On Risk Parity

I was recently asked by a large asset management firm for my opinion on risk parity as a form of portfolio construction. This is what I wrote for them and I thought I’d share it (since there was no mention of an NDA) to spark a bit of debate on a concept I think needs more attention.

Risk Parity (RP), a method of creating portfolios based on allocating a volatility budget equally across asset classes, has gained popularity in recent years. RP differs from Modern Portfolio Theory (MPT) in that it does not involve the optimization of weights given expected returns and covariances. Almost[1] all portfolios constructed using RP are inefficient[2] according to the MPT framework. But MPT suffers from enough pitfalls[3] to leave a large gap for alternatives, such as RP, to get a foothold. RP is gaining traction mostly because its empirical record beats those of mean-variance (MV) portfolios and strategies such as a 60/40 equity bond split[4]. In RP portfolios, weights are more evenly shared across asset classes, and such portfolios do comparatively well in times of stress. But RP suffers from its own shortcomings and lacks adequate theoretical underpinnings. I will argue that because it does not consider expected returns or correlation, uses a poor proxy for true risk and is not optimized according to sources of risk, RP is not a robust form of portfolio construction.

If asset classes represented distinct sources of risk and were priced so as to compensate the investor for taking these risks, constructing a portfolio according to risk budgets would have appeal. But asset classes do not perfectly coincide with sources of risk and equally weighting asset classes according to realized volatility – which the simplest form of RP advocates – is arbitrary. Not all sources of volatility offer a risk-premium, let alone on an equal basis. For example, shorting equities generates volatility in a portfolio, but this is not a source of risk-premium. Constructing portfolios according to an Arbitrage Pricing Theory (APT) framework is more satisfactory from this point of view.

Moreover, realized volatility is not an accurate measure of the risk an investor should expect to face[5]. This is one of the same issues that MV comes up against – in the absence of stationarity, sample variance may be a poor estimator of true variance. For certain asset classes, such as credit, the distribution is quite likely not symmetric; this further reduces the merit of relying heavily on the second moment.

The simplest RP methodology ignores the off-diagonal entries of covariance matrices. Portfolios exist as a means of diversifying idiosyncratic risks; the extent of diversification is determined by correlation coefficients. Low or negative correlation is desirable, so long as it is accompanied by a positive risk premium. RP considers the volatilities of asset classes, but does not optimize with regard to how they interact. This suggests that the diversification benefits of RP would be greater, were the weights to be optimized.

In spite of these theoretical arguments, some studies, such as Hurst, Johnson and Ooi (2010) and  Asness, Frazzini and Pedersen (2011) point to periods of relative out-performance of RP as evidence of its strength. While outperforming an arbitrary, though computationally straightforward, strategy such as 60/40 may be laudable, it has been shown that low beta assets – which RP overweights – systematically outperform high beta assets[6] – which MV and 60/40 have in abundance – on a risk-adjusted basis (i.e. Sharpe Ratio). By inadvertently gaining from a flaw in a competing approach – namely that beta does not work in practice the way it does in theory – RP is flattered. In this case, any portfolios that have a relatively low allocation to high beta assets should outperform, but RP cannot claim to produce the best of these necessarily.

RP leaves open a number of questions that MPT provides answers to, such as what asset classes are in the investable universe and how much leverage is best. That the latter’s answers are wrong or not useful does not commend the silence of the former. If asset-classes could be replaced with distinct sources of risk, and if weights were calculated conditional on the risk premiums on offer, the RP approach might have a stronger footing; but, in its current guise, it will not stand the test of time.


[1] If a set of asset classes have equal Sharpe Ratios and the same correlation coefficients, equally weighting according to volatility would be optimal under MV; Maillard, Roncalli and Teiletche (2010) provide a proof of this.

[2] An RP portfolio, even with leverage, will never sit above the capital allocation line and is therefore no better than holding the market portfolio and using leverage to satisfy tangency with a given set of indifference curves.

[3] MV efficient portfolios are not knowable ex ante and estimates rarely work (see Fama and French 2004). Issues surrounding the market portfolio highlighted by Roll (1977), non-stationary and asymmetrical distributions at the securities level, instability of frontier portfolios, and high sensitivity of outputs to noise in inputs are sufficient to render the empirical success of the MV framework and, by extension, the CAPM quite low.

