The global economy’s problematic re-emergence from the Great Recession revived interest in Alvin Hansen’s 1939 secular stagnation hypothesis. Hansen coined the term to refer to the period of low growth prospects during the 1930s, which came on the back of slowing innovation and an ageing population. The parallels between the economic fundamentals of then and the last decade led Larry Summers to surmise that an era of protracted spells of low growth and low (nominal and real) interest rates would ensue. Indeed, rates across maturities have dropped to all-time low levels around the world.
An NBER working paper, ‘Duration-Based Stock Valuation’, adds to the growing literature examining the impact that these discount rate shocks have had on financial markets. Specifically, the author Jules van Binsbergen pays attention to the valuation of long duration assets by constructing several counterfactual fixed income portfolios that match dividend strips of the aggregate stock market. Counter to two anomalies found in the literature, the equity premium puzzle and the excess volatility puzzle, the following results are presented:
Between 1996 and 2020, a fixed income investor would have achieved similar, and likely substantially better, return performance than an investor in the S&P500 index. Expanding the horizon from 1970 to 2020 and to the Eurostoxx, the results remain valid. As such, Binbergen concludes that investors have received little to no compensation for taking long duration nominal dividend risk over the last fifty years.
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The global economy’s problematic re-emergence from the Great Recession revived interest in Alvin Hansen’s 1939 secular stagnation hypothesis. Hansen coined the term to refer to the period of low growth prospects during the 1930s, which came on the back of slowing innovation and an ageing population. The parallels between the economic fundamentals of then and the last decade led Larry Summers to surmise that an era of protracted spells of low growth and low (nominal and real) interest rates would ensue. Indeed, rates across maturities have dropped to all-time low levels around the world.
An NBER working paper, ‘Duration-Based Stock Valuation’, adds to the growing literature examining the impact that these discount rate shocks have had on financial markets. Specifically, the author Jules van Binsbergen pays attention to the valuation of long duration assets by constructing several counterfactual fixed income portfolios that match dividend strips of the aggregate stock market. Counter to two anomalies found in the literature, the equity premium puzzle and the excess volatility puzzle, the following results are presented:
- Between 1996 and 2020, a fixed income investor would have achieved similar, and likely substantially better, return performance than an investor in the S&P500 index. Expanding the horizon from 1970 to 2020 and to the Eurostoxx, the results remain valid. As such, Binbergen concludes that investors have received little to no compensation for taking long duration nominal dividend risk over the last fifty years.
- Furthermore, the majority of the duration-matched fixed income portfolios exhibit similar (if not higher) volatility to the aggregate stock market. For example, average monthly bond returns on constant maturity zero coupon bond strategies for maturities of 15 years and above have been more volatile over the last 25 years than the S&P 500 index.
The graph provides the cumulative performance of the S&P500 index and compares it with a fixed income counterfactual. The weights in the portfolio are based on the Gordon growth formula for a medium yield dividend, using a cut off of thirty years. It captures concisely the paper’s conclusion: bonds have done at least as well as the market.
Chart 1: Bond Returns Have Equaled, if Not Outpaced,
Equities Over the Past Several Decades
Source: Page 20 of “Duration-Based Stock Valuation“
Duration Matching, Bond Portfolio Returns, and the Data
In order to undertake the analysis, two key components are required: (i) a duration matching strategy and (ii) robust bond portfolio returns. For the former, the author defines the unconditional average returns that an index-implied portfolio of risky dividends of all maturities earns over and above the risk-free government bond counterparts. He estimates this by computing a sample average of expected returns on dividend strips minus a weighted one-period return on an n-year bond.
With regards to the second component, bond portfolio returns are based on bootstrapped zero curves. Returns could, therefore, be affected by the curve fitting methods. Despite this, the implied returns of the zero curves have a 0.998 correlation coefficient with the Vanguard Long-Term Treasury Fund Investor Shares (VUSTX), indicating a fairly accurate representation of actual trading data.
Chart 2: Replicated Returns Are a Close Match With
Vanguard LT Government Bond Returns
Source: Page 26 of “Duration-Based Stock Valuation“
Data on the S&P500 index are obtained from Global Financial Data. The author uses both the total return index and the price index. Monthly dividends are computed in the standard way by taking the difference between the monthly total return on the index and the monthly price appreciating index, multiplied by the lagged index level.
