Vol 2, Issue 2, Quarter 4. 2025.

There is an old saying among investors that the price of a stock is simply “a number from today multiplied by a story about tomorrow.” Therefore, if we want to generate a forecast of the future movements of an equity market you need to know at least two things. The first one (a number from today) is pretty easy to get. The second one (the story about tomorrow) is clearly “a matter of opinion”. That’s a polite way of saying that it’s a wild-assed guess!! Let’s consider the simplest way that I can think of to make such a forecast. We can assume that the Price of a share of stock in the near future (say 12 months from now) will be as a multiple of earnings. If I have earnings (E) and the prevailing Price to Earning ratio (P/E), then I can state the current price. Stated differently, if I can find Earnings today and the current price, I know the prevailing P/E ratio. If I can get a reasonable forecast of earnings (relatively easy) and multiply that by the P/E ratio that will hold in the future (my story about tomorrow) I can predict the future price. Sounds pretty simple right?

Let’s simplify the problem even further. Let’s assume that we all agree on the aggregate earnings forecast for a common unit of analysis, such as the S&P 500. (We all know that this cannot happen in truth but play along for a moment.) Under this assumption, all we have to do is forecast a P/E ratio and we are done. Let’s make the problem even easier by assuming that the risk-free rate of return over the next 12 months is known and will not change over that planning horizon. (Again, this is nonsense, but work with me here.) If all of this is true, then the only reason that the price will change is that the P/E ratio changes. In addition, if we agree on the risk-free rate, then the only change in the P/E ratio comes about due to a change in what is known as the Equity Risk Premium (ERP). The ERP is simply the extra return that you have to expect in order to be enticed to hold equities.

Now, we have reduced our problem to the estimation of a single factor – the Equity Risk Premium. This is true because, if we are given a value for future earnings, the present value of those earnings is a simple function of those earnings and the discount rate. The relevant discount rate is simply the risk-free rate plus the ERP. Stated differently, once we know the ERP, the problem is solved. So all we have to do is to figure out that single number. (I don’t think that I can make it any simpler than that.)

Fortunately for us, eggheads love thinking about this problem. In fact, each year Professor Aswath Damodaran at NYU publishes a lengthy paper on estimating the Equity Risk Premium (ERP) using current data. (For details, see the latest version here: ERP 2025) This particular work is noteworthy because it provides a track record of these estimates over time and discusses how they evolve. There are several ways to get this estimate. First, it can be based on 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 the prices of related options. Let’s look at these three approaches in turn.

One research paper by Fernandez, Aguirreamalloa and L. Corres (2011) (US Market Risk Premium) compared both the level and standard deviation of equity risk premium estimates provided by analysts, companies and academics in the United States. The average estimates 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 information is typically discussed in the Financial news media, where we will hear something like, “the average analysts estimate is 5.5%.” Sounds comforting doesn’t it? However, if we look a bit closer, we see that the range of the estimates from this large group was from 1.5% to 15%. So which number would you choose? The fact that a collection of expert opinions expressed as numbers has an average should not be taken to mean that there is any degree of agreement among those so-called experts. The best informed, highest paid, and most experienced experts are all over the map on this simple question.

If we forget the Academics and CFO’s for a moment, and narrow the discussion to Analysts in the US we see a similar average near 5.8%. However, the underlying estimates ranged from 3.2 to 10.5%. Think about what this means. One analyst believes that the “average” company in the S&P 500  index has to promise a return of 3.2% above the risk-free rate to attract buyers to that company’s stock, while another thinks that the same company has to give at least 10.5% to attract the same dollars. I am willing to bet that the right answer is somewhere in that range, but if you ask me where, I will tell you immediately, I have no idea, and the data suggests that neither do they. Of course, each of these analysts will tell you an exact number when you ask for it and they will state it with a regal air of confidence. After they are shown to be wrong, they will also compose a great story to explain it, but by then your money is already gone.

In addition, this number is not stable. If the ERP drops, then the value of the stock rises. If the ERP rises, then the price falls. Equivalently, if the price rises, the analysts can say that the ERP fell, and if the price falls, they can say that the ERP rose. Exactly what are you supposed to do with that brilliant insight? Again, I have no idea.

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 appeared to hold at that moment in time. We can then average these values in some smart sounding way to come up with an estimate. There are at least 3 problems with this approach. First, it is, by construction a story about yesterday, while current prices are based on a story about tomorrow. 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 span of time is taken to be the sample used.

Most of those who use this approach also argue that the risk aversion of the average investor changes over time. For example, a much wider swath of the US population is invested in the Equity markets today, when compared to prior generations. While this is certainly true, what it implies is an open question. A related problem is that the standard deviation in annual stock returns between 1928 and 2023 is 19.55% (roughly 20%).  Recall your first statistics course when you were taught that the standard error in an estimate is the standard deviation of the underlying data, divided by the square root of the number of observations (SE = SD / n^0.5).

What the hell did he just say?

The confidence in my prediction depends upon how noisy the underlying data is, and how many observation I have. The less noise the better, and the more observations the better.

Why is this a problem? Well one can easily argue that the last 25 years are significantly different than the period from 1926 to 2000. If you want to focus on the last 25 years, then you have a standard error of roughly 20%/5 = 4%. (Remember that 5 is the square root of 25.) 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 evidence that the ERP is different from 0.

Here is another approach. We can look at current earnings and prices and work backward to estimate the ERP in place at the moment. Intuitively, this feels better because, at least we can say it is based on actual, current data. 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.

What’s  the point? We have taken a very hard problem – predicting future equity prices – and made 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 setting, we still end up with an intractable problem.

On top of these difficulties, we also have to wrestle with a host of other problems to come up with earnings estimates, risk free rates, exchange rates, and investor sentiment. If you cannot come up with a convincing number for one component of this problem, how will you ever come up with a number that also includes estimates of 3 other parts of the same 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 your favorite financial news site? 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. For us, that approach is easy to present.

1. The time to invest is NOW. The amount to invest is the money that I do not need to live off of today.
2. The correct share of equities in my portfolio is as much as I can stomach.
3. The correct planning horizon is the retirement of my grandchildren.
4. Diversification is the only free lunch that I know of, and I want it at the lowest possible cost.
5. Until I feel like I have a better model, that I can live with in any possible outcome, this is my plan and I am sticking with it.

Whatever you are selling that deviates from this plan is of no interest to me. Have a nice day!