A new interesting financial research paper gives an idea to build a diversified portfolio of leveraged ETFs (scaled down to have the same risk as a benchmark asset allocation built from a non-leveraged ETFs) to beat benchmark asset allocation. However, caution is needed as the most of the outperformance is due to inherent leveraged position in bonds because excess ratio of cash in portfolio (which is the result of using leveraged ETFs instead of non-leveraged ETFs) is invested in a short to medium term bonds:

Authors: Trainor, Chhachhi, Brown

Title: A Portfolio of Leveraged Exchange Traded Funds

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3272486

Abstract:

Leveraged exchange traded funds (LETFs) are marketed as short-term trading vehicles that magnify the daily returns of an underlying index. With the proliferation of LETFs over the last 10 years, a diversified portfolio that mimics the returns of a 100% investment can be created using only a fraction of the investor’s wealth. Results suggest a portfolio created with LETFs outperforms a portfolio using traditional ETFs by approximately 0.6% to 1.4% annually by investing the excess wealth in a diversified or short to mid-duration bond portfolio. Downside risk is reduced using LETFs because the majority of the LETF portfolio is invested in a relatively safe bond fund.

Notable quotations from the academic research paper:

"Leveraged exchange traded funds (LETFs) were first listed in 2006 by Proshares, although leveraged mutual funds have been around since 1993. Although Proshares introduced +/- 2x products, Direxion upped the leverage ante with +/- 3x funds in late 2008. Because LETFs are designed to return a daily multiple, the constant daily leverage results in uncertain realized leverage over longer periods of time. In general, realized leverage tends to fall over time due to the volatility of returns.

With the expanded scope of the LETF market, it is now possible to create a diversified portfolio of LETFs that mimic a typical investor’s portfolio. By using 2x or even 3x funds, only a fraction of the investor’s portfolio is needed to attain the same exposure an investor has using standard ETFs and/or mutual funds. The downside is the higher expense ratios of LETFs, their internal financing costs, general leverage decay, and trading costs due to needed rebalancing to maintain the correct exposure. The upside is the excess wealth available that can be invested in relatively safe assets, and if the return to the invested excess wealth exceeds the higher cost of LETFs, returns should be enhanced.

This study shows a portfolio using 2x or 3x LETFs outperforms a portfolio using standard ETFs based on the same underlying indexes. This is possible since a 2x needs only 50% while a 3x needs only 33% of the wealth to create the same exposure to the underlying indexes. Even in the low interest environment from 2010-17, a portfolio of 2x LETFs outperforms a portfolio of standard ETFs by 0.9% annually. A portfolio of 3x LETFs outperforms by 1.8% annually.

Simulated LETF returns since 1946 show a portfolio of 2x LETFs can be expected to outperform a standard portfolio by 0.6% while a 3x LETFs outperforms by 1.4% after expenses. The caveat to this strategy is LETF portfolios must be rebalanced as their initial positions deviate from “optimal” asset allocations even faster than standard portfolios. A 10% barrier threshold keeps the risk exposure within reasonable bounds while keeping 2x rebalancing requirements to roughly each quarter and 3x to approximately monthly.

A critical determinant of the success of this strategy is the magnitude of returns to the capital not invested in the LETFs. This study assumes excess capital is invested in a short-term bond ladder and if the return to this ladder exceeds the borrowing cost from the implied leverage of LETFs and their higher expense ratios, LETF portfolios outperform. Historically, this occurs the majority of the time with 0.6% to 1.4% average annual outperformance with a simultaneous reduction in downside risk."

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A new research paper related mainly to:

#41 – Turn of the Month in Equity Indexes

Authors: McGroarty, Platanakis, Sakkas, Urquhart

Title: A Seasonality Factor in Asset Allocation

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3266285

Abstract:

Motivated by the seasonality found in equity returns, we create a Turn-of-the-Month (ToM) allocation strategy in the U.S. equity market and investigate its value in asset allocation. By using a wide variety of portfolio construction techniques in an attempt to address the impact of estimation risk in the input parameters, we show significant out-of-sample benefits from investing in the ToM factor along with a traditional stock-bond portfolio. The out-of-sample benefits remain significant after taking into account transaction costs and by using different rolling estimation windows indicating that a market timing strategy based on the ToM offers substantial benefits to investors when determining the allocation of assets.

