The following chart shows the distribution of future return assumptions that state and local pension funds were using to value their liabilities as of February 2017:

The average expected return was around 7.5%. How can any large fund, much less a pension fund with a conservative mandate, expect to generate such a high return in the current environment? Where exactly would the return come from? Certainly not from anything in the fixed income universe: (source: FRED)

The answer, of course, is equities . Beginning in the early 1950s, pension funds began to shift their allocations out of fixed income and into equities. Today, equities and equity-like “alternatives” represent the primary asset classes through which they generate returns. A 2015 survey of state and local pension funds found that the lowest combined exposure to these asset classes was 61% for the Missouri State Employees Retirement System. The highest was 87% for the Arizona Public Safety Personnel Retirement System. The average exposure was around 70%, which checks with flow of funds data (source: Z.1, L.120, fixed income defined to include cash and equivalents, equity exposure from mutual funds estimated from L.122):

As the chart makes clear, pension fund allocations to equities have increased dramatically over the last several decades. This shift is likely to be one of the primary reasons that equities are more expensive today than they used to be the past. When a large market participant undergoes such an extreme change in its preferences, the impact is bound to show up in prices and valuations.

Fixed income securities pay a defined coupon and mature at a defined value on a defined date. Their best-case future return prospects can therefore be directly inferred from their current prices and valuations. Anyone in the current environment who tries to extrapolate the strong returns that fixed income has delivered over the last few decades will quickly run into the reality of the math itself, which is not compatible with a 7.5% future return expectation.

Equities, in contrast, pay out variable cash flows and have no maturity. Their best-case future return prospects are therefore inherently uncertain, critically dependent on the prices that investors will be willing to pay for them in the future. This uncertainty opens the door for the possibility that their future returns will meet or exceed their past returns even when they’re trading at very high valuations. Growth can always surprise to the upside, and high valuations can always go higher.

When we look at pension fund returns over the last few decades, we see that the 7.5% expectation is consistent with what they’ve actually been able to generate in recent decades. From their perspective, using a 7.5% estimate is simply using the number given in the historical data. Why should any other number be used?

An article from a few days ago in the San Diego Union Tribune made a similar point: that falling pension fund return estimates are not a cause for concern, because pension funds have shown in their actual performances that they are handily beating those estimates. Value conscious investors will surely cringe at this logic. Pension funds have been able to exceed their return expectations not because they possess any special replicable investment skill, but because they’ve been lucky enough to ride the coattails of soaring valuations in public and private equity. The ongoing increase in equity valuations has pulled returns out from the future into the past, creating a situation where extrapolation of the past is almost guaranteed to produce overly optimistic forecasts.

The problem, of course, is that the people who are voicing concerns about valuation today are essentially the same people who were voicing them several years ago, when equity prices were half their current values. And they’re using the same “mean-reversion” arguments to do it, even though the market has persistently shown that it has no inclination to revert back to the valuation averages of any prior era. They overstated their case then, and so people assume that they’re overstating their case now, even though their underlying warnings may now be worth heeding.

In what follows, I’m going to explain why I believe long-term future U.S. equity returns are almost guaranteed to fall substantially short of the 7.5% pension fund target. Unlike other naysayers, however, I’m going to be careful not to overstate my case. I’m going to acknowledge the uncertainty inherent in equity return forecasting, and manage that uncertainty by being maximally conservative in my premises, granting every optimistic assumption that a bullish investor could reasonably request. Even if every such assumption is granted, an expected 7.5% return will still be out of reach.

To begin, we can separate equity returns out into three components: (1) change in valuation (e.g., change in the P/E ratio), (2) per share growth in fundamentals (e.g., earnings per share growth), and (3) reinvested dividend payouts.

On forecast horizons shorter than a few decades, the first component of returns–change in valuation–tends to be the most impactful. It’s also the greatest source of uncertainty in the overall forecast. To see why, consider that the component is derived from two terms: current valuation and terminal valuation (valuation at the end of the forecast period). We know what the market’s current valuation is, but we don’t know what its terminal valuation will be. We can assume that its terminal valuation will gravitate towards some natural average, but history has shown that such an average, if it exists, can change over time. And even if we knew what average valuations will be in the future, our estimate would still contain substantial uncertainty, because valuation is highly cyclical. It oscillates with the condition of the economy and the mood of the investor public. To know where it will be relative to its average on some future date, we need to know where in the cycle the market and the economy will be on that date. That’s not something that can be known in advance, which is why it’s impossible to reliably forecast future equity returns, at least on horizons shorter than a few decades.

