Last week Deutsche Bank sent an internal note arguing that, well, it may be about time for the Fed to raise rates, claiming that ‘in fact, it looks more and more like the Fed is behind the curve’. For such a claim, the note reviewed a series of inflation indicators (e.g. PCE, CPI), but the really interesting chart was the last one, in which the analysts’ consensus for the S&P500 earnings per share was plotted, conveying the message that because the consensus expected higher earnings in the future, at some point wage growth would also follow suit, thus bringing higher levels of inflation in the future.

Beyond the dubious claim that the Fed should raise rates (which we think it should not), the really amusing part is to look at the analysts’ consensus estimates for the next 8 quarters. They are as follows:

Not only are the analysts predicting a rise in corporate profits, but they are saying that in two years’ time EPS will be around 30% higher than they are now. Despite the recovery of the US economy over the last five years, corporate profits have never even reached the $30 threshold – despite of the fact that profit margins have been, for historical standards, at record highs. Also, note that corporate profits have been now declining for 5 quarters in a row, the longest streak since the financial crisis of 2008.

This is just another example of the irrelevance of bottom-up analysts’ estimates (among other problems, such estimates suffer from the well-documented analyst’s bias in thinking that the stocks they follow are almost always cheap) for the S&P500 as a whole – and for that matter, for every other index, and why a top-down analysis is much more useful if one wants to gauge where corporate profits will be in (say) one year’s time. As we explained elsewhere, our outlook for US corporate profits is rather bleak, given the stagnant levels of investment, prospects of a tightening federal fiscal policy (according to the Congressional Budget Office latest projections, although recent figures suggest otherwise) and a challenging worldwide demand outlook. Although the DB economics team argue in a follow-up note that the oil and dollar’s shocks are fading and as a result corporate profits will reap rewards, we think that i) regarding the dollar shock, most of the econometric specifications (and common sense) suggest that the impact takes 4-6 quarters to fully materialize and ii) it is not clear straightaway the impact of the ‘oil shock’ on corporate profits. A micro perspective would not clarify much, because the profits lost by the E&P companies could be more/less/completely offset by the profits earned by (say) airlines and similar industries. From a macro perspective, however, what is clear is that the oil shock has helped the US current account performance and has delayed some investment in the E&P industry, so the overall effect is not as direct as the previous note suggests.

In any case, suggesting that the EPS for the S&P500 will be 30% higher in two years’ time is outright ridiculous.

**A value investing ‘reverse engineering’ exercise**

But the aim of our post is different. Rather than criticizing analysts’ earnings projections, we would like to answer the following question: what would be the implicit rate of return for an investor buying the S&P500 right now if the previous estimates came true? In other words, we give the benefit of the doubt to the analysts and ask what we could obtain under such projections. This kind of analysis that asks the implicit parameters in an equity valuation exercise, rather than obtaining a ‘fair value’ estimate is, of course, a very-well known tool among value investors. Those who have played around with discounted flow models know very well that the value obtained from the exercise is so volatile to small changes in the valuation parameters (i.e. growth rate, discount rate) to the point of almost rendering the whole exercise useless. Benjamin Graham, the father of the value investing approach, was of course very aware of this modeling pitfall, claiming in his masterwork, *The Intelligent Investor*, in the section ‘The New Speculation in Common Stocks’, that:

The concept of future prospects and particularly of continued growth in the future invites the application of formulas out of higher mathematics to establish the present value of the favored issue. But the combination of precise formulas with highly imprecise assumptions can be used to establish, or rather justify, practically any value one wishes, however high, for a really outstanding issue.

Stephen Penman, professor at the Columbia Business School, forcefully backs this observation, proposing equity valuation models whose aim is not to get the right price for a stock, but rather take the share price and one of the two parameters (growth rate, discount rate) as exogenous variables and then see what is implied by the market in the other parameter. In other words, we do not want to get the price right (we wish we could), but rather use the model to challenge market expectations.

For our little exercise we will use a residual earnings valuation model (why the residual earnings model is a superior valuation tool over the oft-used discounted free-cash flow model and why the investment community does not seem to get it right yet may deserve another post). The residual earnings (RE) model says that the value of an asset is the book value plus all the future discounted residual earnings, which are total profits earned over a year minus the ‘required profit’ of the investment (i.e. the book value of the previous period times the required rate of return or discount rate). If an asset is forecasted just to earn the required rate of return indefinitely into the future, then the value of the asset should simply be the current book value.