To construct zero coupon bond strips, Binbergen used the updated term structure data provided by the Federal Reserve. He also used monthly return data for tradable bond index funds as an additional source of long-term bond data. It is also used to verify the accuracy of the implied bond returns that follow from the yield data.
The Important Questions
Why Have Global Interest Rates Been So Low?
Intuitively, the natural real interest rate balances the supply of savings and demand for investment at full employment. In theory, for it to continually drop, savings must be in excess of investment. Larry Summers in his work offers five reasons why this has been the case (you can also read more about this in the Macro Hive directory):
(i) A reduction in demand for debt-financed investment.
(ii) Declining population growth rates.
(iii) Greater inequality.
(iv) A fall in the relative price of capital goods.
(v) The global move to accumulate central bank reserves.
What do the Findings of the Paper Imply for Pension Plans?
Defined benefit pension plans have been in an underfunding crisis for the past few decades. These plans have long duration, often risk free, promises to pension holders. To minimise the impacts of the crisis, they have invested in long duration equities. According to the author’s findings, if the long duration risk premium over the past 50 years is near zero or negative, this riskier strategy has not yielded the ex-ante expected returns.
What is Excess Volatility?
It is widely accepted that short-term stock market volatility is too excessive to be explained by the subsequent variation in the economic fundamentals. Over a longer horizon, however, this fades as greater availability of real information emerges. Nevertheless, a debate remains around whether long-term equity investments command a risk premium relative to fixed-income portfolios.
Does the Puzzle Still Apply?
Binsbergen finds that excess volatility in the stock market is ‘too low’ if we compare it to his fixed income calculations. Otherwise stated, the counterfactual bond portfolios used in the paper are at least as (if not more) volatile as those of the stock index. This, he says, implies that investors have not received any compensation for taking long duration dividend risk over the past five decades. The result calls in to question whether the equity premium puzzle has, therefore, resolved itself.
How Do Risk Premia Factor in?
One unexplored constraint of the puzzle is that risk premia’s need to have a substantial positive mean. Under this scenario, the average risk premium on dividend strips has to be large. The logic implies that, if long-term dividend risk premia are on average low, they have less potential of generating excess volatility.
What Explains the Relatively Lower Risk and Reward We See in the Stock Market?
There are at least five possible reasons offered up in the paper:
- Dividends exhibit a downward-sloping equity term structure.
- Long-term dividends can be increased with inflation, while bonds that offer fixed nominal payments cannot.
- Long-term dividends are mean-reverting to trend levels, while short-term dividends are exposed to disaster-type risks.
- Unexpected downward interest rate movements placed downward pressure on growth rates, explaining in part the poor performance of the stock market relative to duration-matched fixed income portfolios.
- Secular increases in long-term future dividend risk premia have hurt stock market performance by suppressing the value of the equity claim relative to the fixed income claim. Given that expected returns are the sum of dividend yields and expected growth (Gordon growth formula), low current dividend yields are not offset by higher future growth.
Bottom Line
The poor long-term performance of dividends compared with their fixed income counterparts is, in the author’s opinion, explained by the secular decline in long-term expected dividend growth rates. Extrapolating forward, we may look at the Japanese experience to form our future expectations. Interest rates in Japan reached very low level by 1996, after which the Nikkei 225 has not increased in value and bond yields have decreased further.
It seems, therefore, that if dividend yields and growth expectations are low, there will be little room for either nominal or real expected returns going forward. This could have implications for retirement savings, requiring workers to save a substantially higher percentage of their annual incomes to achieve an acceptable living standard in retirement.
Link to full paper: “Duration-Based Stock Valuation”
Sam van de Schootbrugge is a macro research economist taking a one year industrial break from his Ph.D. in Economics. He has 2 years of experience working in government and has an MPhil degree in Economic Research from the University of Cambridge. His research expertise are in international finance, macroeconomics and fiscal policy.
(The commentary contained in the above article does not constitute an offer or a solicitation, or a recommendation to implement or liquidate an investment or to carry out any other transaction. It should not be used as a basis for any investment decision or other decision. Any investment decision should be based on appropriate professional advice specific to your needs.)