## Investment Thesis

The SPDR S&P 500 ETF Trust (NYSEARCA:SPY) has had absolutely fantastic returns over the last 15 years, producing a CAGR of 14.50% per year. That figure is quite a bit higher than the historic average of 10.64% that the US stock market has returned over the last 100 years. This led us, being mainly focused on long-term investing, to ask ourselves whether there could perhaps be a period of lower stock market returns ahead.

According to our valuation models, which we will lay out in this article, the warning signs are flashing bright red in terms of historical valuation. We believe that equities are currently as expensive as they’ve been to a similar extent in the years 1929, 1937, 1968, and 2000 in terms of inflation-adjusted returns. This article will assess our two valuation models, which take into account earnings, inflation and interest rates over the last 100 years to explain why we believe a lost decade could be ahead and why alternative investment options like Treasury Inflation-Protected Securities (“TIPS”) may be a superior alternative to equities at current valuations.

## The Old Framework

Before diving into our most rigid method of evaluating the S&P 500 on a historical basis, we have to explain the more basic metrics which have been used by academia, such as the Shiller PE or CAPE Ratio. The Shiller PE/ CAPE Ratio is a great metric since it gives us the average inflation adjusted P/E Ratio for any given period, usually over the period of the last 10 years.

This is given broadly used metrics such as a normal price to earnings (“P/E”) Ratio or price to book (“P/B”) are necessarily not that good in predictive returns, while CAPE/ Shiller PE however are tremendous estimators of future returns as multiple studies have pointed out. And after running our own regression model, we found that over the past 40 years there has been a strong correlation between the Shiller PE Ratio and future real (inflation-adjusted) returns. Over the same period, we also included real yields on 10-year US Treasury bonds, which ranged from -1.89% to 8.16% real yield, with an average of about 2.86% real yield.

So according to this model, over the last 40 years there may well have been a point at which 10-year Treasuries became a more viable alternative, providing on average for higher returns and less volatility above a 31.07x Shiller PE multiple. The regression model also shows that expected real returns on anything above a Shiller PE of 34.14x is likely to yield on average negative real returns. Which is an interesting predicament given we’re currently at a 35.65x Shiller PE Ratio, which means according to this 40-year model, future expected returns are estimated to be -1.16% annual real returns while the 10-year Treasury inflation protected securities are yielding 2.15%, offering a much higher return while exhibiting much less volatility.

To make our model more complete, we ran the same regression with data we pulled from over the last 100 years both for inflation adjusted returns in equities and 10-year Treasuries going all the way back to 1924, and generally came to the same conclusions. This time we plotted both curves on a logarithmic curve, which told us that above 36.05x Shiller PE, future real returns are expected to be negative. It also tells us again that at a 24.62x Shiller PE, 10 year Treasuries have arguably been a better option, yielding on average a 2.01% real return during the 100-year analyzed period.

If we plot both curves on a linear plot, however, equities are already expected to yield negative real returns above a 31.55x Shiller PE Ratio, with the tradeoff between bonds becoming a more viable option already at a 24.8x Shiller PE Ratio. So in general, we can draw some meaningful conclusions from the Shiller PE Ratio that across multiple timeframes, it’s generally not a good idea to buy equities above a Ratio of approx. 25x, it being arguably a better option to buy a 10-year Treasury instead. Plus, at a Shiller P/E of approx. 32x and above, where we’re at today, historically on average real returns have always been negative.

Also as a sidenote, most of the very negative real yields on 10-year Treasuries in the observed period were mostly during and after the war in the 1940s, a time when there was active financial repression with deliberately low rates and high inflation. While we wouldn’t rule out the possibility of financial repression, and in fact find it even likely with the amount of government debt and fiscal deficits, we still can’t ignore the fact that the real yield on 10 year TIPS is 2.15%. Which means we don’t really face the same risks today, after only quite recently TIPS got introduced in 1997 by the US Treasury.

In past history before the 2000s, you could’ve argued that you were talking a risk in terms of not knowing what future inflation would be like while buying bonds, but that simply doesn’t hold up anymore ever since TIPS got introduced. We could even make a case that the threshold for buying 10 year TIPS should be lower than the 25x Shiller PE threshold, given equity holders have to stomach tons of volatility and downside risk versus TIPS, which historically have been among the least volatile asset classes out of all that exist if held to maturity.

## The ECY Framework

While the Shiller PE model is quite a rigid framework, having shown a high long-term predictive power in history, it does have some downsides. It for example doesn’t take into account extreme trends in interest rates, which have gone down over the last 40 years and were bound to the 0 range for quite some time during Zero Interest-Rate Policy (“ZIRP”).

And the first rule of valuation is that equities should be valued against their risk-free rate, usually the 10-year U.S. Treasury yield. Which is why we use the Excess CAPE Yield (“ECY”) model. This model takes the inverse of the Shiller PE, or the “Shiller Yield” and subtracts the 10-year U.S. Treasury yield adjusted for inflation. We view the Excess CAPE Yield as a tremendous representation of whether current equities are under or overvalued depending on a formula of a lot of handful useful metrics like inflation, interest rates and earnings over a long-term horizon. In the graph below, we calculated what this respected Excess CAPE Yield would look like over the last 100 years, with a higher Excess CAPE Yield meaning a cheaper valuation and a lower Excess CAPE Yield meaning a more expensive valuation.

