AgPa #81: Equity Risk Premiums and Interest Rates (1/2)

Honey, the Fed Shrunk the Equity Premium: Asset Allocation in a Higher-Rate World (2024)
Thomas Maloney
The Journal of Portfolio Management 50(6), URL/AQR

Risk-free interest rates, the most fundamental anchor of asset prices, increased dramatically in 2022 and are still considerably higher than over the last 10+ years. At the same time, equity markets around the world posted strong performance in 2023 and 2024 (so far). Many investors thus wonder how this fits together. Why should we pay the same multiple for stocks when the risk-free alternative is much better than a few years ago? Or more technically, why should we accept such a low equity risk premium? This week’s AGNOSTIC Paper is the first of two that sheds some light on this (very important, but also very difficult) issue.

Everything that follows is only my summary of the original paper. So unless indicated otherwise, all tables and charts belong to the authors of the paper and I am just quoting them. The authors deserve full credit for creating this material, so please always cite the original source.

Setup and Idea

What return should you expect when you invest in the overall stock market right now?1Also see AgPa #57 for more on that. There are countless approaches, methods, and philosophies that desperately try to find answers for this question. One of the most common, however, is very simple. You start with a risk-free rate, usually the yield on a government bond from a non-chaotic country, and add the equity risk premium. The first one is (relatively) easy and readily available, the second is not. How much more return do you want to have for living through the swings of equity markets? Everyone has their own answer and – just like stock prices – the number changes everyday.

So what are reasonable estimates? For the US, the 10-year government bond yield currently hovers around 4.3%. Aswath Damodaran (URL), a finance professor famous for providing estimates on the subject, estimates a 4.12% equity risk premium for the S&P 500 index from a discounted cash flow (DCF) model as of June 1, 2024. Taken together, that gives us a long-term expected return of around 8.4% for the S&P 500. That is pretty reasonable and in-line with long-term realized returns.

In fact, most (serious) people probably agree that 6-8% per year is a reasonable return expectation for the overall stock market. In some sense that is striking. Armies of researchers and practitioners devote their time to come up with models and ways to estimate the equity risk premium, yet we mostly end at “Something around 6-8% for the stock market over the long-term”.

Importantly, those expected returns are the flip-side of stock prices. Buying a stock gives you the right on future cash flows (dividends, buybacks, profits). The more you pay for the same cash flow (higher price), the lower your expected return from the investment. All else equal, expected returns thus increase when the market crashes (prices down) and decrease when the market rises (prices up). The following equation summarizes this logic somewhat more mathematically.

Except for risk-free rates, however, it is quite difficult to get the inputs right. Let’s see what happened over the last years. In 2022, risk-free rates increased massively and stock prices tanked. Beautiful, interest rates up – prices down. Everything works as it should. In 2023 and 2024, however, stock markets performed strongly despite higher interest rates.

Now, I fully acknowledge the limitations of the DCF model. There are many other things that influent stock prices, in particular over shorter time horizons like the 1.5 years I am at looking here. Having said that, the DCF is one of the few fundamental anchors we have to think about stock prices over the long-term.

To explain the strong performance of stock markets with the equation above, we either need higher future cash flows, a lower equity risk premium, or some combination of the two.2Again, this is a model world that works over long horizons (if at all). Many other aspects also contributed to the strong performance over the last years. As there are very few all-else-equal situations in finance, the third one is probably most appropriate. It is also what at least I observe in current discussions. The economy is still quite strong and analysts expect further earnings growth. At the same time, many investors complain about a narrowing equity risk premium as valuations have not adjusted to the higher interest-rate world.

Why is this important? Well, if you buy stocks today, you get less compensation for the risk you are taking than for example at the end of 2022. Damodaran estimates a 5.94% equity risk premium for the S&P 500 at the end of 2022 versus just 4.12% as of June 2024. So if investors indeed decide that the current risk premiums are too narrow, they sell their stocks until prices go down (expected returns go up). This is good for the early sellers and those who buy later at lower prices, but it is of course not good for those who remain invested.

