wrestle with a host of other problems to come up with earnings estimates, including risk free rates, exchange rates, and investor sentiment. If you cannot come up with a number for one single component of the larger problem that you have confidence in, how will you ever come up with a number that also includes estimates of 5 other parts of the equation?
With all of these issues in place, why would you ever have any confidence what-so-ever in the market prediction that you ran across this morning on the news? The only reasonable response seems quite clear. Your prediction means nothing to me. I am going to choose the approach that makes the most sense to me and stick with it.
REFERENCES
Damodaran, Aswath, Equity Risk Premiums (ERP): Determinants, Estimation, and Implications – The 2024 Edition (March 5, 2024). Available at SSRN: https://ssrn.com/abstract=4751941 or http://dx.doi.org/10.2139/ssrn.4751941
Fernandez, P., T. Garcia and J.F. Acin, 2023, Survey: Market Risk Premium and Risk-free Rate used for 80 countries in 2023, SSRN Working Paper, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4407839