Notable quotations from the academic research paper:

"Seasonality is a well-known characteristic of financial markets with much empirical literature noting various types of seasonality in stock returns. Simple seasonality-driven investment strategies have attracted significant interest from academics and investors over the last forty years.

Amongst the calendar effects, the turn-of-the-month (ToM hereafter) has been acknowledged as one of the strongest and persistent seasonality found in stock returns. The ToM effect is the tendency of the stock market returns to display particularly high returns on the last trading day of the month and the first three trading days of the next month.

This study contributes to the literature on calendar anomalies in several dimensions. We examine the out-of-sample portfolio benefits resulting from adding the ToM portfolio to (i) a traditional equity-bond mix, (ii) a market portfolio, (iii) a portfolio which consists of the market portfolio, the small size portfolio and the value portfolio, and (iv) a portfolio, which consists of the market, the small size, the value portfolio and the winner portfolio.

We employ a wide variety of sophisticated and popular asset allocation techniques to provide robustness to our results. Specifically, we employ the mean-variance (Markowitz) portfolio optimization, portfolio optimization with higher moments, Bayes-Stein shrinkage, Bayesian diffuse-prior portfolio, Black-Litterman and another portfolio construction method that combines individual portfolio techniques, to ensure that our results are not just a peculiar artefact on one particular asset allocation technique. Finally, we assess the ToM for low, medium and high-risk averse investors, as its effectiveness in the portfolio might depend on the investor’s level of risk aversion.

Our empirical evidence suggests that the ToM portfolio adds value when included in different portfolios. Our results hold for different levels of risk aversion, portfolio techniques and estimation windows. Finally, our results are not eliminated by the including realistic transaction cost estimates, indicating that the creation and implementation of a ToM factor should be of great interest and potential value to investors.

"

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Short answer? – Probably no … A new academic research paper concludes that "the recent worldwide regime of increased liquidity, apart from some exceptions, is not accompanied by robustly significant decreases of anomalous returns in the US and the majority of other markets." Research paper related mainly to:

#14 – Momentum Effect in Stocks
#25 – Size Premium
#26 – Value (Book-to-Market) Anomaly
#77 – Beta Factor in Stocks

Authors: Auer, Rottmann

Title: Have Capital Market Anomalies Worldwide Attenuated in the Recent Era of High Liquidity and Trading Activity?

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3275377

Abstract:

We revisit and extend the study by Chordia et al. (2014) which documents that, in recent years, increased liquidity has significantly decreased exploitable returns of capital market anomalies in the US. Using a novel international dataset of arbitrage portfolio returns for four well-known anomalies (size, value, momentum and beta) in 21 developed stock markets and more advanced statistical methodology (quantile regressions, Markov regime-switching models, panel estimation procedures), we arrive at two important findings. First, the US evidence in the above study is not fully robust. Second, while markets worldwide are characterised by positive trends in liquidity, there is no persuasive time-series and cross-sectional evidence for a negative link between anomalies in market returns and liquidity. Thus, this proxy of arbitrage activity does not appear to be a key factor in explaining the dynamics of anomalous returns.

Notable quotations from the academic research paper:

"Recent years have been characterised by unprecedented changes in trading technology and transaction costs. A lot of authors document significant advances in algorithmic trading and increased utilisation of online brokerage accounts and observe drastic declines in, for example, standardised aggregate costs of trading for NYSE, NASDAQ and AMEX stocks of on average 97% from 146 basis points in 1980 to 11 basis points in 2006. Standard measures of liquidity have increased substantially because this new market environment of reduced trading frictions stimulates trading activity. For example, they present evidence that:

(i) the average monthly share turnover on the NYSE rose from about 5% in 1993 to about 26% in 2008 (and the average daily number of transactions increased about ninetyfold in the same period), whereas it was almost unchanged in the decades before,

(ii) mainly institutional trading volume accounts for this increase and

(iii) increased volume is associated with higher market quality (i.e., closer conformity to random walk behaviour).

Motivated by these observations, several studies have analysed whether increased liquidity has triggered greater anomaly-based arbitrage and thus attenuated capital market anomalies. In their conclusion, Chordia et al. (2014, p. 57) argue that  "return predictability would diminish to a greater extent in countries that have experienced greater enhancements in trading technologies and larger increases in trading activity and liquidity" and that this "hypothesis awaits rigorous testing in an international context". This is where we step into the picture. We extend the hedge portfolio evidence of Chordia et al. (2014) to an international setting.