In my perception, this is exactly the problem many investors see for equities right now. Interest rates have adjusted, but valuations are still on the same level. All else equal, this makes equities less attractive when compared to bonds and they should eventually adjust. But no one, of course, wants to be part of the adjustment.

So much for the theory. Thom Maloney looks in this week’s paper at the empirics. Without spoilering too much, there are both good and bad news. The good news are that tighter equity risk premiums are at least historically not unusual when interest rates increase. So we are not necessarily doomed for an immediate adjustment that leads to a market crash. The bad news are that equity returns were historically lower (but still very positive) in Higher Rates environments.

Data and Methodology

The data and methodology of the paper is relatively straight-forward. The author constructs a Long Dataset for equities, treasuries, and investment grade (IG) credit in the US that spans from 1926 to 2023. He also constructs a Broad Dataset that covers more asset classes (equities, treasuries, IG credit, private equity, real estate, equity market neutral, trend following) for the period from 1990 to 2023. The data comes from reputable sources and the paper is peer-reviewed, so data-quality shouldn’t be an issue.

With respect to return premiums, the author follows a slightly different approach than my introductory examples above. He calculates excess returns against the 3-month T-Bill rate. Practically, that’s the short-term risk-free “cash rate” or at least its closest proxy. On the one hand, this is more precise as this rate doesn’t include a term premium and moves closer with monetary policy. On the other hand, many investors prefer to use longer-term risk-free rates (like the 10-year treasury) as those are more in-line with their investment horizons.

The author uses three classification rules to separate Lower Rates and Higher Rates regimes and averages the results across all rules for more robustness. First, he simply uses the full-sample median as breakpoint. This is of course very naive, forward-looking, and unrealistic. He therefore also employs rolling classifications based on trailing and centered windows. None of those methods is perfect and there are endless ways to classify interest rate regimes instead. In my view, however, the three methods are reasonable and averaging across all of them is the most intellectually-honest approach to do it. He also provides a chart of the results (see below) which looks reasonably to me.

Exhibit 2 of Maloney (2024).

All further results are essentially just averages of excess returns across those regimes and elementary regression analyses. The paper is mostly an ex-post scenario analysis with all the associated strengths and weaknesses. History rarely repeats itself perfectly, but I think it still makes sense to look at it.

Important Results and Takeaways

Equity returns and risk-premiums were lower in higher-rates environments

The following exhibit summarizes the key results of the paper. The excess returns of equities over cash is significantly smaller in Higher Rates environments (Panel A, purple bars). It is important to mention the difference between expected and realized risk premiums at this point. The Damodaran estimates above are expected risk premiums. What Maloney analyzes in the paper are realized risk premiums. The latter ultimately count for investors.

As I mentioned, equity performance for 2023 and 2024 was very strong. So we had high realized equity risk premiums, but the expected premium going forward continuously narrowed. Time will tell whether that will eventually realize. For the moment, however, I really like this analysis. It debunks the comments of doomsayers who argue that the market must collapse to adjust to the new interest rate world. At least historically, lower equity risk premiums in times Higher Rates seem quite normal and should be expected.

Exhibit 3 of Maloney (2024).

The author next adds cash rates to examine the total nominal and real returns in Panel B. There are a couple of observations. Realized nominal returns increase for cash and fixed income assets when rates are higher. That is not surprising. For equities, however, nominal returns decrease quite substantially. Remember that this is a historical average and not representative for every point in time. But at least historically, it seems that higher rates do not arrive in equity returns. The slimmer equity risk premium thus dominates the higher risk-free rate.

The effect is even stronger for real returns. After inflation, the average real return on equities decreases from 10% per year in Lower Rates environments to about 7% in Higher Rates environments. That is a very substantial decline, but 7% per year after inflation is still amazingly good.3Note that this analysis covers the S&P 500, a positive outlier in terms of performance. Most other stock markets had lower returns. For Cash and Treasuries, real returns are still higher in Higher Rates environments while they are virtually unchanged for IG Credit.

