Summary
- In this commentary, we discuss what we mean by the phrase, “no pain, no premium.”
- We re-frame the discussion of portfolio construction from one about returns to one about risk and argue that without risk, there should be no expectation of return.
- With a risk-based framework, we argue that investors inherently act as insurance companies, earning a premium for bearing risk. This risk often manifests as significant negative skew and kurtosis in the distribution of asset returns.
- We introduce the philosophical limits of diversification, arguing that we should not be able to eliminate risk from the portfolio without eliminating return as well.
- Therefore, we should seek to eliminate uncompensated risks while diversifying across compensated ones.
- We explore the three axes of diversification – what, how, and when – and demonstrate how thinking in a correlation-driven, payoff-driven, and opportunity-driven framework may help investors find better diversification.
1. Is it About Risk or Return?
For graduate school, I pursued my Masters of Science in Computational Finance at Carnegie Mellon University. One of the first degrees of its kind in the late 1990s, this financial engineering program is a cross-disciplinary collaboration between the finance, mathematics, statistics, and computer-science departments.
In practice, it was an intensive year-and-a-half study on the theoretical and practical considerations of pricing financial derivatives.
I do not recall quite when it struck me, but at some point I recognized a broader pattern at play in every assignment. The instruments we were pricing were always about the transference of risk in some capacity. Our goal was to identify that risk, figure out how to isolate and extract it, package it into the appropriate product type, and then price it for sale.
Risk was driving the entire equation. Pricing was all about understanding distribution of the potential payoffs and trying to identify “fair compensation” for the variety of risks and assumptions we were making.
For every buyer, there is a seller and vice versa and, at the end of the day, sellers who did not want risk and would have to compensate buyers to bear it.
1.1 Stocks for the Long Run
The idea that reward is compensation for risk is certainly not a new one. It is, more or less, the entire foundation of modern finance.
But sometimes, it seems, we forget it.
We are often presented with a return-based lens through which to evaluate the world of finance. Commonly reprinted are graphs like the one below, demonstrating century-long returns for stocks, bonds, and cash and accompanied by broad, sweeping generalizations like, “stocks for the long run.”
The truth is, if you plot anything on a log-axis over a long enough time horizon and draw it with a thick enough crayon, the line will eventually look pretty straight.
But if we zoom in to a horizon far more relevant to the lifecycle of most individual investors, we see a very different picture.
What we see is the realization of risk. We have to remember that the excess returns we expect to earn over the long run are compensation for bearing risk. And that risk needs to manifest, from time-to-time. Otherwise, if the probability of the risk being realized goes down, then so should the excess premium we expect to earn.
From a quantitative perspective, risk is often measured as volatility. In our opinion, that’s not quite right. We believe, given a long enough return history with enough realized risk events, risk can be better measured in a return’s distribution symmetry and fat-tailed-ness (i.e. “skew” and “kurtosis” respectively).
Below we plot the annualized excess real return distribution for U.S. equities over the last 100 years. We can see that the distribution is “leaning” to the right, indicating that large losses are more frequent than large gains.
We would argue that when we buy equities, what we are really buying is a risk. In particular, we are buying an uncertain stream of cash flows.
Now, this might seem a little weird. Why would we ever pay someone to bear their risk?
The answer is because, in many ways, we can think of equities as a swap of cashflows: one up-front bullet payment for the rights to an uncertain stream of future cash flows generated by the underlying business.
In theory, the price we pay today should be less than the net present value of all those future cash flows, with the difference representing the premium we expect to earn over time.
Uncertainty is the wedge between the values. Without uncertainty, no rational seller would give up their future cash flows for less than they are worth (or, if we do have an irrational seller, we would expect buyers to compete over those cashflows to the point they are fairly valued).
Thus, the premium will be driven both by certainty about the future cash flows (growth rate and duration) as well as the market’s appetite for bearing risk.
The more certain we are of those future cash flows or the higher the market’s appetite to bear risk, the smaller the expected premium should be.
1.2 “Funding Secured”
To get a better sense of the play between certainty and premium in the market, we can explore an example where we effectively collapse price into a binary “yes or no” event.
On August 7th, 2018, Elon Musk sent out the following tweets:
At the time he sent the tweet, Tesla shares were trading around approximately $365. The stock had opened around $340 that day and had jumped on news reporting that the Saudi sovereign fund had built a $2b stake in Tesla and some speculation about a potential buy-out.
Now let’s assume, for a moment, that Elon’s tweet said, “Deal struck to take Tesla private at $420, effectively immediately” What should the price of Tesla’s stock jump to? $420, of course.
Now Elon’s tweet merely said he was considering it. He also did not specify a timeline. But let’s consider two cases:
- The market believes a deal will be struck to take Tesla at $420 in the near future.
- The market does not believe Tesla will be taken private.
In the former case, the right price is approximately $420. In the latter case, the appropriate price is whatever the shares were trading at before the announcement.
Thus, where price trades between the two points can be interpreted as to the market’s confidence in the deal being done.
Hence, I tweeted the following:
(Note that when I sent out the first tweet, I hadn’t realized trading had been halted in Tesla.)
Assuming the entire day’s move was attributed to the buyout news, a price change from $340 to $380 only represents a 50% move towards the buy-out price of $420. The market was basically saying, “we give this coin-flip odds.”
1.2 Well ‘Skews Me
While modern portfolio theory uses volatility as the measure of risk, the connection between excess realized premia and volatility is tenuous at best. It certainty falls apart in highly skewed, fat-tailed return distributions.