The best way to mitigate the uncertainty associated with future changes in valuation is to extend out the horizon of the return estimate as far as possible. Unlike the other two components, change in valuation is a one-time contributor to total return. As the horizon of the return estimate is increased, the one-time contribution that it makes will get spread out over longer and longer periods of time, reducing its impact in “annualized” terms. As we increase the forecast horizon out to infinity, the contribution will fall all the way to zero, eliminating the uncertainty altogether. The problem, of course, is that if we extend the horizon out too far, the estimate will becomes useless to allocators. Allocators want to know what returns will be over the next 10, 20, 30 years, not the next 100 or 1,000 or 1,000,000 years.

To generate a conservative upper limit forecast on horizons of interest, I propose the following compromise. Valuations today are in the 97th percentile of all valuations in history and the 83rd percentile of valuations over the last twenty years (itself a period of very high valuations). Rather than assume that they will revert back to some past average, let’s start by granting the very bullish assumption that they will remain exactly where they are today forever . This will zero out the contribution from change in valuation, removing it from the problem altogether. It will also reduce the need to specify a concrete time horizon for the forecast–e.g., 5, 10, 20, 30 years–given that there will no longer be a one-time mean-reversion event whose effects need to be “annualized” across varying lengths of time. Our forecast will simply involve projecting out rates of growth and rates of return on reinvested dividends using known historical data.

Of course, on this approach, our upper limit forecast will be exposed to the risk that valuations will make a sustained rise to even higher numbers in the future. But that seems like a reasonable risk to accept. And if valuations fall to lower numbers, a possibility that seems much more likely, then the return will suffer accordingly, keeping our upper limit estimate intact.

What many people fail to initially realize is that if valuations remain where they are today, the contribution from the third component, reinvested dividend payouts, will end up being significantly depressed relative to the past. From 1871 to 2018, the S&P composite index generated a 6.92% real total return. The return on price alone was only 2.38%, which means that the bulk of the return came from dividends. Crucially, to get the full return, it wouldn’t have been enough for the dividends to simply have been paid out. They would have needed to have been paid out and reinvested back into the S&P. If they were to have instead been reinvested into treasury bills, the real total return would have only been 2.94%:

This result highlights the importance of the compounding produced by the reinvestment of dividends back into the market. A key determinant of the rate of that compounding is the valuation at which the reinvestment takes place. If we assume that valuations will remain where they are today, multiples above prior historical averages, then the future rate of that compounding is going to be reduced accordingly. As we will later see, the effect will not be small.

The future contribution from the second component, per share growth in fundamentals, will also potentially be depressed if valuations remain elevated. As our economy ages and matures, the need for capacity expansive real investment will fall. Corporations will have to return more of their profits to shareholders. The most tax efficient way for them to do that is through share buybacks, which is why share buybacks have surpassed dividends as the primary mechanism through which capital is returned to shareholders. In terms of estimating future returns, the critical question is, will the per share growth generated from share buybacks be able to match the per share growth that the corporate sector was able to historically achieve through real investment? The answer will obviously depend on the valuation at which the shares are bought back. If valuations are going to remain elevated, then each round of returned returned capital will end up buying back fewer effective shares, which will reduce the ensuing per share growth accordingly. Later on, I’m going to introduce a rough methodology for estimating the impact of this effect–the results will be somewhat surprising.

This is what we’re trying to figure out: if the S&P stays at its current valuation indefinitely into the future, what return will it likely deliver? The best way to answer that question is to assume that the S&P had always traded at its current valuation, and calculate what it’s historical return would have been on that assumption. The calculated return can then be used as a conservative upper limit on the kind of return for that current investors can reasonably expect.

To make this calculation, we need a reliable valuation standard to use. The best standard would probably be the Shiller CAPE, but we know that its current value is being distorted by large writedowns undertaken during the financial crisis. Fortunately, we’re now far enough away from the financial crisis to eliminate that distortion by tweaking the lookback period. If, for example, we shorten the lookback period from 10 years to 7 years, earnings numbers from the financial crisis will entirely drop out. The following table shows the impact:

The current CAPE10 is 33.33, which is 136% above its historical average. By taking out the financial crisis, the CAPE7 falls to 28.44, which is 105% above its historical average. The 31% difference between these numbers may not matter much in today’s expensive market, but it definitely would have mattered several years ago when valuations were reasonable but were being made to look expensive by the distortions.

