3 Useful Equity Return Models
Forming expectations for equity performance from different perspectives
Attempting to forecast equity market returns could very often turn out to be a fool’s errand. But we, as investors, already know that reality will most likely be different from whatever our models, computer simulations and formulas can tell us. The real value in such attempts is gaining a better understanding of how things could develop in the future when conditions and markets change (including under various scenarios) and the potential risks related to that. Breaking down what drives performance gives us insights relevant to our asset allocation decisions and our reactions in a dynamic environment that tests our ability to navigate challenges and unexpected shocks. Thankfully, there are many academic studies of models that have some useful applications (at least in some stock markets) for estimating expected returns on equities — and here I will briefly review 3 of them.
The content of this post does not constitute financial or investment advice. It is intended for information and education purposes only. The author is not affiliated with any brokerage, bank or European institution cited below.
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1. Long-term returns: yield, growth, valuation
A team of researchers from Australia and New Zealand has recently tested several modifications of a long-term equity return model and the results were published in a study, included in the latest Financial Analysts Journal. The methodology suggested by the authors is useful because it offers improvements over simpler models (like the Capital Asset Pricing Model, or CAPM) that are much less accurate for long-term forecasting. They show that 10- to 20-year expected returns can be estimated ex-ante and out-of-sample, with forecast enhancements over historical mean forecasts as large as 30% (in terms of R²).
The fundament of the proposed model factors are the expected dividend yield, the future dividend growth and a valuation change component. The first two elements are familiar from the Gordon model, while the latter is added to factor in the impacts of behavioral and risk aversion changes over time, which could lead to periods of over- or undervaluation, respectively low or high expected returns. A practical problem is, of course, how these elements are estimated to create a forecast, and in what combination should such estimates be used.
By running the methodology in various combinations (yield alone, yield and growth, valuation alone, and yield-growth-valuation) for the S&P 500 log returns over 10 and 20 years, the researchers show that there are 4 different proxies for the valuation change that are useful in practice:
– the current market price divided by the 10-year average of the inflation-adjusted earnings per share (TRCAPE);
– the ratio of equity market cap in the economy to the rest of the wealth in that economy (WPC);
– the Buffett valuation ratio (BUF, i.e., market value of equity divided by quarterly GDP);
– a consumption expenditure proxy for non-durables and services (CON).
The estimate combinations of the Gordon model elements are as follows:
– for the yield: dividend yield, total yield, net total yield, and cyclically adjusted total yield (CATY);
– for the growth: earnings growth, dividends growth, total yield growth, and CATY growth, respectively.
The 3-component model (yield-growth-valuation) that uses valuation change estimates based on the cyclically adjusted price-to-earnings ratio (CAPE) of Campbell and Shiller (in the total return version) is the most consistent performer. The authors conclude that this model generates significant improvements compared to historical mean model forecasts and to asset allocations, which based on the model forecasts can raise a stock-bond-portfolio’s Sharpe ratio by over 60% and reduce portfolio Value-at-Risk by more than 50%. (Note that the authors have not tested this methodology on other indices in the US or in other countries.).
2. The Fed’s impact on stocks
With the significant changes in monetary policy in the US (and other major economies) after the financial crisis (GFC) and the repeat of the same playbook at the start of the pandemic, investors and academics have made efforts to understand and quantify the impact that these actions have had on financial markets. One such study by Tālis J. Putninš is shown here and presents an intriguing look at how stock markets reacted to the massive expansion of the Fed’s balance sheet.
During COVID, the Fed doubled its assets from $4.17tn to $8.33tn (37% of US GDP), which was a scale and speed of growth (most of it during the first 5 months of the pandemic in 2020) exceeding even that of the 2008–2009 GFC and post-GFC quantitative easing (QE) programs. As a result, the author emphasizes, the stock market reacted to the Fed’s balance sheet expansion with positive returns in the 1–4 weeks following the Fed’s actions: a 10% growth of the Fed’s balance sheet is estimated to result in a positive 9.1% impact on cumulative stock market returns over the following 5 to 10 weeks, with most of the effect occurring in the 5 weeks after the Fed’s intervention. But the opposite is also true: the Fed steps in to respond to stock market drops and crashes — the estimates show that a 10% decline in equity markets leads to a cumulative balance sheet expansion of around 5.6% over the following 10–15 weeks, with most of the effect occurring in the 2 months following the shock.
It is important to understand the asymmetries here:
– the Fed responds more forcefully to negative stock market returns (balance sheet growth) than to positive returns (shrinking the balance sheet);
– the market is more sensitive to the Fed’s balance sheet shrinkage than to the expansions;
– the impact is unequal: more cyclical sectors (e.g., consumer durables) are more sensitive to the Fed’s interventions than less cyclical sectors (e.g., utilities); small stocks are substantially more sensitive to the Fed’s actions than large stocks.