Rather, skewness appears to be a much better measure of risk for most financial assets. And when we look at equity markets around the globe, we see the same fact pattern emerge: return distributions with negative skew indicating that losses tend to be (much) bigger than gains.
2. You’re An Insurance Company
What this type of risk-based thinking all boils down to is that you – and your portfolio – are really acting as an insurance company of sorts.
When we purchase insurance, we are really transferring our associated risk to the insurance company. To incentivize them to bear the risk, we have to pay an annual premium.
Similarly, when we buy stocks, we are really trading a certain cashflow today (the price) for a stream of uncertain cash flows in the future. The discount between the price we pay and the net present value of future cash flows is the premium we expect to earn. And when we sell stocks, we are effectively paying that premium.
So in building our portfolios, we should think like an insurance company.
Like an insurance company, we want to diversify the premiums we earn. Not only do we want to diversify within a given type of insurance, but we probably also want to diversify the type of insurance we offer. And, in an ideal world, the type of insurance would be uncorrelated!
2.1 Diversifying with Bonds
Enter the most traditional portfolio diversifier: bonds. Typically considered to be a “safe” asset, if we look at them through the lens of real excess returns, we can see that bond returns also exhibit negative skew and fat tails.
This makes sense, as when we buy a bond we are still bearing all sorts of risks. Not only do we bear the risk of a default, but we also bear inflation risk and interest rate path-dependency risk.
With U.S. Treasuries, default risk is likely minimized (depending on your perspective), and the other two risks might be less correlated than the traditional risks (e.g. economic growth) we see with equities. So combining stocks and bonds should help us control skew, right?
Well, not quite. Below we plot the annualized excess real returns for a 60/40 portfolio.
We see that skew and kurtosis remain. What gives?
Well, one answer is that while a 60/40 portfolio might be close to balanced in the terms of notional dollar exposure to each asset, it is completely unbalanced from the perspective of residual volatility.
Below we plot the relative contribution to risk of stocks and bonds over time in a 60/40 portfolio.
Because the payout for bonds is far more certain than the payout for stocks, not only is the expected excess premium much lower, but volatility tends to be much lower as well. This means that the premium earned from holding bonds is not large enough to offset the losses realized in equities.
Savvy readers will recognize this as the driving thesis behind risk parity. To strike a balance, we need to allocate to stocks and bonds in such a manner that they provide equal contribution to portfolio risk.
Below, we plot the annual excess real return distribution for a stock/bond risk parity portfolio that is levered to a constant volatility target of 8%.
What do we see? Skew and fat tails remain. Perhaps the answer is simply that we need more diversification. While in practice this might mean buying different assets, in theory it means exposing ourselves to different types of risk sources that lead to uncertainty in the value of future cash flows. We enumerate a few below.
In traditional asset allocation, trying to isolate and add these different exposures is very difficult.
First, it is worth acknowledging that not every type of risk necessarily deserves to earn compensation. In theory, we should only be compensated for un-diversifiable risks.
Furthermore, many of these risks have time-varying correlations and magnitudes, and often collapse towards a single risk factor during crisis states of the world.
Yet we would argue that there is a deeper, philosophical limit we should consider.
3. The Philosophical Limits of Diversification
What we keep running up against is what we call the “philosophical limit of diversification.”
The simplest way to think about the limit is this: If we can diversify away all of our risk, we should not expect to earn any reward.
After all, if we found some magical combination of assets that eliminated downside risk in all future states of the world, we would have constructed an arbitrage. We could simply borrow at the risk-free rate, invest in the appropriate blend of assets, and reap our risk-free reward.
That is why years like 2018, when 90% of assets lose money, have to occur from time to time. Without the eventual realization of risk, there is no reason to expect return.
3.1 The Frustrating Law of Active Management
A corollary of this philosophical limit is what we like to call “The Frustrating Law of Active Management.”
We go further in depth into this idea in another commentary, but the basic idea follows: if an investment strategy is perceived both to have alpha and to be easy, investors will allocate to it and erode the associated premium.
How can a strategy be “hard”? Well, a manager might have a substantial informational or analytical edge. Or, the manager might have a structural moat, accessing trades others do not have the opportunity to pursue.
But for most well-known edges (e.g. most major style premia), “hard” is going to be behavioral. The strategy has to be hard enough to hold on to that it does not get arbitraged away. Which implies that,
For any disciplined investment approach to outperform over the long run, it must experience periods of underperformance in the short run.
This also implies that,
For any disciplined investment approach to underperform over the long run, it must experience periods of outperformance in the short run.
For active managers, the frustration is that not only does their investment approach have to under-perform from time-to-time, but bad strategies will have to out-perform. The latter may seem confusing until we consider that a purposefully bad strategy could simply be inverted to create a purposefully good one.
And, as above, we cannot simply diversify our way out of the problem. After all, if there were a magic combination of active strategies that earned the same expected alpha but reduced the risk, everybody would pursue that combination.
4. Investment versus Investor Returns
So is the answer here to just, “suck it up?” Do we simply look at periods like 2000-2010 and say, “it’s the price we pay for the opportunity to earn long-run returns?”
We would argue both “yes” and “no.”
It all depends upon where an investor falls within their lifecycle. Young investors who are pursuing growth mandates may simply need to accept that skew and fat tails are the cost of earning the long-run premium. Too much diversification may lead to “failing slow.”
For investors in the later stages of their lifecycle, however, the math changes. Indeed, this is true for any individual or institution where withdrawals are concerned. When we have a withdrawal-driven mandate, it is the risk of “failing fast” that we need to concern ourselves with.
