**Expected Stock Returns When Interest Rates Are Low (2022)***David Blitz*

The Journal of Portfolio Management 48(7), URL/SSRN

The second AGNOSTIC Paper on equity risk premiums when interest rates are high(er). This one was actually published before the last one, so David Blitz deserves credit for the original idea. He also examines a longer and more comprehensive dataset that serves as a nice out-of-sample test. So I think it makes sense to conclude the posts on equity risk premiums and interest rates with this more comprehensive paper.

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

The setup and idea of the paper is almost identical to the previous one and I kindly refer you to the respective section in AgPa #81.

## Data and Methodology

The author, David Blitz, examines two separate datasets that cover a long history. For the US, he uses Kenneth French’s (URL) market portfolio and risk-free T-Bill rates back to 1926. He extends this sample even further with the data from Baltussen et al. (2021) that goes back to 1866 (see AgPa #42). To control for the impact of valuations, Blitz uses Robert Shiller’s (URL) CAPE ratio from 1881 onwards. In addition to that, he also constructs momentum (AgPa #37), term spread, and default spread control factors.

The data for international markets comes from the “The Rate of Return on Everything” paper by Jordà et al. (2019) that I also covered in AgPa #5. Depending on the country, the sample starts between 1870 and 1900 and covers 15 countries beyond the US (16 in total). The data is unfortunately only available on annual periodicity. However, I really like the approach of analyzing everything that is out there instead of waiting for the perfect data that probably never comes. The author also mentions that he removes a few extreme return observations during hyperinflations and wars. In my view, all of this is reasonable and the dataset should be quite robust.

## Important Results and Takeaways

### Equity risk premiums were lower when interest rates are higher

The following chart illustrates the key result for the US market. Blitz calculates average realized equity risk premiums for different interest rate levels. While the level-classifications are arbitrary, I think they are reasonable and illustrate the point quite well.

Just like last week, we find that the equity risk premium was historically smaller (larger) when interest rates are higher (lower). For rates <2%, for example, the equity risk premium was a staggering 9% per year. For rates >6%, it was not even positive.

In my view, the result supports various points that I already made last week. First, smaller equity risk premiums are historically not too special when rates are higher and should be expected. Second, although they are smaller, equity risk premiums remain positive for all but one interest rate regime. Even more important, the total return (risk-free rate + equity risk premium) also remains strongly positive, although some of this certainly comes from the exceptional performance of the US equity market (see below and AgPa #58). Overall, the results therefore indeed suggest that equity markets became less attractive when interest rates increase. But only relative to bonds. The total return by itself was still heavily positive.

The figure above shows the same chart for the international sample from the other dataset. It is thus a very interesting out-of-sample test.^{1}As you know, I am quite religious about out-of-sample tests. They are the best we have in messy environments like stock markets… Quite unsurprisingly, there is a lot of variation across countries. By and large, however, the overall relation seems to hold. Equity risk premiums tend to be lower when interest rates are higher and vice versa. The author also supports this with a regression analysis (see below).

In addition to that, the charts also once again highlight that the strong performance of the US is not necessarily representative for stock markets in general (see AgPa #57 and #58). Also remember that the author removes extreme observations during wars and hyperinflations from the sample. So for countries like Germany or Japan, for example, the true long-term averages probably look even worse.

### Controlling for other factors doesn’t change the negative relation

The conditional averages from the charts above are nice and intuitive, but it is of course even more interesting to test the relation more thoroughly. The author thus regresses the realized equity risk premium on the level of interest rates and various control factors (CAPE earnings yield, equity momentum, bond momentum, term spreads, default spreads). For more robustness, he also splits the 140 year sample period in two independent 70 year slices and examines them separately.

The table above summarizes the results for the US data. The highlighted numbers are the regression coefficients for the level of interest rates, our main focus here. With one exception (the first 70 year sub-sample period), the coefficients are significantly negative and meaningful. For example, the first coefficient of -2.07 suggests that the equity risk premium decreases by 2.07%-points when interest rates increase by 1%-point (all else equal). This is fully in-line with the negative relation from the charts above.

The next chart summarizes the regression results for the international sample. We need to be somewhat more cautious with those results as the international data is only available on an annual basis and lacks the valuation control variables. It is not perfect, but the best we have.