In our methodology for discounting, we used both CPI adjusted 10-year yields, breakeven yields and TIPS yields as they became available throughout history since we believe TIPS currently entail the most accurate representation of valuation, even though the results are almost the same if only using CPI adjusted 10-year yields.

Again, we can see that the metric offers quite some depth in terms of valuation with periods like 2000, 1969, 1937 and 1929 registering on the indicator as low periods, and coincide with the major recessions/ depressions over the last 100 years or periods after which inflation adjusted returns were severely hampered. This whilst periods like the 1950s, early 1980s and 2009 were all periods registering with a high Excess CAPE Yield and subsequently delivering very impressive returns in the following 10+ years.

But as you can also see on this graph is the fact that it leaves us today in a predicament as we’re entering a territory of a very low Excess CAPE Yield. Currently, we’re at a Shiller PE Ratio of 35.65x, or 2.81% when converted to a yield, which we have to subtract with a 10-year TIPS yield which equals 2.15%. That only leaves us with a 0.66% Excess CAPE Yield, the lowest since the dot-com bubble. More so, we plotted a regression again with data from over the last 100 years, which shows us a pretty strong correlation between Excess CAPE Yield and subsequent 10-year inflation adjusted returns, similar to the traditional Shiller PE model.

In this model too, we can see where a possible tradeoff would lie in which 10-year Treasuries become a more valid option, as where both trend lines cross, below an Excess CAPE Yield of 2.33% you have had on average a higher real return with 10-year Treasuries. On the other hand, we don’t have to guess today what the real yield will be on a 10-year Treasury, since we can buy 10-year TIPS currently for a 2.15% real yield and hold them to maturity.

And according to our ECY model, expected real returns from equities is 0.25% right now at a 0.66% Excess CAPE Yield. Which is why we are quite perplexed at why equity investors are accepting potentially lower real returns, and much more volatility at 0.25% real returns with equities, when the real yield on 10-year TIPS is currently 2.15%. Generally, over the last 100 years, below an Excess CAPE Yield of 0.3%, where we’re getting close to, there has not been a 10-year period in which real returns were even positive.

If we look deeper at the ECY model, we can see that for example some of the good returns at a low Excess Shiller Yield have also been during periods which lead into the dot-com bubble, but still saw terrible results in the following years given the model is mean reverting. This makes sense, given investors who bought equities which were already richly valued in 1990 would’ve still seen terrific returns leading into the dot-com bubble in 2000 when the Shiller PE went even higher, to nearly 45x.

But if those shares had been held for another 5–10 years, the returns would have been dismal, to say the least. If you bought shares in March 1999, close to the peak of the dot-com bubble, 10 years later would be March 2009, which would give you about -5% real return. So over a long-term period and taking into account the mean reverting nature of the model, it is very telling and has great predictive capabilities. The model especially seems to have very high predictability at both the extremes such as -2% ECY and +14% ECY, indicating either very negative or very positive real returns. It is almost as if it is one of the most overlooked predictors of both bull and bear markets.

## Fully Priced

Now that we know both valuation models, we can reverse engineer at which level the S&P would be fully priced and where fair value should be. Since you can lock in a real return of 2.15% with TIPS, that would translate into an Excess CAPE Yield of 2.16% for the same historical return. And so if we add the 10-year real return of 2.15% to the Excess CAPE Yield, we would get a Shiller Yield of 4.31% or a Shiller PE of 23.20x.

In other words, at a Shiller PE Ratio of 23.20x the SPY S&P 500 ETF should trade at $354.31 when fully priced, since at that point we see that real bond yield and the real equity yield are fully equal. And while that would already be a huge haircut from current price levels, we should include a premium for owning equities given the volatility and uncertainty. So in reality, at the historical median 3.31% Excess CAPE Yield and adding the 2.15% real yield, we would get a Shiller Yield of 5.46% or an 18.32x Shiller PE. At these valuations, the SPY should only trade at $280.30.

Based on the classic Shiller PE valuation model, a real return of 2.15% for TIPS would mean a Shiller PE of 25.70x for the same historical return. That would mean the SPY would be fully priced at $393.22. On the other hand, at the median Shiller PE over the past 150 years of 15.98x, the S&P 500 would only be trading at $244.50. In conclusion, from a long-term perspective we would be very cautious about buying above the average of where both models find the SPY to be fully priced, which is currently $373.77, and would prefer 10-year TIPS instead.

## The Bottom Line

Looking at the S&P 500 from the perspective of earnings, inflation and interest rates, our rational observation is that at current levels, future returns are more than fully priced in and there are certainly prospects for a lost decade. As in 2000, 1968, 1929, and 1937, we see indicators like the Excess CAPE Yield flashing red, while according to the classic Shiller PE model, valuations are as expensive as they have been since 2021 and the dot-com bubble.

Still, we find it interesting that 10-year TIPS still offer attractive yields with a real return of 2.15%, or presumably a nominal return of 5.44% given that inflation has averaged 3.29% over the past 110 years. This compares with our Excess CAPE Yield model which suggests real future returns of 0.25%, with the traditional Shiller PE model suggesting a real return of merely 0.06%, highlighting the probability of a lost decade. Even more daunting is the fact that, according to our calculations with the classic Shiller PE model, over the past 100 years, above a 35 Shiller PE Ratio, 10-year real returns have never been positive.