The 2020 plague grounded Antti Ilmanen from his regular job at AQR advising institutions on asset allocations. While he was not as productive as Isaac Newton was when he escaped the plague in 1665, it allowed him to update his classic Expected Returns (2011), which surveys the basic statistics of the major investment classes. Any investment professional should be familiar with the data and arguments presented in this book. At only 250 pages (including many footnotes), it is a concise source to start or refresh your knowledge in this space.
The problems highlighted in this book can be seen in this graph of US Treasury bond yields since 1877.
The first thing to note is that interest rates were relatively stable until 1950, revealing a seemingly steady bond return of around 4%. However, when interest rates started rising after World War 2, they rose continuously to record levels over the next three decades. One can empathize with the many economists in the 1960s who kept predicting yields would fall because they were at historical highs in a data set that went back 100 years, unaware they would have to wait 10 years to see mean-reversion kick in.
The second half of this chart involved the slow process of leaving the gold standard, which started in 1934 and was finalized by 1971. Given the enormous rise in inflation at the beginning of the fiat era and the latter decline, we have two observations in this dataset regardless of how many minutes, months, or years. Financial data can give the illusion of many degrees of freedom, but for many assets, the critical issue is how they behave over a full market cycle. Alas, the US has had only 11 bear markets since 1945.
This is why it is good to look not merely at countries like the US but also at other countries. For example, in the early 1920s, hyperinflation destroyed bonds in Austria, Germany, Greece, Hungary, and Poland. It's common to omit these as outliers, the result of mistakes our stupid ancestors made, as exemplified by the eponymous hero of the do-gooder economist tribe:
"A preference for a gold currency is … a relic of a time when governments were less trustworthy in these matters than they now are."
~ John Maynard Keynes, Indian Currency and Finance (1913)
We should remember the theme of the Old Testament's book of Judges, written three thousand years ago: a generation that grows up in good times will forget the virtues that got them there.
The average annual bond returns for countries lucky enough to win the big wars and avoid socialism may be 2% above cash, but this is a selective sample, and a 1% probability of a disaster event would reduce the US sample return by 50% (see Barro’s Rare Disasters and Asset Markets in the Twentieth Century). The real possibility of a regime change makes base rate data interesting, but not compelling.
A final point on the chart above is that the past 40 years have seen a continuous decline in interest rates. Antti estimates this added a whopping 2% annually to bond and equity returns over the past generation. This trend gives Antti the title of his book, in that we should get ready for an era where interest rates are, at best, no longer going to help us.
Below are observations on various asset classes mentioned.
Low Volatility Premium
Antti mentions two models that explain the low volatility effect: Black (1972) and Asness, Frazzini, and Pedersen (2020). The latter paper is empirical but references a model by Frazzini and Pedersen (2014). Black's model was inspired by the idea that only the government can borrow at the risk-free rate, anchoring the Security Market Line (SML) above the risk-free rate and making it flatter. The approach of Frazzini and Pedersen (F&P) involves investors reaching for greater market exposure, as rules of thumb constrain them (e.g., the 60-40 equity-bond mix), and so try to get more of the equity premium by taking on higher beta. This also flattens the SML.
The problem for both of these models is that they can explain why low vol stocks have positive alpha and high vol stocks have negative alpha, but not why returns are flat or declining by beta/volatility. That is, they explain why the slope of the standard CAPM should be flatter, but it should still be upward sloping. In the F&P model, investors are reaching for high beta because they think it will generate higher returns, but such stocks have historically generated lower returns. A plausible theory should get the sign correct.
On a more technical note, the F&P model is a representative agent model, masking as a more general one. All you need to break their model is to add a single unconstrained agent, and she would arb the bejesus out of the SML, shorting high beta stocks and going long lower beta stocks. It would be a money pump, which is not an equilibrium. In practice, this would be hedge funds given prime broker margining of around 6-fold leverage, the leverage constraint rarely binds. I have worked at several significant hedge funds, and the consistent tilt was towards high volatility/beta stocks, just like one sees with mutual fund managers, and there is the ability but little interest in shorting high volatility stocks hedged by a long position in lower-volatility stocks.
Further, if investors are reaching for high beta qua high beta, we should see this in retail demand, but we don't. The high volatility ETF is ten times less popular than its low volatility counterpart (SPHB vs. SPLV). Sure, investors love volatile assets like bitcoin, ARK, and FAANG stocks, but not when presented as volatility unrelated to an investment thesis. Volatility or beta stripped of its incidental nature, it is not attractive, contra the F&P model.