[5] Various writings and quotes  from James Montier and Warren Buffett provide arguments supporting this.

[6] See Frazzini and Pedersen (2013) and Black, Jensen, Scholes (1972) for more details. One explanation comes from Asness, Frazzini and Pedersen (2011) who suggest that MV fails, in part, due to leverage aversion, whereby investors are reluctant or unable to invest more than 100% in the market portfolio and instead opt to invest in higher beta assets. This increases the price and lowers the expected return of these securities, thereby giving low-beta securities disproportionately better returns. 

Speculator’s Option: “Told you so”

Mr. Speculator says that the market is going to go down. It goes up 10%, then down 5%. “Told you so.”

Mr. Speculator lists 10 “must own” stocks. One goes up 50%. “Told you so.”

He is a sales man. He makes selective use of the truth. Being wrong doesn’t bother him as much as others thinking he might be wrong in future. He works to protect the latter. And because those he needs to convince are not robots, it can work. At least for long enough that the speculator has either made enough money or forged a fallback career path.

Mr. Speculator is almost surely not directly accountable for the outcomes. He can tell a story. You might see him as a sales guy at an investment bank. Or maybe you think of an amateur day-trader or someone in the lower echelons of the finance hierarchy. Serious professional investors can see through him. They learn to ignore him. There is no mechanism or incentive to expose him as a charlatan.

The speculator’s option, much like the more conventional puts and calls, captures the fact that the speculator can derive value from the comments that work and ignore (at no additional cost) those that don’t. Usually the holder of an option has to pay for it but speculators can actually get paid to be in this position.

No one should put this guy in charge of money. But it’s not as simple as finding him and tying his hands behind his back so he can’t pick up the phone or punch commands into Bloomberg.

Mr. Speculator exists not as an individual but as a part of the market psyche. Everyone exhibits his traits to some extent. The point is that one first needs to be aware of his existence before working to eliminate his destructive forces, first at the personal level, then within the investment process.

To that end, I would recommend studying (not just reading) books and articles by Daniel Kahneman, Nassim Taleb, Dan Ariely and Michael Mauboussin. Then watch out for Mr. Speculator and make sure he is never in the money.

Why Good Luck is a Bad Look

When a combination of skill and luck is what determines whether you win or lose, the skillful tend to win over time. For short periods of time the lucky can imitate the skillful (the signal is blustered by the noise), but there are several reasons why this can’t last. As Michael Mauboussin has been calmly pointing out for years, it’s process, not outcome, that matters.

The best poker players, athletes and investors share a trait: they work on the process and let the outcome follow.

“I should have…” “I knew it…” “Told you so…” All these phrases are red flags that point towards someone overly focused on outcome. Of course, if you can get away with it, it is so much easier to focus on the outcome to justify a decision than the process. But process is what differentiates the skillful from the lucky when making decisions under uncertainty.

In the absence of a unique and unerring strategy on picking the right stocks, getting to the final table at poker tournaments or winning a football match, it is, however, not advisable to ignore the outcome altogether. It is a source of feedback. The crucial point to figure out is how to use the feedback and incorporate it into the process.

This is where having a grasp of the basics of statistical analysis comes in handy. There are rules to bear in mind when drawing inference from the outcomes of random processes. I’d recommend reading The Signal and the Noise (if you haven’t already) for a non-technical and enlightening discussion of this.

Getting to a situation where you win more often than you lose is a typical objective. But, being in a situation where the wins are attributable to skill and the losses are down to bad luck, is a better objective. Relying on good luck is not a good way to get ahead.

The message from the table below has been stuck in my head since first seeing it laid out like this by Michael Mauboussin. While it may not always be clear at first which of the four boxes an outcomes falls into, a combination of good data analysis and a critical sense of why a process should or should not work usually points in the right direction.

Process Table

Discounting the Fed Model

This week’s Buttonwood column examines the Fed model. This rule of thumb compares bond yields to the inverse of price-earnings ratios of equities (or, simply, the earnings yield). It is widely considered a flawed model as it ignores risk, inflation and growth, but that doesn’t stop some people pushing it to help their cause. Proponents argue that when bond yields are below the earnings yield, equities are worth buying. However, neither the theory nor the data back up the view that equity prices should always be higher because bond yields are lower.

Future real equity returns were negative when bond yields were at their lowest and high when bond yields were highest.