Figure 1, reporting trends and growth rates for the number of traded shares in different regions of the world, shows positive tendencies worldwide and that there are indeed differences in the timely development of trading activity. For example, trading activity appears to have increased more significantly in European markets than in the US. Thus, we would not only expect to find evidence on vanishing anomaly returns in other markets as well but also that the magnitudes of the changes in anomaly returns are quite different across individual markets.

Using a novel dataset containing arbitrage portfolio returns for the four well-known anomalies of size, value, momentum and beta for a wide range of developed stock markets, we start our analysis by testing whether these anomalies still exist and whether the corresponding arbitrage portfolio returns exhibit trending behaviour. We also investigate trends in market liquidity in a more detailed fashion than in our previous illustration.

Using a novel dataset covering three decades, we find that the recent worldwide regime of increased liquidity, apart from some exceptions, is not accompanied by robustly significant decreases of anomalous returns in the US and the majority of other markets. We cannot establish a persistent negative link between arbitrage portfolio returns and share turnover in both the time-series and the cross-sectional dimension. These results suggest that aggregate liquidity may be a measure too coarse for our purposes or that liquidity in general may not be the key driver of the dynamics of international anomaly portfolios."

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A new financial research paper gives an ideas of how to allocate capital across several well known factor strategies:

Authors: Blin, Ielpo, Lee, Teiletche

Title: Factor Timing Revisited: Alternative Risk Premia Allocation Based on Nowcasting and Valuation Signals

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3247010

Abstract:

Alternative risk premia are encountering growing interest from investors. The vast majority of the academic literature has been focusing on describing the alternative risk premia (typically, momentum, carry and value strategies) individually. In this article, we investigate the question of allocation across a diversified range of cross-asset alternative risk premia over the period 1990-2018. For this, we design an active (macro risk-based) allocation framework that notably aims to exploit alternative risk premia’s varying behavior in different macro regimes and their valuations over time. We perform backtests of the allocation strategy in an out-of-sample setting, shedding light on the significance of both sources of information.

Notable quotations from the academic research paper:

"Alternative risk premia investing has grown rapidly in popularity in the investment community in recent years. They provide systematic exposures to risk factors and market anomalies that have frequently been widely analyzed in academic research. The vast majority of the academic literature solely focuses on the identification and the analysis of individual alternative risk premia strategies. On the contrary, this article addresses the question of allocation among alternative risk premia.

The standard approach in the industry is to apply a risk-based allocation mechanism, particularly equal risk contribution (ERC) in which one allocates the same risk budget to all components in the portfolio. One of the perceived key benefits of this approach is that it does not require expected returns as input but solely risk measures, hence the name “risk-based”. This no-views/agnostic feature alleviates the pitfalls of forecasting, which is already a challenge for traditional assets but even more so for alternative risk premia that are newer or are perceived as more complex strategies.

Despite this, recent research lends more support to the idea of some predictability of factor returns. In this article, we extend those results by focusing on the relationship between alternative risk premia and macro regimes that we define through nowcaster indicators. We consider that three major macroeconomic risks that affect risk premia: growth, inflation and market stress/volatility.

To model the influence of these macro risks, a regime approach has proven effective. To characterize macro regimes for growth, inflation and market stress, we build our own nowcasting (contraction of “now” and “forecasting”) indicators since 1990. Seeking for simplicity, our nowcasters are simple averages of z-scores of a large cross section of indicators across a large set of countries. For instance, the “growth” nowcaster contains close to 500 economic times-series across major developed and emerging countries accounting for 85% of world GDP. In Appendix A, we provide more details on the construction of the nowcasters.

To characterize economic regimes in a more precise way, we use both the average of all properly scaled economic indicators (the “nowcaster” per se) but also take advantage of the information in the cross-section by accounting for the proportion of indicators that are improving or deteriorating for every period (called “diffusion” index below). In practice, the diffusion index gives some further indication about whether the economy is improving (when diffusion index rises) or deteriorating (when diffusion index declines). On the basis of the nowcaster and diffusion indices, we define four regimes:

– Low-Up: negative nowcaster (Low) and diffusion index above 50% (Up)
– Low-Down: negative nowcaster (Low) and diffusion index below 50% (Down)
– High-Up: positive nowcaster (High) and diffusion index above 50% (Up)
– High-Down: positive nowcaster (High) and diffusion index below 50% (Down)

For the growth factor, this is similar to the usual Recession (Low-Down) / Recovery (Low-Up) / Expansion (High-Up) / Slowdown (High-Down) classification.