The problem is that investment-centric thinking often makes diversification seem foolish. To quote Brian Portnoy, “diversification means always having to say you’re sorry.”
Not only do we have to contend with the fact that the relative performance of the investments in our portfolio will vary wildly from one another year-to-year, but evidence suggests that so will the investor’s utility function.
Consider the graphic below, where the investor’s utility oscillates between relative (“I didn’t do as well as my peers!”) and absolute returns (“I lost money!”), making the diversified profile a consistent loser.
Source: BlackRock.
(3/14/2019 Update: It was pointed out to me that based upon the numbers in the table above, the total return reported the Diversified Portfolio is actually understated. Total return should be 202.4%, with $100K turning into $302,420.)
However, if we actually think about investor returns, rather than investment returns, the picture changes. Below we plot the growth of $1,000,000 since 2000 with a fixed $40,000 withdrawal. In this highly simplified example, we can begin to see the benefits of increased diversification.
Despite the philosophical limits of diversification, we clearly should not forgo it entirely. But what is the right framework to think about diversification and how it can be introduced into a portfolio?
5. The Three Axes of Diversification
At Newfound, we talk about three potential axes of diversification that investors can try to exploit.
We call these axes the what, the how, and the when axes, and they aim to capture what we invest in (“correlation driven”), how we make the decisions (“pay-off driven”), and when we make those decisions (“opportunity driven”).
Below, we explore each axis individually and how to might be able to contribute to a portfolio’s overall diversification profile.
5.1 What Axis (“Correlation Diversification”)
The “what” axis asks the question, “what are we investing in?” It captures the traditional notions of asset class and geographic diversification. As we have explored in this commentary, it also implicitly captures risk-based diversification.
We can also think of this axis as being responsible for “correlation-driven” diversification. As we will see, however, the empirical evidence of the effectiveness of this type of diversification is limited.
5.1.1 It’s Hard to Allocate Our Way Out of a Bear Market
Empirical evidence suggests that correlation-driven diversification is not tremendously effective at limited losses in crisis events. Consider the returns plotted below for a number of asset classes during 2008. We can see that by the end of the year, almost all had fallen between -20% to -50%.
As it turns out, most of the risk reduction benefits seen in a traditional asset allocation are not actually due to diversification benefits, but rather simply due to outright de-risking.
In their 2016 paper The Free Lunch Effect: The Value of Decoupling Diversification and Risk, Croce, Guinn and Robinson demonstrate that most of the risk reduction seen in moving from and all-stock portfolio to a balanced portfolio is simply due to the fact that bonds are less volatile than stocks.
That is not to say that de-risking is without its own merits. Outright de-risking a portfolio is simple way to reduce total loss potential and is one of the driving forces behind the benefits of glide-path investing’s ability to control sequence risk.
Investors looking to maintain a return profile while reducing risk through the benefits of diversification, however, may be disappointed.
In When Diversification Fails, Page and Panariello demonstrate that asset correlations tend to be bi-modal in nature. Unfortunately, the dynamics exhibited are the exact opposite of what we would like to see: diversification opportunity is ample in positive market states, but correlations tend to crash towards one during equity crises.
This does not make traditional diversification outright worthless, however, for growth-oriented investors.
Consider the table below from a paper titled, The Risk of Premiums, in which the author summarizes his findings about the statistical significance of different realized equity risk premia around the globe over different time horizons.
The five countries with stars on the left-hand side of the table have historically exhibited statistically significant risk premia across rolling 1-, 5-, 10-, and 20-year periods. Those with stars on the right did not exhibit statistically significant risk premia across any of the rolling periods.
It is important to remember that risk premia are expected, but by no means guaranteed. It is entirely possible that markets mis-estimate the frequency or magnitude with which risks manifest and fail to demand an adequately compensating premium.
Things have worked out exceptionally well for U.S. investors, but the same cannot be said for investors around the globe.
With the exception of explicit de-risking, what diversification may not necessarily provide much support in managing the left-tails of systematic risk factors. Nevertheless, what diversification may be critical in helping reduce exposure to idiosyncratic risks associated with a specific geographic region or asset class.
5.2 The How Axis – Payoff Diversification
The how axis asks the question, “how are we making our investment decisions.”
How need not be complex. Low-cost, tax-efficient passive asset allocation is a legitimate how.
But this axis also captures the variety of other active investment styles that can create their own, and often independent, return streams.
One might go so far as to call them “synthetic assets,” but most popular literature simply refers to them as “styles.” Popular categories include: value, momentum, carry, defensive (quality / low-volatility), trend, and event-driven.
The how axis is able to take the same what and create what are potentially unique return streams. The return profile of a currency momentum portfolio may be inherently different than a commodity value portfolio, both of which may offer diversification from traditional, economic risk factors that drive currency and commodity beta.
If the what axis captures correlation driven diversification, we would argue that the how axis captures pay-off driven diversification.
5.2.1 Style Diversification
In When Diversification Fails, Page and Panariello also found that correlations for many styles are bi-modal, but some may offer significant diversification in equity crisis states.
2018, however, once again proved that there are philosophical limits to the benefits of diversification. For styles to work over the long run, not only do there have to be periods where they fail individually, but there have to be periods where they fail simultaneously.
If we want to keep earning reward, we have to bear some risk in some potential state of the world.