All else equal, lower bond yields make equities relatively more attractive and increase the prices investors are willing to pay. This simultaneously lowers the discount rates, or costs of equity, and hence the returns investors can expect to earn. However inflation, growth and risk can offset this effect. Higher nominal growth increases the value of equities while higher prospective risk around cash flows does the opposite. The conclusion from the quote above is that investors (possibly blindly following some version of the Fed model) have tended to pay too much attention to the role of the discount rate and too little to what else is going on.

In a low growth world with little in the way of inflationary pressures, and no signs of risks abating, earnings yields should be quite a bit higher than the yield on bonds. And they are. But in the unlikely event that the earnings yield falls and the gap gets close to zero,  investors should be worried. It is more likely that the gap will narrow because bond yields increase. In that case, equities would lose some of the luster that the Fed model ostensibly gives them now.

Investments That Really Work

Commodity prices are important determinants of corporate profitability and hence of equity valuations. This relates to the fact that they are an input (i.e. raw material) to a wide range of production processes. Including commodities in an investment portfolio, in theory, should enable portfolio managers to hedge some of the risk that the profits of the companies they own are impacted unexpectedly by changes in the price of oil or wheat, for example. However, a recent paper from Marco Lombardi and Francesco Ravazzolo published by the BIS argues that “the popular view that commodities are to be included in one’s portfolio as a hedging device is not grounded”.

This led me to wonder whether any other inputs could reasonably be included in a portfolio instead. Most lack the desirable characteristics one might look for in an investment, such as the ability to offer a return. (You could argue that commodities do not fulfill this requirement – I have). I’m unlikely to convince you that you should invest in Post-it notes or red paint, but what about one of the most important inputs in almost all production processes: labour?

Unlike commodities, there is a dividend to labour in the form of wages. It is conceivable that wages could be securitised in much the same way as mortgages or car loans.  Imagine offering a large number of people a lump sum for, say, 30% of all their wages for next 5 or 10 years. Pooling a large number of workers together means that statistical and actuarial methods could be used to price the risk of “default”.

From the point of view of the worker this could be a very good deal. The lump sum could help finance the purchase of a house, an alternative to a mortgage where the risk is partly transferred to investors. Of course, armies of smart lawyers and behavioural economists (like Dan Ariely or Richard Thaler) would need to be recruited to minimize the increased incentive for you to quit your job (or laze around looking at cat videos on YouTube all day) once the lump sum is paid. From the portfolio manager’s point of view investing in a securitised product like this would be a nice hedge against inflation that actually offers a return.

Admittedly, there are some potential social issues and governments might not like private firms muscling in on their monopoly over taking a chunk of people wages at source. But from an investment stand-point I think this idea has some merit. Can anyone convince me otherwise? And, at the very least, based on this line of reasoning, is labour less eligible to be called an “asset class” than commodities?

What’s a Quarter Worth?

As the second quarterly reporting season of 2013 kicks off, it’s worth putting some context around what the numbers mean. Investment banks tout their analysts who’s estimates have been on the money and quickly brush over instances where they were wide of the mark. All the fuss created around the numbers draws investors in and this has led to a situation where too much weight is given to what has just happened in the last 3 months.

The chart below is a stylised illustration of the value of an equity (or equity index, if you like). The red sliver at the bottom is the value of one quarter. The red and light blue sections together make up the value from one year. And the darker blue section is the remaining value in the equity. So, assuming you are an equity investor, which would you rather devote time to analysing? Quarter Stack

Non-Fundamental Stuff

Greg Ip, The Economist’s U.S. Economics Editor, explores the different roles economists and traders play in financial markets. Economists tend to assume market prices are correct until they are told otherwise. Traders assume prices are incorrect until they make money. But traders, by design, will have opposing views of the incorrectness – so on average the economist should be right.

However, the economist won’t change the price to reflect “non-fundamental stuff”, the trader will. Yes, sometimes he changes prices too much one way or the other. And yes, estimating the probabilities of a million possible states of the world is going to make the output look like the interaction of a 2 year-old holding red and green crayons and a newly painted living room wall. But, as Greg points out, there is a signal in all the noise that those setting monetary policy should heed (carefully!).

Central banks can only control the interest rates that permeate through economies to a limited degree, so they are reliant on the markets to enact certain policies accordingly. The interaction between monetary policy and the market is at a critical juncture – neither can afford to get it wrong.