In Figure 1, we represent the different macro factor nowcasters and highlight different regimes by using a distinctive color scheme.

To give a first sense of the sensitivity of alternative risk premia to macroeconomic regimes, we represent in Figure 2 growth regime-conditional excess Sharpe ratios, i.e. the difference between Sharpe ratios in each growth regime and the long-term (unconditional) Sharpe ratio. Some strategies can be seen as being “defensive”, as they tend to do relatively well in either slowdowns (High-Down regime) or recessions (Low-Down regime), such as equity quality, equity low-risk, trend-following, or bonds carry. Conversely, some strategies benefits from better economic conditions such as equity size, FX carry or volatility carry.

In next section, we define and implement a process to allocate among alternative risk premia which incorporates, along other dimensions, each risk premium’s sensitivities to the macro regimes. The approach is based on the active risk-based methodology derived in Jurczenko and Teiletche (2018) which adapts Black and Litterman (1992) framework to the risk-based world. In practice, the model ends up combining a risk-based strategic portfolio with a set of dynamic allocation active views.

As our focus is on dynamic signals, we do not seek to improve the strategic portfolio. We adopt a simple ERC portfolio, which consists of equal contributions to portfolio volatility across all alternative risk premia. The strategic portfolio is then modified to incorporate dynamic deviations in two steps.

In a first step, we compute z-score reflecting dynamic allocation based on an equal-weight of two z-scores, for macro factors and valuation respectively. Regarding macro factors (growth, inflation, market stress), z-scores are computed as the excess return in the current (“nowcasted”) regime vs full sample return scaled by historical volatility.

In the second step, these dynamic z-scores are transformed into active portfolio deviations calibrated to deliver 1% tracking-error relative to the strategic portfolio. The sum of active deviations is set to zero, so that the portfolio is fully invested, similar to the strategic allocation.

Table 4 summarizes the performance statistics of the portfolio. The first column shows the strategic ERC portfolio. The second to fourth columns show the “dynamic” portfolios that incorporate active tilts, based on nowcasters and valuation signals individually and in combination.

"

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A new financial research paper has been published and is related to all equity long short strategies but mainly to:

#33 – Post-Earnings Announcement Effect

Authors: Li

Title: Does Too Much Arbitrage Destablize Stock Price? Evidence from Short Selling and Post Earnings Announcement Drift.

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3249254

Abstract:

Stein (2009) suggests that too much arbitrage capital exploiting underreaction can lead to overreaction, pushing price further away from fundamental value. I test this hypothesis by investigating the relation between changes in short interest ratio around earning announcement and the subsequent drift return. There are two main findings in this paper. First, my results suggest that too much arbitrage capital does contribute to overreaction (with a t-statistics around 4 on average). These findings are robust to alternative sample periods or length of the window for drift calculation. Second, contrary to the findings in prior literature that show that short sellers mitigate the magnitude of drift, my results show that almost all of this effect are actually contributed by the observations that are more likely to represent overreaction.

Notable quotations from the academic research paper:

"Conventional wisdom believes that as more arbitrage capital starts to trade a given anomaly, any abnormal returns will be eventually eliminated (up to risk and limits to arbitrage) and stock prices will be pushed closer to fundamental values. In other words, the more arbitrage capital, the more efficient the market is likely to become. However, Stein (2009, Presidential Address: Sophisticated Investors and Market Efficiency) questions this simple intuition and shows that when the anomaly does not have a fundamental anchor and when arbitrageurs are not aware about how many other arbitrageurs are trading the same anomaly, arbitrage activity may lead to price overshoot, pushing price further away from fundamental value. Prior literature has very little empirical evidence regarding this implication. Therefore, in this study I try to test whether too much arbitrage capital destabilizes stock price.

The anomaly utilized in this paper is post earnings announcement drift (henceforth, PEAD). Three major advantages associated with PEAD makes it an ideal setting for testing the above implication.