The 2 main channels of impact are long-term bond yields (i.e., bond purchases compressing yields and discount rates, hence pushing up stock prices) and expected macro conditions (i.e., future expansion or contraction influencing economic conditions and hence impacting corporate earnings). But during COVID, the Fed also directly purchased corporate bond exchange-traded funds (ETFs), a scope of policy change that likely also had a strong impact on the stock market. We need to keep in mind that other central banks, such as the Bank of Japan (BoJ) directly bought stock ETFs.
The model that Putninš uses is a vector autoregression (VAR) that links the logarithmic weekly growth of Fed assets to the weekly stock market (S&P 500) returns. The historical data used covers the period January 2009 to October 2020 and captures the first more significant contraction of the Fed balance sheet since the GFC that took place in 2018 and was followed by a significant drop in the stock market. The model can be employed as an estimate of the impulse reaction function of the Fed and the market to each other. For example, as the author demonstrates, an investor could model how the stock market would develop without interventions under various scenarios or to a different magnitude of unanticipated shocks to the balance sheet or the market.
What this research shows is that the Fed’s interventions tend to create a disconnect between the stock market and the real economy because the moment when expectations are supposed to lead to a drop in stock prices, steps in, expands its balance sheet and influences market participants, prices and earnings. Similarly, unwinding these overblown balance sheets can be expected to have an asymmetric impact on equities.
3. Good old macro
One of the most widely employed approaches to create forecasts is by using macroeconomic factor models. Unfortunately, the vast set of macro variables, their availability and frequency, as well as their differences (including methodological) across countries make developing such models very location-specific. There have been many papers published, covering mostly countries in Europe, the Americas and Asia. The model presented here is one version of a vector autoregression that includes only a few variables but can be reduced or expanded depending on what is shown to work for the respective country’s markets.
For instance, the model with the first five macro variables has been shown (in different specifications) to have good predictive power in the Nordic countries (specifically, Sweden, Finland, Denmark and Iceland), while a model incorporating industrial production, money supply (M1), inflation and treasury yield or discount rate has been shown to work for Japan and the US in other studies.
The economic logic behind such models is usually well understood, but the exact specification (also in terms of lags) can be quite tricky. Generally, it is assumed that changes in macro variables have an impact on consumption and investing behavior in the economy, hence also impacting earnings and, ultimately, asset prices, including stock prices. But the exact transmission mechanism for each variable can be different (and sometimes quite complex), for instance:
– future consumer spending rates or government spending rates are often linked to unemployment levels, inflation, and GDP;
– changes in monetary policy (e.g., via interest rates or money supply) often have an impact on investor expectations (such as corporate earnings).
Empirical literature is probably the best source of “inspiration” when it comes to selecting the right variables. Existing research has shown, for example, that interest rates are the variable with the most significant impact in terms of predictive power, across many industrialized countries. This is likely because rates have an impact on the affordability of debt funding and financing and default risks in general, as well as on discount factors used to price various assets.
The model above can be specified using just some of the variables given. For example, running a VAR OLS (ordinary-least-squares regression) and using the OMX equity indices for Sweden (monthly data), it has been shown that the most significant factors in predicting stock returns are the repo rate, the inflation rate and the slope of the yield curve. Additionally, for some model specifications, the first differences might be less appropriate compared to log changes. And finally, these choices could also depend on the market or segment (e.g., sector) for which a forecast is needed.
References
1. Rui Ma, Ben R. Marshall, Nhut H. Nguyen, and Nuttawat Visaltanachoti, CFA, Estimating Long-Term Expected Returns, Financial Analysts Journal, 2024
2. Boudoukh, Jacob, Matthew Richardson, Robert F. Whitelaw, The Myths of Long-Horizon Predictability, Review of Financial Studies, 2008
3. Devpura, Neluka, Pareshm K. Narayan, and Susan S. Sharma, Is Stock Return Predictability Time-Varying?, Journal of International Financial Markets, Institutions and Money, 2018
4. Tālis J. Putniņš, Free Markets to Fed Markets: How Modern Monetary Policy Impacts Equity Markets, Financial Analysts Journal, 2022
5. Andreas Humpe, Peter Macmillan, Can Macroeconomic Variables Explain Long-Term Stock Market Movements? A Comparison of the US and Japan, CDMA Working Paper №07/20, 2007
6. F. Cavalli, A. Naimzada, N. Pecora, A stylized macro-model with interacting real, monetary and stock markets, Journal of Economic Interaction and Coordination, 2021
7. Ferreira, M. A. and Santa-Clara, P., Forecasting stock market returns: The sum of the parts is more than the whole, Journal of Financial Economics, 2011
Author: Nikolay
Founder of MoneyCraft