To challenge our use of the CAPE7, critics could reasonably point out that we’re essentially using hindsight to make the current lookback period a recession-free period, when most lookback periods throughout history included at least one recession with an associated earnings drop. That’s a fair criticism, but it only serves to increase the conservatism of our upper limit estimate. By using a metric that understates the market’s current expensiveness, we will make our upper limit estimate even more robust.

Looking closely at the details of our approach, we see that it’s highly conservative with respect to each of the contributors to total return:

Change in Valuation : it’s conservative with respect to the contribution from change in valuation because it removes that contribution from the equation, even though the contribution is far more likely to be negative than positive going forward.

Per Share Growth in Fundamentals : it’s conservative with respect to the contribution from per share growth in fundamentals because it effectively assumes that growth rates in the future will equal growth rates in the past, even though we live in an aging, highly-developed economy that has clearly shown a propensity for slower growth relative to the past. It’s also conservative in that it ignores the effect that today’s high valuations will have on the per share growth generated from share buybacks.

Reinvested Dividend Payouts : it’s conservative with respect to the contribution from reinvested dividends because it calculates reinvestment prices using a valuation measure that likely understates the market’s current expensiveness, given that the measure uses a recession-free 7 year Shiller lookback period when most lookback periods across history contained at least one recession and associated earnings drop.

The following table shows what the component returns for the S&P would have been from 1871 to 2018 if the market’s valuation had always been what it is today, CAPE7 of 28.44:

The total return would have been 3.95% compared to the actual number of 6.92%. The difference, which represents almost half the overall return, is what is lost when you reinvest dividends at elevated prices and remove the one-time contribution from secular increases in valuation. Adding in 2% for inflation, we get a 5.95% nominal upper limit total return estimate for U.S. equities.

Pension funds are therefore left to choose from the following investment menu, U.S. equity included:

Clearly, it would be impossible to reliably generate a 7.5% return from a diversified portfolio of items taken from the above menu. Unless pension funds plan to lever up irresponsibly or take on a massive overweight in foreign assets, they have little hope of collectively achieving their current targets. Their future return estimates therefore need to fall–by much more than they already have.

Now, we can identify at least three key risks to our upper limit estimate, all of which seem unlikely to play out:

First, valuations could keep going up. Interestingly, if over the course of the forecast horizon, they go up and then revert back to where they are today, the effect on the return will actually be negative , because there will be no net change in valuation, but some of the ensuing dividends will have been reinvested at higher valuations than those available today. The real risk is that valuations could go up and stay up indefinitely, or for the length of the forecast horizon. In that case, the change in valuation will make a net positive contribution to the overall return, which could push the total return well above 5.95%, particularly on shorter forecast horizons where the annualized effect of the contribution would be greater. But with valuations already in the 97th percentile of record history, a sustained long-term rise to even higher valuations seems like a lot to ask for.

Second, valuations could go down, and then increase back to where they currently are by the end of the forecast horizon. Suppose, for example, that the forecast horizon is 20 years. In the next few years, the cycle could turn, with the CAPE7 falling back to a trough value of, say, 13. The CAPE7 could then hover around a value of say 17 to 22 for a decade or so and then eventually return to its current value of 28 in another market boom that peaks right around the end of the forecast period. This would allow dividends to be reinvested (and buybacks and acquisitions to be carried out) at lower prices, while preventing any net contribution from a change in valuation from showing up in the overall return for the period. But if the CAPE7 is set to drop from its current value to a substantially lower value, there will be enough pain and loss for those involved in that process to make the question of the longer-term return from here less important.

Third, per share growth could exceed the averages of prior eras. Theory and evidence, however, suggest that the opposite outcome is more likely–per share growth will continue to come in below the averages of prior eras, because the population is older than it was in those eras and is growing at a slower pace, and also because the corporate sector has fewer low-hanging fruits that it can pull on to increase productivity and output through real investment. The current cyclical upturn notwithstanding, capital allocation is likely to continue to shift away from real investment towards share buybacks, which will further contribute to the drop in per share growth, given that the buybacks (and acquisitions) will end up being carried out at today’s very expensive prices.