It is no surprise, then, that it appears that most major styles appear to offer compensation for their own negative skew. In their 2014 paper Risk Premia: Asymmetric Tail Risks and Excess Returns, Lemperiere, Deremble, Nguyen, Seager, Potters and Bouchaud find that not only do most styles exhibit negative skew, but that there appears to be a positive relationship with skew and the style’s Sharpe ratio.
As with asset classes, return appears to be a compensation for bearing asymmetric risk.
The two exceptions in the graph are trend and equity value (Fama-French HML).
The authors of the paper note that the positive skew of equity value is somewhat problematic, as it implies it is an anomaly rather than a risk compensation. However, using monthly returns to recreate the above graph shifts the skew of equity value back to negative, implying perhaps that there is a somewhat regime-driven nature to value that needs to be further explored.
Trend, on the other hand, has long-been established to exhibit positive skew. Indeed, it may very well be a mathematical byproduct of the trading strategy itself rather than an anomaly.
5.2.2 Payoff Diversification
While the findings of Lemperiere, Deremble, Nguyen, Seager, Potters and Bouchaud (2016) imply that style premia are not exceptions to the “no pain, no premium” rule, we should not be dissuaded from considering the potential benefits of their incorporation within a portfolio.
After all, not only might we potentially benefit from the fact that their negative states might be somewhat independent of economic risk factors (acknowledging, as always, the philosophical limits of diversification), but the trading strategies themselves create varying payoff profiles that differ from one another.
By combining different asset classes and payoff functions, we may be able to create a higher quality of portfolio return.
For example, when we overlay a naive trend strategy on top of U.S. equities, the result converges towards a distribution where we simply miss the best and worst years. However, because the worst years tend to be worse than the best years are good, it leads to a less skewed distribution.
In effect, we’ve fought negative skew with positive skew.
At Newfound, we often say that “risk cannot be destroyed, but only transformed.” We tend to think of risk as a blob that is spread across future states of the world. When we push down on that blob in one future state, in effect “reducing risk,” it simply displaces to another state.
Trend may have historically helped offset losses during crisis events, but it can create drawdowns during reversal markets. Similarly, style / alternative premia may be able to harvest returns when traditional economic factors are going sideways, but may suffer during coincidental drawdowns like 2018.
Source: PIMCO
That is why we repeat ad nauseam “diversify your diversifiers.”
5.2.3 Specification Risk
While the above discussion of how pertained to style risks, there is another form of risk worth briefly discussing: specification risk.
Specification risk acknowledges that two investors implementing two identical styles in theory may end up with very different results in practice. Style risk tells us that equity value managers struggled as a category in 2016; specification risk tells us how each manager did individually.
Whether we are compensated for bearing specification risk is up for debate and largely depends upon your personal view of a manager’s skill.
In the absence of a view of skill, what we find is that combining multiple managers tends to do little for a reduction in traditional portfolio volatility (except in highly heterogenous categories), but can tremendously help reduce portfolio skew as well as the dispersion in terminal wealth.
For example, below we generate a number of random 30-stock portfolios and plot their returns over the last decade.
We can see that while the results are highly correlated, the terminal wealth achieved varies dramatically.
If instead of just picking one manager we pick several – say 3 or 4 – we find that the potential dispersion in terminal wealth drops dramatically and our achieved outcome is far more certain.
You can read more on this topic in our past commentary Is Multi-Manager Diversification Worth It?
5.3 When Axis
We believe that the when axis may be one of the most important, yet overlooked opportunities for diversification in portfolio construction. So much so, we wrote a paper about it titled Rebalance Timing Luck: The Difference Between Hired and Fired.
The basic intuition behind this axis is that our realized portfolio results will be driven by the opportunities presented to us at the time we rebalance.
In many ways, diversification along the when axis can be thought of as opportunity-diversification.
For example, Blitz, van der Grient, and van Vliet demonstrated in their 2010 paper Fundamental Indexation: Rebalancing Assumptions and Performance that the quarter in which an annually-rebalanced fundamental index is reconstituted can lead to significant performance disparity. For example, the choice to rebalance the portfolio in March versus September would have lead to a 1,000 basis point performance difference in 2009.
This difference was largely driven by the opportunities perceived by the systematic strategy at the time of rebalancing.
This risk is not limited to active portfolios. In the graph below we plot rolling 1-year return differences between two 60/40 portfolios, one of which is rebalanced at the end of each February and one that is rebalanced at the end of each August.
We can see that the rebalance in early 2009 lead to a 700 basis point gap in performance by spring 2010.
While we believe this has important implications for how research is conducted, benchmarks are constructed, and managers build portfolios, the more practical takeaway for investors is that they might benefit from choosing managers who rebalance on different schedules.
6. Summary
Investors often focus on returns, but it is important to keep in mind why we expect to earn those returns in the first place. We believe a risk-based mindset can help remind us that we expect to earn excess returns because we are willing to bear risk.
In many ways, we can think of ourselves and our portfolios as insurance companies: we collect premiums for bearing risk. Yet while we can we can seek to diversify the risks we insure, there are few truly independent risk factor and the premiums aren’t often large enough to offset large losses.
We also believe that there exist theoretical limits to diversification. If we eliminate risk through diversification, we also eliminate reward. In other words: no pain, no premium.
This does not inherently mean, however, we should just “suck it up.” The implications of risk-based thinking is dependent upon where we are in our investment lifecycle.
The primary risk of investors with growth mandates (e.g. investors early in their lifecycle) is “failing slow,” which is the failure to growth their capital sufficiently to outpace inflation or meet future liabilities. In this case, our aim should be to diversify as much as possible without overly de-risking the portfolio. With a risk-based mindset, it becomes clear why approaches like risk parity, when targeting an adequate volatility, may be philosophically superior to traditional asset allocation.
