When I was a sell-side analyst, I was obliged to publish EPS and consequently, valuation estimates for companies that I published on. An exercise that reminded me of whistling in the dark- a method whereby one attempts to distract themselves from a difficult (or scary) situation by whistling a happy tune. Before I bash estimates (as many are prone to do as they are simply too easy), I think that there are some pragmatic reasons that brokers publish estimates- mostly related to their business of making money by transacting buy/sell trades for their clients in asset management. There is also the very good reason that by publishing estimates, that a consensus is formed and can be tracked and used as a buy/sell signal as well as contribute to market efficiency by encouraging some measure of rigor for EPS estimates and thereby valuation.

However, toward the end of my brief stint(s) on the sell-side, I realized that point estimates were only good for a brief thought by my clients. What I wanted was a framework for them t0 think about EPS and valuation. So I developed a way to test the boundaries and understand and grasp the risks as they considered a stock. I needed a tool to see the broader valuation impacts due to changes in the business climate or management mistakes. So I developed a simple matrix of potential EPS values and earnings multiples that was based upon a combination of prior history. To demonstrate, see the picture below of the S&P 500 2010 valuation matrix:

Figure 1. S&P500 Valuation Matrix

I have taken the earnings per share (EPS) and multiplied it by the trailing 12 month earnings multiple. Simple. What I find useful is that I have taken the 10 year EPS and corresponding multiple and found some basic descriptive statistics including:

- Mean (arithmetic average) EPS over the most recent 10 year period
- Mean (arithmetic average) earnings multiple over the most recent 10 year period
- Standard deviation of EPS over the most recent 10 year period
- Standard deviation of earnings multiple over the most recent 10 year period
- Min/max EPS over the most recent 10 year period
- Min/max of earnings multiple over the most recent 10 year period

I also used the Standard and Poor’s published 2010 estimate for the S&P500 index EPS. (FYI-You can download the original spreadsheet from S&P at the URL listed directly under the pic.) In the past, I would pick a point estimate, assign a multiple based upon some reasoning and make that my target. But I began to think that a matrix centered upon the estimate makes more sense. And rather than arbitrarily select upper and lower boundary values for the matrix, it seemed to make sense to use plus or minus 1 standard deviation and the outer edges of the matrix being the high/low points in the past 10 years.

In the case of the S&P500, if the Operating EPS by Dec 2010 reaches its target estimate ofÂ $46.89 and the market assigns an historical average multiple value of 19.3x, then the resulting level of the S&P500 would be $904.3, representing an 18.1% increase from its current level of $766.04. Now let’s explore what other levels the index might hit. If the 2010 recovery is tepid or nonexistent, then it is reasonable to assume that S&P500 EPS would not achieve its $46.89 level. If it were within one standard deviation on the downside and the earnings multiple were also at minus 1 standard deviation then the value of the S&P500 would be at $392.8. That is bad news. (please note I am not making any predictions here, merely describing how the matrix works.)

If we look at the scenario of minimum historical EPS and minimum historical multiple, then the level falls even further to $222.2. Of course the corresponding upside is max EPS/max multiple yielding an index value of $2703.1.

A couple of points:

- I am using prior data. Now your investment adviser would say that I am making a mistake by looking backwards. While it is theoretically correct that in perfectly random markets, the past does not correlate to the future, I will say that these are known data points in the distribution. This is also merely a tool to look at boundary conditions and potential risk to the upside and downside.
- This remains a work in progress. I am considering using a percentage for the initial upside and downside to EPS and multiples…. say +/- 15% and the outer edges being +/- 1 standard deviation. I may give it a whirl and post it here.
- This is not a predictive tool. It is an exploratory tool. While you may say, what’s the difference? I think there are a couple. Firstly, I am not anchored to a value. As an analyst, I was compelled by my management to make a valuation call. This effectively tied me to a position on a stock that I either had to defend or change and then explain why. This matrix allows us to be intellectually honest and investigate multiple scenarios.
- Lastly, given the hsitorical parameters, I have got to wonder if the risk we undertake in the markets is not much greater than we are compensated by its average returns? Now I am aware of CAPM and beta and the equity risk premium. But when I look at this matrix and see that this underlying distribution has in the past 10 years included the values in the edges of the matrix, then I have to wonder if the equity risk premium is high enough?