The blue bars show the regression coefficients for the level of interest rates and the orange bars the associated t-statistics. All of the coefficients are negative and mostly somewhere between -0.5 and -1. The average stands at -1.10, the median at -0.94. This suggests that equity risk premiums are indeed negatively related to interest rates, even across countries. For 7 countries, the coefficients are statistically significant at the 5% level. For the 10% level, this number increases to 12. This is not super-robust statistical evidence, but it goes in the direction of the effects we observe.^{2}Note that the other control variables apparently do matter. The coefficients for the US-only data with control variables are even more negative than in the analysis here.

### EPS growth seems to explain the pattern

After identifying the empirical patterns, the next logical question is where they come from. The author examines three reasonable explanations. Risk, the “there is no alternative” (TINA) narrative, and fundamentals.

I already mentioned the risk-based explanation last week and the idea is straight forward. When equities are less risky during times of lower risk premiums, the world in the sense of efficient markets is fine. By means of volatility, Blitz argues that this is not reasonable. With few exceptions, the high realized risk premiums were earned during relatively calm times. So it is quite the opposite of the proposed idea.

The idea of TINA, a very popular narrative during the recent low-rate period, is that investors buy into equities in a reach for yield. When risk-free rates are low, investors have to invest in more risky assets like equities to reach their return objectives. The idea is that such behavior pushes up valuation multiples and leads to strong equity performance (see AgPa #53). While this was certainly true since the financial crises 2008/09, Blitz doesn’t find a robust relation between interest rates and valuations over the long term. So he discards this explanation as well.

Finally, he turns to the fundamental component of stocks and examines the relation between earnings-per-share (EPS) growth and interest rates. He finds a weakly significant negative relation. On average, EPS growth tends to be higher when interest rates are lower and vice versa. Thom Maloney finds the same result in last week’s paper (AgPa #81).^{3}Needless to say, this indicates some robustness. You don’t want to have two papers that look at the same data and find vastly different results… Both authors mention, however, that it is very difficult to explain the relation by one particular mechanism and are rather cautious. The evidence we have, however, points towards fundamental performance as main driver of the equity risk premium.

## Conclusions and Further Ideas

In the final part of the paper, Blitz discusses some interesting challenges and potential critiques. First, he cites research that argues against the predictive power of analyses like his for timing purposes. The idea is that changes in the equity risk premium are not sufficient to profitably short the market. In fact, the author mentions that his analyses would recommend to be long equities 100% of the time. This is again a point that I already stressed last week. History shows that equity risk premiums were indeed lower in times of higher rates, but they are still mostly positive. The same is (even more) true for total returns.

So if not for timing, for what can we use the results instead? Blitz argues that they should be considered on the level of strategic asset allocation. I fully agree with him. The analyses show that when interest rates are high, investors tend to get less compensation for bearing equity risk. As a consequence, they should use less risky assets to reach their return objectives. In a sense, we all know that. Suppose I am a pension plan that needs 4% per year. When rates are low, I need some equities to achieve that. When rates are high, I can just buy treasuries.

The second block of challenges are the usual suspects. 140 years of data is a very long history, but it remains just history. I generally like long samples to see what happened outside my lifetime, but going forward, I also believe their practical value is limited. The behavior of today’s people certainly still shares some commonalities with that from 100 years ago, but by and large, the economy and markets are now wildly different. Blitz rightly mentions that the *“[…] insights are too striking to be ignored”*, but I still recommend to view them as what they are. Historical averages – not more, not less.

Overall, I think the message from the two papers is relatively straight forward. History suggests that stocks become relatively less attractive when interest rates are higher. At the same time, equity risk premiums never really turned negative and stocks produced positive total returns throughout history.

Both are important information for investors and in particular those who have to do strategic asset allocation. Based on the papers (and some common sense), it doesn’t make sense to use a fixed assumption for the equity risk premium all of the time. This has important consequences. For example, the results from the papers help to explain why stock prices are currently still high despite higher rates. Equity risk premiums are simply smaller than a few years ago.

- AgPa #82: Equity Risk Premiums and Interest Rates (2/2)
- AgPa #81: Equity Risk Premiums and Interest Rates (1/2)
- AgPa #80: Forget Factors and Keep it Simple?
- AgPa #79: The Momentum OGs – 30 Years Later

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## Endnotes

1 | As you know, I am quite religious about out-of-sample tests. They are the best we have in messy environments like stock markets… |
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2 | Note that the other control variables apparently do matter. The coefficients for the US-only data with control variables are even more negative than in the analysis here. |

3 | Needless to say, this indicates some robustness. You don’t want to have two papers that look at the same data and find vastly different results… |