First, it does not have a fundamental anchor so that arbitrageurs do not have a benchmark to gauge the level of under or over valuation. Second, it is one of the most persistent anomalies that are often followed by actively managed hedge funds. Third, it allows me to pin down the time at which arbitrageurs are most likely to take actions – that is, if an arbitrageur was to maximize his profit, he would be more likely to take action in a tight window around the earnings announcement date.

The proxy for arbitrage capital is the change of short interest ratio around earnings announcement date. It is widely documented that short sellers tend to be informed traders who incorporate information and move prices closer to fundamental values. Also note that, in this study, I only focus on announcements with negative earnings surprise since these are the stocks that short sellers are more likely to target.

The relation between PEAD and change of short interest ratio is illustrated in figure 1.

Day 0 is the date when the earning announcement is released. Day -1 is one day before and Day 1 is one day after the announcement date. Together, the 3-day window forms the initial response period in which arbitrageurs will trade most intensively. The solid line illustrates the return pattern for negative earnings surprise announcement with insufficient arbitrage capital. In this case, a minor negative return is realized in the initial response period which is followed by a further negative drift. The dashed line illustrates the case when there is sufficient arbitrage capital. In this case, more arbitrage capital adjusts the price to fundamental value faster and therefore a moderate negative return (more negative than the solid line) is realized and no obvious further drift follows. The crossed line illustrates the case when there is too much arbitrage capital. In this case, due to too much arbitraging, a large negative initial response (potential overshoot) is followed by a positive drift (correction).

My findings suggest that too much arbitrage does seem to destabilize stock price. First, holding all else equal, announcements with larger increase in short interest ratio experience significantly more negative initial response (more correction). Next, I show that negative earnings announcements with positive abnormal drift have significantly higher change in short interest ratio than those with negative abnormal drift. Moreover, I find that, holding all else equal, stocks with the largest increase in short interest ratio (SIR decile 10) is almost 10% more likely to result in overreaction than stocks with the largest decrease in short interest ratio (SIR decile 1). In the end, I show that, holding all else equal, change in short interest ratio significantly contributes to overreaction. In particular, within stocks that have positive abnormal drift, the ones that experience the largest increase in short interest ratio average 1.55% higher drift than the ones that experience the largest decrease in short interest ratio. Robustness tests show that my results are not likely to be driven by extreme values in abnormal drift, particular year observations, or length of window for return calculations."

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We have mentioned it several times – we are quants but we love history and we love research papers like this:

Author: McQuarrie

Title: The First Eighty Years of the US Bond Market: Investor Total Return from 1793, Combining Federal, Municipal, and Corporate Bonds

Link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3260733

Abstract:

US securities markets took root after Alexander Hamilton’s refunding of the Federal debt in the early 1790s. Accordingly, a market in bonds has been in operation in the US for over two centuries. Until recently, however, little was known about the bond market prior to 1857. This paper focuses on investor holding period returns, using newly compiled data on bond prices, rather than focusing on the movement of yields, as in Homer (1963). It incorporates the relatively familiar Treasury securities from before President Andrew Jackson paid off the debt in 1835, but also includes state and city debt, which ballooned beginning in the 1820s, as well as corporate debt, from its beginnings about 1830 to its explosion after 1850. I find that all three classes of bonds provided investors with similar total returns, excepting a brief period in the 1840s when state securities plunged before recovering. I also find that real returns in the eight decades following 1793 were generally higher than the long-term average return of 3.6% proposed for bonds in Siegel (2014). I further find that in these early years, bonds sometimes out-performed stocks over periods of several decades, again contrary to Siegel’s thesis. The paper considers the implications of a demonstration that stocks and bonds performed differently in the nineteenth century as compared to the twentieth century.

Notable quotations from the academic research paper:

"The importance of the nineteenth century, in the context of financial history, is to provide a check on hasty generalizations from limited data. Returns from a few decades in the twentieth century, first made available in Fisher and Lorie (1964), must be regarded as limited indeed. This limited twentieth century data, which emerged as financial history was developing as a discipline and has been widely diffused in publications by Ibbotson (2016, Stocks, Bonds, Bills & Inflation), has strongly inflected conclusions about what investors can expect over the long-term. The twentieth century US data, especially following WW II when the US economy bestrode the world as a colossus, paints a very sunny picture for stocks, and a sad cloudy picture for bonds, memorialized in Siegel (2014, Stocks for the Long Run).