Misunderstanding the essence of the low vol anomaly generates observations like that Buffet's alpha was the unintended result of being the accidental OG of low vol investing. You could say he was lucky to have loaded up on the low vol factors, but that’s a pretty lame takeaway. Buffet has articulated his investing philosophy at his annual meetings since the 1960s, and he is no Straussian; there's no esoteric meaning disguised within paradoxical statements. He likes value companies, those with strong balance sheets and high cash flows. He likes to buy monopolies, firms with big moats, just as Peter Theil recommends in his book Zero to One. Companies with strong cash flows, little debt, and monopoly power unsurprising have low vol. Low vol is incidental to his strategy.
One might be tempted to think the low-vol anomaly is, therefore, a consequence of Buffet's Graham & Dodd investing principles, but the problem here is that among the many non-value companies these value investors ignore, returns go down the higher the volatility.
Antti mentions skew as an explanation but does not reference a model. This is for a good reason, as these models are inconsistent. Initially, Harvey and Siddique (2000) emphasized co-skewness, a baby step from the traditional paradigm in that it emphasized the marginal effect on a diversified portfolio. That ‘co’ nuance is irrelevant. Still, the thought was some sort of transformation was possible within the standard framework. Post, Levy, and Van Vliet (2008) showed that if you add a skew parameter to a standard utility function, it only explains the low returns to high vol stocks if it also removes global risk aversion, which removes the equity premium.
I think it’s possible to generate a preference for skew or positive tails within a standard model by acknowledging that a long low-beta/short high-beta portfolio is risky due to its relative risk or benchmark deviation. Thus it is not possible to completely offset the natural demand for high volatility stocks, which are attractive for several reasons (newsworthiness, bullish selection bias, lottery preference, convex institutional incentives, etc., see Blitz, Falkenstein, and van Vliet (2014)).
Nassim Taleb is well-known for advocating a strategy of buying options because people underestimate the probability of outliers to the normal distribution, what he calls Black-swan events. By definition, any time someone generates a 100%+ return an improbable event occurred and these happen often, from your weekly lottery winner to those who bet the farm shorting mortgages in 2008. On average, however, assets with option-like characteristics are money-losing investments. People who sell lottery tickets make money, and they make more money on those lotteries with $100MM payoffs than those with $20 payoffs. Selling options, things with convex payouts, is known as shorting volatility and can involve the VXX ETF, variance swaps, staddles (a put and call), and more exotic options that focus on isolating gamma (e.g., calendar spreads) or out-of-the-money strikes.
The best data we have on the returns to volatility or gamma is on equity options from the mid-1980s, which shows that option sellers make money on average. This volatility-selling premium is like the equity premium in that they are highly correlated given their tendency to perform poorly in bear markets. The returns on far out-of-the-money options are even more decisive in favor of option selling, made significantly worse due to the relative size of the bid-ask spread (making it essential to not simply use end-of-day prices, which average to mid-prices).
Antti presents the returns to selling puts and it’s clearly positive. He did not mention it, but one could have presented the short vol strategies of selling the VXX, variance swaps, etc. I found it amusing that he offers his contrasting take with Taleb in such a nonforceful way ("judge for yourself", p. 211). If you could make money on average buying volatility or convexity, it would imply the most obvious trade: get paid to buy insurance. Many hucksters find Taleb’s view convenient because one can always point to a poor track record and say, 'only a fool looks at sample data!' (note: all data is ‘just’ sample data). If you sincerely believe that is true, I suppose “judge for yourself” is a nice way to say, “good luck with that.”
Antti states that "risk is not rewarded within asset classes (p. 105)." The italics imply they are rewarded across asset classes. Yet the only obvious demonstration of this would be the term premium (overnight to 30-year maturity), credit premium (government bonds to corporates), and the equity premium to corporate bonds. Thus, we read two pages later that there is no risk premium across industries, countries, or currencies, i.e., do not expect a premium for investing in technology vs. utilities, Mexico vs. Canada, or the Bolivar vs. the Swiss Franc.
We should not presume a 'risk' premium exists until someone can create a version of this theory that explains at least half of the data. The efficient market hypothesis explains the difficulty of outperforming the market, but as everyone knows of anecdotal exceptions, most are skeptical. Meanwhile, the risk-reward theory of asset pricing (i.e., the CAPM and its APT spawn) are accepted with hardly any skepticism, even though it can merely explain why T-bills have the lowest returns, bonds something higher, and everything else like equities higher still.
It would be better to say, riskless securities require a near-zero return because they have a significant convenience yield, in that they can be hypothecated as cash collateral (e.g., T-bills are often considered ‘cash securities’). Debt requires a lower return premium because of its non-discretionary payment schedule and seniority in bankruptcy. 'Risk premia' are just excess returns over these special return-deficient assets. Risky investments generate positive returns over time for the simple reason that if they did not, investors would pull their money out of risky assets, which is not an equilibrium.