For investors taking withdrawals (e.g. those late in their lifecycle or endowments/pensions), the primary risk is “failing fast” from large drawdowns. Diversification is likely insufficient on its own and de-risking may be prudent. Diversifying payoff types and introducing positive skew styles – e.g. trend – may also benefit the investment plan by creating a more consistent return stream.
Yet we should acknowledge that even return opportunities available along the how axis appear to be driven largely by skew, re-emphasizing that without potential pain, there should be no premium.
No Pain, No Premium
By Corey Hoffstein
On February 4, 2019
In Popular, Risk & Style Premia, Risk Management, Weekly Commentary
Summary
1. Is it About Risk or Return?
For graduate school, I pursued my Masters of Science in Computational Finance at Carnegie Mellon University. One of the first degrees of its kind in the late 1990s, this financial engineering program is a cross-disciplinary collaboration between the finance, mathematics, statistics, and computer-science departments.
In practice, it was an intensive year-and-a-half study on the theoretical and practical considerations of pricing financial derivatives.
I do not recall quite when it struck me, but at some point I recognized a broader pattern at play in every assignment. The instruments we were pricing were always about the transference of risk in some capacity. Our goal was to identify that risk, figure out how to isolate and extract it, package it into the appropriate product type, and then price it for sale.
Risk was driving the entire equation. Pricing was all about understanding distribution of the potential payoffs and trying to identify “fair compensation” for the variety of risks and assumptions we were making.
For every buyer, there is a seller and vice versa and, at the end of the day, sellers who did not want risk and would have to compensate buyers to bear it.
1.1 Stocks for the Long Run
The idea that reward is compensation for risk is certainly not a new one. It is, more or less, the entire foundation of modern finance.
But sometimes, it seems, we forget it.
We are often presented with a return-based lens through which to evaluate the world of finance. Commonly reprinted are graphs like the one below, demonstrating century-long returns for stocks, bonds, and cash and accompanied by broad, sweeping generalizations like, “stocks for the long run.”
The truth is, if you plot anything on a log-axis over a long enough time horizon and draw it with a thick enough crayon, the line will eventually look pretty straight.
But if we zoom in to a horizon far more relevant to the lifecycle of most individual investors, we see a very different picture.
What we see is the realization of risk. We have to remember that the excess returns we expect to earn over the long run are compensation for bearing risk. And that risk needs to manifest, from time-to-time. Otherwise, if the probability of the risk being realized goes down, then so should the excess premium we expect to earn.
From a quantitative perspective, risk is often measured as volatility. In our opinion, that’s not quite right. We believe, given a long enough return history with enough realized risk events, risk can be better measured in a return’s distribution symmetry and fat-tailed-ness (i.e. “skew” and “kurtosis” respectively).
Below we plot the annualized excess real return distribution for U.S. equities over the last 100 years. We can see that the distribution is “leaning” to the right, indicating that large losses are more frequent than large gains.
Now, this might seem a little weird. Why would we ever pay someone to bear their risk?
The answer is because, in many ways, we can think of equities as a swap of cashflows: one up-front bullet payment for the rights to an uncertain stream of future cash flows generated by the underlying business.
In theory, the price we pay today should be less than the net present value of all those future cash flows, with the difference representing the premium we expect to earn over time.
Uncertainty is the wedge between the values. Without uncertainty, no rational seller would give up their future cash flows for less than they are worth (or, if we do have an irrational seller, we would expect buyers to compete over those cashflows to the point they are fairly valued).
Thus, the premium will be driven both by certainty about the future cash flows (growth rate and duration) as well as the market’s appetite for bearing risk.
The more certain we are of those future cash flows or the higher the market’s appetite to bear risk, the smaller the expected premium should be.
1.2 “Funding Secured”
To get a better sense of the play between certainty and premium in the market, we can explore an example where we effectively collapse price into a binary “yes or no” event.
On August 7th, 2018, Elon Musk sent out the following tweets:
At the time he sent the tweet, Tesla shares were trading around approximately $365. The stock had opened around $340 that day and had jumped on news reporting that the Saudi sovereign fund had built a $2b stake in Tesla and some speculation about a potential buy-out.
Now let’s assume, for a moment, that Elon’s tweet said, “Deal struck to take Tesla private at $420, effectively immediately” What should the price of Tesla’s stock jump to? $420, of course.
Now Elon’s tweet merely said he was considering it. He also did not specify a timeline. But let’s consider two cases:
In the former case, the right price is approximately $420. In the latter case, the appropriate price is whatever the shares were trading at before the announcement.1
Thus, where price trades between the two points can be interpreted as to the market’s confidence in the deal being done.
Hence, I tweeted the following:
(Note that when I sent out the first tweet, I hadn’t realized trading had been halted in Tesla.)
Assuming the entire day’s move was attributed to the buyout news, a price change from $340 to $380 only represents a 50% move towards the buy-out price of $420. The market was basically saying, “we give this coin-flip odds.”
1.2 Well ‘Skews Me
While modern portfolio theory uses volatility as the measure of risk, the connection between excess realized premia and volatility is tenuous at best. It certainty falls apart in highly skewed, fat-tailed return distributions.
Rather, skewness appears to be a much better measure of risk for most financial assets. And when we look at equity markets around the globe, we see the same fact pattern emerge: return distributions with negative skew indicating that losses tend to be (much) bigger than gains.