EPS growth, valuations, and interest rate changes explain the effect

Maloney mentions various ideas that might explain those patterns. The first one is risk. If equities are less risky in Higher Rates environments, the risk premium should be lower. The average annual volatilities are 19.4% for Lower Rates and 17.4% for Higher Rates. This goes in the right direction, but the risk-adjusted performance (Sharpe ratio) is still better for Lower Rates. So he discards this idea rather quickly.

A much more promising explanation is earnings-per-share (EPS) growth. The average annual EPS growth after Lower Rates environments is 11% versus just 1% for Higher Rates. That is a big fundamental difference and certainly explains a lot of the return gap.

Two further aspects are valuations and changes in interest rates. For that purpose, the author regresses monthly excess returns on cash rates and the inverse of the Cyclically-Adjusted-Price-to-Earnings ratio (CAPE). The results are in line with expectations. Both higher cash rates and higher valuations suggest lower equity returns going forward. On a more cautious note, the author also mentions that returns tend to be particularly low when rates and valuations are high at the same time – just like they currently are.

Finally, he also controls for interest rate changes and finds that the negative relation between interest rates and equity excess returns increases even further. What is the intuition? Equity markets are probably more sensitive to changes in interest rates than to their level. History, by means of this sample, suggests that rates are more likely to fall (increase) when the starting level is high (low). Since equity markets tend to do well (bad) when rates are falling (rising), controlling for rate changes reveals a “truer” relation between cash rates and equity risk premiums.

Treasuries and absolute-return strategies historically benefitted from higher rates

The author finally repeats his analyses for the Broad Sample with more asset classes, but shorter history. The following chart summarizes the results.

Exhibit 6 of Maloney (2024).

The results are generally similar and even more pronounced for the period from 1990 to 2023. Private Equity, Public Equity, and Real Estate all post considerably lower excess returns in Higher Rates environments which also translate into lower total returns despite a higher cash rate. Treasuries and Credit, in contrast, again profit from higher rates.

We should note at this point that Thom Maloney works for AQR Capital Management which is a reputable provider of liquid alternative / hedge fund strategies. I have no concern that this influences the results, but I think it is fair and important to mention. Based on the sample, liquid alternatives (equity market neutral, trend following) tend to benefit from higher rates and posted both higher excess returns and higher total returns.4It is interesting that many asset managers (not AQR as far as I know) also marketed such strategies as particularly attractive yield-replacements in the low-interest world. Part of this comes from portfolio construction as such strategies tend to use derivatives and/or short-sales which require collaterals that usually earn the cash rate. The author finally highlights the importance of cash hurdle rates for the performance fees of such strategies.

Conclusions and Further Ideas

The motivation for choosing this paper was that I am somewhat tired of the doomsday-discussions around a pending equity market crash. No doubt that unchanged or recently even increasing valuations for stock markets seem strange in a world with much higher cash rates when compared to 2021. No doubt that this makes fixed income investments more attractive and justifies re-allocations. No doubt that liquid alternatives and hedge fund strategies deserve a spot in a portfolio. The results in this paper and a little common sense all support this.

In my view most importantly, however, the paper shows that narrower equity risk premiums are somewhat “normal” for Higher Rates environments when we look at history. Of course, everyone who argues against stock markets at current valuations and interest rates has a fair point. But the real question is how and when they will adjust. In my view, it is quite unlikely that we see a one-time valuation adjustment (in English, a crash) and “historically normal” returns thereafter. As the paper shows, a period of lower but still positive returns appears more likely. That doesn’t make it better (no one likes lower returns), but this low-expected-return challenge is something we have to live with (see AgPa #53, for example).

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1 Also see AgPa #57 for more on that.
2 Again, this is a model world that works over long horizons (if at all). Many other aspects also contributed to the strong performance over the last years.
3 Note that this analysis covers the S&P 500, a positive outlier in terms of performance. Most other stock markets had lower returns.
4 It is interesting that many asset managers (not AQR as far as I know) also marketed such strategies as particularly attractive yield-replacements in the low-interest world.