Equity Returns and GDP Growth
Interestingly, there is almost zero correlation between economic growth and equity returns, over the past 20 years, as well as the 1900-2000 period among 17 developed nations. For example, Latin America has relatively poor GDP/capita, but generally, solid equity returns, while China has grown spectacularly since 1990 while generating low equity returns.
This suggests the equity return is more like an equilibrium feature of a negotiation, which varies based on the cultural and legal framework as opposed to anything generated by a representative agent with a standard utility function. This has the nice implication that if the US becomes a basket-case like Argentina, those fortunate enough to have capital will still find equities an attractive investment.
The credit premium refers to the return premium from Treasuries to corporate debt (i.e., BBB+ to AAA is Investment Grade, BBB- to B and lower is High Yield). He finds a 1% premium for IG and 2.5% for HY. I am skeptical. Much of the problem is because we only have good data on fixed income credit returns dominated by a falling interest rate background, so disentangling the duration correctly is very important. Given that HY bonds generally are callable the duration is subject to not obvious.
His data is based on basically two data sources, the Barclays and ICE BankAmerica corporate bond indices. These are not directly tradable. The two highest volume HY ETFs have been around since 2008, and generate returns lower by 1.6% annualized (note the ICE’s total return towering over the real traded junk ETFs, HYG and JNK). While these HY ETFs generate a return premium over the investment-grade bond ETF, it is by a mere 0.5% annualized, considerably less than the 1.5% Antti presents. In any case, at 0.5% or 1.5%, the HY spread has varied from 2.5% to 20%, which indicates an asset class where timing is crucial.
Environmental, Social, Governance
Antti briefly notes that ESG metrics are weakly correlated among its providers. This is understandable in that people are not so much rational as rationalizing creatures, so as a practical matter the question of whether a tree harvesting company is beneficial or horrible for the environment is more a political than a scientific question (see the debate on wood pellets here). It would have been nice to see some data on that point.
Momentum and Trend Following
Interestingly, he presents these together though they are quite different in application. Momentum is a cross-sectional strategy of selling or avoiding relative laggards and buying or tilting towards relative winners within an asset class. Trend-following is going long only when an asset class like the stock market has gone up and avoiding it when it has gone down (e.g., today, 5/24/22). Antti merely provides the chart for this tactic’s performance, but if you apply a simple past-12-month rule to the US stock market, you generate a slightly higher return compared to simply going long and also miss the latter half of our worst bear markets (see a simple spreadsheet of its performance below).
As a practical matter, however, trend following is vastly different than momentum, since one is applied continuously and the other in a conspicuous and disruptive on/off method. If one did apply a market timing rule, it would set a precedent for considering other market timing rules, and while these rules are often popular, they are almost always counterproductive. A general rule of never applying such rules might be a better policy than trusting your organization to apply only one trend-following rule, and not let these other bad rules get implemented.
Interestingly, the 'roll' component of commodity futures returns went away around 2005, when Erb and Harvey (2006) highlighted it in the Financial Analyst Journal. This is where one would go long futures in normal backwardization and short those with contango, riding the futures price like a pull-to-par on a Treasury Bill to reap the yield. This factor potentially generated at least half of commodity returns. This out-of-sample failure highlights the perils of subtle patterns, but also generates the comforting fact that when these patterns disappear, they tend to go to zero, not negative (e.g., see pairs trading).
Another interesting fact is that while commodities show an attractively low correlation with equities, they also offer an attractive 3% return. This is even though the average geometric return on individual commodities is zero. This is a case where one can take advantage of rebalancing to generate positive returns.
If we knew the means, volatilities, and correlations of all the asset classes, investing would be an unambiguous engineering problem. Finance will never be that way. The human networks that generate asset prices are not stationary systems like planetary orbits and are continually undergoing non-repetitive development. Since the printing press made it easy to record and disseminate information, every era of civilized human history is novel and ontologically distinct because humanity learns from the past only to create new emergent problems no one could anticipate. Bear markets recur, but these financial crises are similar in their effects rather than their causes.
Nonetheless, you have to frame your investment decision relative to something. Reading about base rates, volatilities, and historical performance, is essential for generating reasonable estimates. There are no asset return laws, and even trends are ephemeral at some level, but there are stupid estimates for these things (e.g., risk-free 20% return on a stablecoin), and we all strive to be less stupid under the sun.
This is wonderful. Your work has been a joy to read, study and steal. I have done my best to incorporate your insights about risk and volatility into our family office's investment algorithm; and the results have been anything but stupid - even for someone with my limited brainpower.
God bless. Stefan Jovanovich