2. You’re An Insurance Company
What this type of risk-based thinking all boils down to is that you – and your portfolio – are really acting as an insurance company of sorts.
When we purchase insurance, we are really transferring our associated risk to the insurance company. To incentivize them to bear the risk, we have to pay an annual premium.
Similarly, when we buy stocks, we are really trading a certain cashflow today (the price) for a stream of uncertain cash flows in the future. The discount between the price we pay and the net present value of future cash flows is the premium we expect to earn. And when we sell stocks, we are effectively paying that premium.
So in building our portfolios, we should think like an insurance company.
Like an insurance company, we want to diversify the premiums we earn. Not only do we want to diversify within a given type of insurance, but we probably also want to diversify the type of insurance we offer. And, in an ideal world, the type of insurance would be uncorrelated!
2.1 Diversifying with Bonds
Enter the most traditional portfolio diversifier: bonds. Typically considered to be a “safe” asset, if we look at them through the lens of real excess returns, we can see that bond returns also exhibit negative skew and fat tails.
This makes sense, as when we buy a bond we are still bearing all sorts of risks. Not only do we bear the risk of a default, but we also bear inflation risk and interest rate path-dependency risk.
With U.S. Treasuries, default risk is likely minimized (depending on your perspective), and the other two risks might be less correlated than the traditional risks (e.g. economic growth) we see with equities. So combining stocks and bonds should help us control skew, right?
Well, not quite. Below we plot the annualized excess real returns for a 60/40 portfolio.
We see that skew and kurtosis remain. What gives?
Well, one answer is that while a 60/40 portfolio might be close to balanced in the terms of notional dollar exposure to each asset, it is completely unbalanced from the perspective of residual volatility.
Below we plot the relative contribution to risk of stocks and bonds over time in a 60/40 portfolio.
Because the payout for bonds is far more certain than the payout for stocks, not only is the expected excess premium much lower, but volatility tends to be much lower as well. This means that the premium earned from holding bonds is not large enough to offset the losses realized in equities.
Savvy readers will recognize this as the driving thesis behind risk parity. To strike a balance, we need to allocate to stocks and bonds in such a manner that they provide equal contribution to portfolio risk.
Below, we plot the annual excess real return distribution for a stock/bond risk parity portfolio that is levered to a constant volatility target of 8%.
What do we see? Skew and fat tails remain. Perhaps the answer is simply that we need more diversification. While in practice this might mean buying different assets, in theory it means exposing ourselves to different types of risk sources that lead to uncertainty in the value of future cash flows. We enumerate a few below.
In traditional asset allocation, trying to isolate and add these different exposures is very difficult.
First, it is worth acknowledging that not every type of risk necessarily deserves to earn compensation. In theory, we should only be compensated for un-diversifiable risks.
Furthermore, many of these risks have time-varying correlations and magnitudes, and often collapse towards a single risk factor during crisis states of the world.
Yet we would argue that there is a deeper, philosophical limit we should consider.
3. The Philosophical Limits of Diversification
What we keep running up against is what we call the “philosophical limit of diversification.”
The simplest way to think about the limit is this: If we can diversify away all of our risk, we should not expect to earn any reward.
After all, if we found some magical combination of assets that eliminated downside risk in all future states of the world, we would have constructed an arbitrage. We could simply borrow at the risk-free rate, invest in the appropriate blend of assets, and reap our risk-free reward.
That is why years like 2018, when 90% of assets lose money, have to occur from time to time. Without the eventual realization of risk, there is no reason to expect return.
3.1 The Frustrating Law of Active Management
A corollary of this philosophical limit is what we like to call “The Frustrating Law of Active Management.”
We go further in depth into this idea in another commentary, but the basic idea follows: if an investment strategy is perceived both to have alpha and to be easy, investors will allocate to it and erode the associated premium.
How can a strategy be “hard”? Well, a manager might have a substantial informational or analytical edge. Or, the manager might have a structural moat, accessing trades others do not have the opportunity to pursue.
But for most well-known edges (e.g. most major style premia), “hard” is going to be behavioral. The strategy has to be hard enough to hold on to that it does not get arbitraged away. Which implies that,
This also implies that,
For active managers, the frustration is that not only does their investment approach have to under-perform from time-to-time, but bad strategies will have to out-perform. The latter may seem confusing until we consider that a purposefully bad strategy could simply be inverted to create a purposefully good one.2
And, as above, we cannot simply diversify our way out of the problem. After all, if there were a magic combination of active strategies that earned the same expected alpha but reduced the risk, everybody would pursue that combination.
4. Investment versus Investor Returns
So is the answer here to just, “suck it up?” Do we simply look at periods like 2000-2010 and say, “it’s the price we pay for the opportunity to earn long-run returns?”
We would argue both “yes” and “no.”
It all depends upon where an investor falls within their lifecycle. Young investors who are pursuing growth mandates may simply need to accept that skew and fat tails are the cost of earning the long-run premium. Too much diversification may lead to “failing slow.”
For investors in the later stages of their lifecycle, however, the math changes. Indeed, this is true for any individual or institution where withdrawals are concerned. When we have a withdrawal-driven mandate, it is the risk of “failing fast” that we need to concern ourselves with.
The problem is that investment-centric thinking often makes diversification seem foolish. To quote Brian Portnoy, “diversification means always having to say you’re sorry.”
Not only do we have to contend with the fact that the relative performance of the investments in our portfolio will vary wildly from one another year-to-year, but evidence suggests that so will the investor’s utility function.