The US had a rather different economy in the nineteenth century, especially the antebellum years which have been the focus of this paper. Likewise, the US economy then held a very different and much more minor position in the world economy. Hence, it was rhetorically powerful for Siegel (2014) to advertise that two centuries of data told one consistent story: stocks are splendid, bonds are laggards. Consistent performance across two such wildly different epochs was strongly supportive of his thesis.

It now appears that Siegel’s (2014, Stocks for the Long Run) early nineteenth century database was both thinner than many readers may have realized (e.g., dividend payments were estimated rather than observed; many prominent stocks were excluded), and more prejudicial to bonds than may have been grasped (e.g., by taking the minimum of Federal and municipal yields, even after Federal bonds gained circulation privileges). The much thicker datasets here do not support Siegel’s attempt to generalize from mid-twentieth results to the very different circumstances faced by US investors in the early nineteenth century. As it becomes possible to stitch together an unbroken multi-century record for both stocks and bonds, discussion may turn to the factors that determine when stocks (bonds) will do well, and when stocks (bonds) will do poorly. There is now a counter to Siegel’s thesis: that both investments follow a random walk within bounds, and that these bounds may not differ by much across these two major categories of investment.

Stocks did out-perform bonds in the middle of the twentieth century, per Ibbotson and Siegel; but stocks did not out-perform bonds in the first few decades of the nineteenth century. Generalizations from the middle of the twentieth century do not hold—these now appear as simple extrapolations. Gainsaid in the nineteenth century, these extrapolated returns may not apply to the twenty-first century either.

Examining Figure 1, the pattern is straightforward. Yields rose through the 1790s, then declined until the War of 1812 (prior to the war, the government steadily paid down its debt). After the war Federal yields resumed their decline, ending at their low point for the period charted.

A simple summary of the newly uncovered sixty-four years of bond returns charted in Figure 12 might state:
1) returns for the period were well above the long-term average cited by Siegel (2014);
2) bonds are as subject to bull and bear markets as stocks;
3) bond returns can be depressed or super-charged over periods decades in length.

The most straightforward interpretation of Figure 14 is that bond investors never received the average return over any lengthy period. Rather, from time to time bond investors suffered depressed returns, most notably from the 1940s through 1980, but also from 1793 through 1814, while at other times, bond investors enjoyed sustained periods of unusually high returns, most notably from the end of the Civil War to the beginning of World War I, but also from the end of the War of 1812 to the beginning of the Civil War, and from 1981 to the present day. Bond investors were also vulnerable to sudden sharp shocks in which the real value of a bond portfolio dropped 30% or even 40% over a few years (these were mostly associated with bouts of wartime inflation). Conversely, during favorable periods bond investors could rack up multi-decade returns comparable to those expected from stocks. Over the eighty-seven years beginning in 1814, bond investors received an annualized real return of 7.12%–somewhat higher than the long-term return to be expected from stocks, according to Siegel, of 6.6%.

Figure 15 combines fifty years of bond data gathered in this paper with fifty years of stock returns. The pattern is not supportive of Siegel’s claim that stocks must out-perform bonds over decades-long periods. Nor does the pattern support Siegel’s (and Bernstein’s) expectation that real stock returns, measured over the long-term, will converge on an underlying constant, currently estimated by Siegel as 6.6%. Rather, stocks significantly underperformed this standard over the 1793-1843 period.

If Siegel (2014) had never published his thesis about stocks for the long run, and Figure 15 were the only evidence available on historical stock and bond returns in the nineteenth century, what would be the most straightforward interpretation of it?

Answer: that over most periods decades in length, stocks and bonds return about the same. Second, that returns fluctuate, consistent with a random walk within bounds, in which strings of good or bad performance, of any length, may occur. Accordingly, in the fullness of time sharp drops may occur, and stocks and bonds may drop together or not. Likewise, stocks and bonds may register an above-trend performance, lasting decades, which may be coincident or not. If the analyst is free to select an arbitrary beginning point, subject only to that point being decades in the past, then when measured at exactly the right (wrong) time, stocks can be shown to have under-performed bonds “over the long run.” The fifty years from 1793 provide such an example. Stocks returned 3.96% real annualized, while bonds returned 4.88%. As before, the difference sounds small until converted into ending portfolio values. Over those fifty years, perhaps one of the worst five-decade periods in the history of the US securities markets, stocks turned an investment of $1000 into $6,963, but bonds turned that $1000 into $10,807."

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