If a shift from investment to share buybacks does continue to occur, how significant will the downward effect on per share growth rates be? To answer the question, we need a way to estimate the rates of return that real investment and share buybacks at current valuations can be expected to deliver, respectively. The following table, which I explain below, is an example of a crude way of using historical data to make that estimate:

We start by noting that the return contribution from reinvested dividends is functionally identical to the return contribution from share buybacks. The only difference is that in a share buyback, the company reinvests the “dividend” for the shareholder, buying shares in the shareholder’s name and thereby eliminating the unnecessary tax event that would have occurred if the dividend were paid to the shareholder in cash and redundantly reinvested in those same shares.

Buybacks are a relatively recent thing in market history, so we can assume that all of the earnings that were historically not paid out as dividends were reinvested into businesses. The only place where the shareholder “value” of this reinvestment can show up is in EPS growth. Consequently, to estimate the historical rate of return that real corporate investment was able to produce for shareholders, we compare the historical return contribution that shareholders received from EPS growth to the average “amount” of earnings that corporations historically retained and devoted to it. Similarly, to estimate the historical rate of return that dividends (or share buybacks, which are the same thing) were able to deliver for shareholders, we compare the historical return that shareholders received from reinvested dividends to the average “amount” of earnings that corporations historically used to pay them.

That’s what the table does: it divides the historical return contribution that was received from EPS growth and reinvested dividends, 1.73% and 4.55%, respectively (column 3), by the historical percentages of EPS that the corporate sector devoted to each activity, 40% to real investment and 60% to dividends, respectively (column 2). The result (column 4), gives the return contribution for each activity per 100% of EPS spent, 4.28% and 7.63%, respectively.

What the numbers in column 4 are telling us is that that for every 100% of EPS deployed into real investment, shareholders received a 4.28% real return (which came from EPS growth). Similarly, for every 100% of EPS deployed into reinvested dividends (which are the same as share buybacks), shareholders received a 7.63% real return. We can use these numbers to estimate what the effect on the total return would have been if the corporate sector had shifted the EPS payout towards one source and away from the other. As we see in column 6, if we assume that 15% of EPS had been retained and deployed into investment, and 85% had been deployed into dividends and share buybacks, the aggregate return that shareholders would have realized from these sources would have increased from 6.28% to 7.13%. In other words, looking across the entire period from 1871 to 2018, shareholders would have been better off if the corporate sector had returned a greater portion of EPS in the form of dividends and buybacks, because that activity offered a higher rate of return, at least at the actual market prices that the dividend reinvestments and share repurchases would have taken place at.

This crudely calculated result is consistent with the academic finding that corporations who favor real investment over the return of capital have historically generated lower returns for shareholders. The finding appears to extend to the macroeconomic level as well–shareholders in the larger economy got a much bigger bang for their buck when cash was returned to them as dividends than when it was deployed into capital expenditure.

We should mention that an alternative way to explain the result, likely to be favored by bearish investors, would be to argue that earnings have historically been overstated. The argument would be that a significant portion of the earnings retained by the corporate sector across history was actually spent on maintaining capital and output capacity in their current states, as opposed to being “invested” in new projects to grow them. Instead of being accounted for as “earnings”, the money deployed into these maintenance activities should have been treated as part of the expense of doing business. Had the money been appropriately expensed in that way, retained earnings would have been lower, and the calculated return on the genuine new investments that the earnings were deployed into would have been higher.

Now, the above table still doesn’t give us what we want. It tells us how returns would have been affected if a greater portion of earnings had been devoted to the repurchase of shares at actual market prices across history, prices that were much cheaper than today’s prices. What we want to know is how returns would have been affected if shares had always been repurchased across history at today’s expensive valuation level (i.e., a CAPE7 of 28.44). The table below gives us that information:

As you can see, at current valuations, a shift in EPS deployment from the historical 40/60 split to a new split of 15% real investment and 85% share buybacks (or reinvested dividends) would have lowered the S&P’s real total return from 3.95% to 3.81% (or, on an assumption of 2% inflation, from 5.95% to 5.81% nominal). This result is the “somewhat surprising” result that I referred to earlier. I initially suspected that the impact of shifting EPS away from real investment towards share buybacks at expensive valuations would have been substantial, but that turned out not to be the case. Corporate investment has historically delivered the same kind of return that buying back shares at today’s valuation would have delivered, roughly 4% real for every 100% of EPS invested. If past markets had always traded at today’s valuation, any effect of shifting from one to the other would have largely been a wash.