In Table 1 we present the valuation of the S&P, taking analysts’ projections up to the second quarter of 2018, and then assuming a quarterly growth rate for the residual earnings terminal value of 0.6%, in line with historical values (incidentally, one of the advantages of the RE model over the DCF model is that, because the current book value obviously does not depend on the growth rate assumed, the amount of future value to bring forward in a valuation is less than in the DCF model and so the final number is less sensitive to changes in the parameters). Regarding the terminology, BVPS stands for book value per share, EPS is earnings per share, DPS is dividends per share, ROE is return on equity and REPS is residual earnings per share:

As you can see, given the previous assumptions, and for a S&P500 value of 2,126 (around the current value), the breakdown of the S&P500 would be as follows: around 758 points would be explained by the current book value, 121 by the residual earnings of the following two years and 1,246 by the residual earnings earned from two years ahead thereafter. On the other hand, a (quarterly) discount rate of 1.92% would be needed in order to reconcile the assumed growth rate with the analysts’ projections and the current level of the S&P500. Such a quarterly rate would correspond to a (nominal) annual rate of 7.7%, not very far away (the actual returns were slightly higher) from what equity investments have delivered in the US in the last 100 years. In other words, analysts’ estimates are implicitly saying that if you buy the S&P500 right now (at a forward PER of 17 and at a P/BV of 2.8x) you would obtain average returns from your investment.

Or looking at it from another perspective, the previous valuation tells you that if you believe than in two years’ time corporate profits will be approx. 30% higher than they are now (36 against 27, quarterly), and then you apply a terminal value with a perpetual quarterly growth rate of 0.6% (a bit demanding, in our opinion), and, on top of that, you apply a REPS of 19.45 (vs. an expected REPS of 14.9 for Q3’16) in calculating your terminal value, then you would just obtain an average (slightly below average) return from your investment – as a technical note, the model is strictly telling you that if you were able to reinvest future dividends in an S&P500 with the same fundamental features (i.e. valuation metrics) indefinitely in the future, then you would obtain precisely that return; because of that assumption, we believe the actual returns for the next few periods (say, 4-7 years) would be somewhat even lower than the one given by the model, but increasing as the time goes by and the investor is able to reinvest in a cheaper S&P500, and that’s why we think our exercise delivers higher values than the one carried out by GMO.

But, as many value investors (such as Penman and Siegel) would say, don’t pay too much for growth in your valuations. So we have run an additional scenario assuming a flat level of earnings up to 2Q’18 (in fact earnings are now falling, justifying the scenario) and then applying a terminal growth rate of 0.3% (quarterly). A truly conservative scenario from a value investing perspective would have been to assume a zero growth rate in the terminal value to see what would imply that assumption for the rate of return. Also, the fact that we think a flat path for earnings is still an optimistic one (see above) together with the fact that we think that future residual earnings growth will be lower than in the past makes us comfortable with the assumed new rate. The dividend pay-out ratio has been assumed to be constant and the BVPS has been retrieved as the difference between earnings, dividends and the book value of the previous period – notice that with the flat pay-out assumption we are effectively assuming that the REPS will be declining over the two-year horizon. With these changes, the valuation would be now as follows:

Given the new earnings forecasts, and with a forward PER of around 20, the new valuation tells us that buying the S&P500 now would deliver a 1.35% quarterly nominal return, around 5.4% in annual terms, which after taking into account inflation would be even less. Not bad in comparison to the rest of the asset classes (although the comparison should be taken with a pinch of salt, given their tight returns for historical standards), but not enough for a conservative investor who is comfortable sitting on piles of cash. Finally, remember that our short-term outlook for corporate profits is not very optimistic, so further downside could be expected. Therefore, our recommendation for a passive investor wishing to invest now in the S&P500 would be ‘wait and see’.

If nominal returns of 5,4% are considered low by the investment community a repricing of assets would be ensured, which would produce a sell off to a new base price that would subsequently guarantee much better returns, more in accordance with stock market history. Should that occur in the next months, short terms returns will be highly negative, probably the most likely scenario, and our justification for a ‘wait and see’ attitude.