Consider the graphic below, where the investor’s utility oscillates between relative (“I didn’t do as well as my peers!”) and absolute returns (“I lost money!”), making the diversified profile a consistent loser.
(3/14/2019 Update: It was pointed out to me that based upon the numbers in the table above, the total return reported the Diversified Portfolio is actually understated. Total return should be 202.4%, with $100K turning into $302,420.)
However, if we actually think about investor returns, rather than investment returns, the picture changes. Below we plot the growth of $1,000,000 since 2000 with a fixed $40,000 withdrawal. In this highly simplified example, we can begin to see the benefits of increased diversification.
Despite the philosophical limits of diversification, we clearly should not forgo it entirely. But what is the right framework to think about diversification and how it can be introduced into a portfolio?
5. The Three Axes of Diversification
At Newfound, we talk about three potential axes of diversification that investors can try to exploit.
We call these axes the what, the how, and the when axes, and they aim to capture what we invest in (“correlation driven”), how we make the decisions (“pay-off driven”), and when we make those decisions (“opportunity driven”).
Below, we explore each axis individually and how to might be able to contribute to a portfolio’s overall diversification profile.
5.1 What Axis (“Correlation Diversification”)
The “what” axis asks the question, “what are we investing in?” It captures the traditional notions of asset class and geographic diversification. As we have explored in this commentary, it also implicitly captures risk-based diversification.
We can also think of this axis as being responsible for “correlation-driven” diversification. As we will see, however, the empirical evidence of the effectiveness of this type of diversification is limited.
5.1.1 It’s Hard to Allocate Our Way Out of a Bear Market
Empirical evidence suggests that correlation-driven diversification is not tremendously effective at limited losses in crisis events. Consider the returns plotted below for a number of asset classes during 2008. We can see that by the end of the year, almost all had fallen between -20% to -50%.
As it turns out, most of the risk reduction benefits seen in a traditional asset allocation are not actually due to diversification benefits, but rather simply due to outright de-risking.
In their 2016 paper The Free Lunch Effect: The Value of Decoupling Diversification and Risk, Croce, Guinn and Robinson demonstrate that most of the risk reduction seen in moving from and all-stock portfolio to a balanced portfolio is simply due to the fact that bonds are less volatile than stocks.
That is not to say that de-risking is without its own merits. Outright de-risking a portfolio is simple way to reduce total loss potential and is one of the driving forces behind the benefits of glide-path investing’s ability to control sequence risk.
Investors looking to maintain a return profile while reducing risk through the benefits of diversification, however, may be disappointed.
In When Diversification Fails, Page and Panariello demonstrate that asset correlations tend to be bi-modal in nature. Unfortunately, the dynamics exhibited are the exact opposite of what we would like to see: diversification opportunity is ample in positive market states, but correlations tend to crash towards one during equity crises.
This does not make traditional diversification outright worthless, however, for growth-oriented investors.
Consider the table below from a paper titled, The Risk of Premiums, in which the author summarizes his findings about the statistical significance of different realized equity risk premia around the globe over different time horizons.
The five countries with stars on the left-hand side of the table have historically exhibited statistically significant risk premia across rolling 1-, 5-, 10-, and 20-year periods. Those with stars on the right did not exhibit statistically significant risk premia across any of the rolling periods.
It is important to remember that risk premia are expected, but by no means guaranteed. It is entirely possible that markets mis-estimate the frequency or magnitude with which risks manifest and fail to demand an adequately compensating premium.
Things have worked out exceptionally well for U.S. investors, but the same cannot be said for investors around the globe.
With the exception of explicit de-risking, what diversification may not necessarily provide much support in managing the left-tails of systematic risk factors. Nevertheless, what diversification may be critical in helping reduce exposure to idiosyncratic risks associated with a specific geographic region or asset class.
5.2 The How Axis – Payoff Diversification
How need not be complex. Low-cost, tax-efficient passive asset allocation is a legitimate how.
But this axis also captures the variety of other active investment styles that can create their own, and often independent, return streams.
One might go so far as to call them “synthetic assets,” but most popular literature simply refers to them as “styles.” Popular categories include: value, momentum, carry, defensive (quality / low-volatility), trend, and event-driven.
The how axis is able to take the same what and create what are potentially unique return streams. The return profile of a currency momentum portfolio may be inherently different than a commodity value portfolio, both of which may offer diversification from traditional, economic risk factors that drive currency and commodity beta.
If the what axis captures correlation driven diversification, we would argue that the how axis captures pay-off driven diversification.
5.2.1 Style Diversification
In When Diversification Fails, Page and Panariello also found that correlations for many styles are bi-modal, but some may offer significant diversification in equity crisis states.
2018, however, once again proved that there are philosophical limits to the benefits of diversification. For styles to work over the long run, not only do there have to be periods where they fail individually, but there have to be periods where they fail simultaneously.
If we want to keep earning reward, we have to bear some risk in some potential state of the world.
It is no surprise, then, that it appears that most major styles appear to offer compensation for their own negative skew. In their 2014 paper Risk Premia: Asymmetric Tail Risks and Excess Returns, Lemperiere, Deremble, Nguyen, Seager, Potters and Bouchaud find that not only do most styles exhibit negative skew, but that there appears to be a positive relationship with skew and the style’s Sharpe ratio.
As with asset classes, return appears to be a compensation for bearing asymmetric risk.
The two exceptions in the graph are trend and equity value (Fama-French HML).
The authors of the paper note that the positive skew of equity value is somewhat problematic, as it implies it is an anomaly rather than a risk compensation. However, using monthly returns to recreate the above graph shifts the skew of equity value back to negative, implying perhaps that there is a somewhat regime-driven nature to value that needs to be further explored.
Trend, on the other hand, has long-been established to exhibit positive skew. Indeed, it may very well be a mathematical byproduct of the trading strategy itself rather than an anomaly.
5.2.2 Payoff Diversification
While the findings of Lemperiere, Deremble, Nguyen, Seager, Potters and Bouchaud (2016) imply that style premia are not exceptions to the “no pain, no premium” rule, we should not be dissuaded from considering the potential benefits of their incorporation within a portfolio.
After all, not only might we potentially benefit from the fact that their negative states might be somewhat independent of economic risk factors (acknowledging, as always, the philosophical limits of diversification), but the trading strategies themselves create varying payoff profiles that differ from one another.
By combining different asset classes and payoff functions, we may be able to create a higher quality of portfolio return.
For example, when we overlay a naive trend strategy on top of U.S. equities, the result converges towards a distribution where we simply miss the best and worst years. However, because the worst years tend to be worse than the best years are good, it leads to a less skewed distribution.
In effect, we’ve fought negative skew with positive skew.
At Newfound, we often say that “risk cannot be destroyed, but only transformed.” We tend to think of risk as a blob that is spread across future states of the world. When we push down on that blob in one future state, in effect “reducing risk,” it simply displaces to another state.
Trend may have historically helped offset losses during crisis events, but it can create drawdowns during reversal markets. Similarly, style / alternative premia may be able to harvest returns when traditional economic factors are going sideways, but may suffer during coincidental drawdowns like 2018.
Source: PIMCO
That is why we repeat ad nauseam “diversify your diversifiers.”
5.2.3 Specification Risk
While the above discussion of how pertained to style risks, there is another form of risk worth briefly discussing: specification risk.
Specification risk acknowledges that two investors implementing two identical styles in theory may end up with very different results in practice. Style risk tells us that equity value managers struggled as a category in 2016; specification risk tells us how each manager did individually.
Whether we are compensated for bearing specification risk is up for debate and largely depends upon your personal view of a manager’s skill.
In the absence of a view of skill, what we find is that combining multiple managers tends to do little for a reduction in traditional portfolio volatility (except in highly heterogenous categories), but can tremendously help reduce portfolio skew as well as the dispersion in terminal wealth.
For example, below we generate a number of random 30-stock portfolios and plot their returns over the last decade.
We can see that while the results are highly correlated, the terminal wealth achieved varies dramatically.
If instead of just picking one manager we pick several – say 3 or 4 – we find that the potential dispersion in terminal wealth drops dramatically and our achieved outcome is far more certain.
You can read more on this topic in our past commentary Is Multi-Manager Diversification Worth It?
5.3 When Axis
We believe that the when axis may be one of the most important, yet overlooked opportunities for diversification in portfolio construction. So much so, we wrote a paper about it titled Rebalance Timing Luck: The Difference Between Hired and Fired.
The basic intuition behind this axis is that our realized portfolio results will be driven by the opportunities presented to us at the time we rebalance.
In many ways, diversification along the when axis can be thought of as opportunity-diversification.
For example, Blitz, van der Grient, and van Vliet demonstrated in their 2010 paper Fundamental Indexation: Rebalancing Assumptions and Performance that the quarter in which an annually-rebalanced fundamental index is reconstituted can lead to significant performance disparity. For example, the choice to rebalance the portfolio in March versus September would have lead to a 1,000 basis point performance difference in 2009.
This risk is not limited to active portfolios. In the graph below we plot rolling 1-year return differences between two 60/40 portfolios, one of which is rebalanced at the end of each February and one that is rebalanced at the end of each August.
We can see that the rebalance in early 2009 lead to a 700 basis point gap in performance by spring 2010.
While we believe this has important implications for how research is conducted, benchmarks are constructed, and managers build portfolios, the more practical takeaway for investors is that they might benefit from choosing managers who rebalance on different schedules.
6. Summary
Investors often focus on returns, but it is important to keep in mind why we expect to earn those returns in the first place. We believe a risk-based mindset can help remind us that we expect to earn excess returns because we are willing to bear risk.
In many ways, we can think of ourselves and our portfolios as insurance companies: we collect premiums for bearing risk. Yet while we can we can seek to diversify the risks we insure, there are few truly independent risk factor and the premiums aren’t often large enough to offset large losses.
We also believe that there exist theoretical limits to diversification. If we eliminate risk through diversification, we also eliminate reward. In other words: no pain, no premium.
This does not inherently mean, however, we should just “suck it up.” The implications of risk-based thinking is dependent upon where we are in our investment lifecycle.
The primary risk of investors with growth mandates (e.g. investors early in their lifecycle) is “failing slow,” which is the failure to growth their capital sufficiently to outpace inflation or meet future liabilities. In this case, our aim should be to diversify as much as possible without overly de-risking the portfolio. With a risk-based mindset, it becomes clear why approaches like risk parity, when targeting an adequate volatility, may be philosophically superior to traditional asset allocation.
For investors taking withdrawals (e.g. those late in their lifecycle or endowments/pensions), the primary risk is “failing fast” from large drawdowns. Diversification is likely insufficient on its own and de-risking may be prudent. Diversifying payoff types and introducing positive skew styles – e.g. trend – may also benefit the investment plan by creating a more consistent return stream.
Yet we should acknowledge that even return opportunities available along the how axis appear to be driven largely by skew, re-emphasizing that without potential pain, there should be no premium.