Strategic Asset Allocation Revisited
How to beat the market with zero leverage and strictly less risk
Erkko Etula, who pioneered intermediary asset pricing in his doctoral dissertation at Harvard and is now a Managing Director at Goldman, tried to convince me that ‘market timing’ is impossible. This was in the context of the volatility trade. I had figured out that dealers buy up the short end of the VIX futures curve when their risk constraints bite, so that if one tracks the slope of the VIX futures curve one can detect the onset of market risk-offs in real time. This insight suggested a straightforward strategy of tactically selling volatility — sell volatility in normal times, but start buying as the VIX futures curve begins to invert. As I have shown out-of-sample, this is a highly profitable strategy.
But Erkko has a point. Banking on your ability to anticipate risk-offs is still a risky proposition. Selling volatility is inherently risky. Even a tactical strategy informed by a convincing theory of how risk-offs happen can expose you to very bad outcomes. And since predictable risk-offs are rare, it may be the case that the game is not worth the candle. So, I see Erkko’s point about market timing.
However, this does not mean that the only strategies open to a risk-averse informed investor involve cross-sectional arbitrage — where one bets against short-term cross-asset mispricing. The point of Strategic Asset Allocation was to show that it is possible to construct systematic rebalancing strategies that dynamically adjust exposure to risk assets based on a signal of risk appetite. In that case, the signal was the equity allocation of US investors. We showed that one can beat the market without any leverage and without taking any more risk.
But there were two problems with the strategy proposed in Strategic Asset Allocation. First, as Erkko pointed out, there is an announcement lag in the equity allocation series, which means that it cannot, in practice, be used to inform asset allocation in real time. But it still tells us about the structure of the world, so it is important to understand nonetheless. Second, the series is only available at the quarterly frequency. This means that it may be of interest to patient ‘real money’ investors. But it is not much use to leveraged intermediaries (dealers and hedge funds) who live at a higher frequency.
In trying to solve the problem of constructing a highly informative index of global financial conditions, I have stumbled upon the real solution to the problem taken up in my post on strategic asset allocation. In what follows, we will demonstrate a simple systematic strategy that handily beats the market without any leverage and with less risk. Once one has extracted a good signal of the global financial cycle, we will show, strategic asset allocation yields higher average returns with lower volatility and therefore a higher Sharpe ratio. In fact, we will document a stronger result: strategic asset allocation based on our signal second-order stochastically dominates holding the SP500. This means that any weakly risk-averse investor should prefer strategic asset allocation to the buy-and-hold strategy.
We construct the signal as before: we use partial least squares (PLS) to obtain a linear combination of risk spreads with the strongest covariation with market returns. However, we adjust our signal extraction in two ways. First, we do everything in real time, with information that is available at the time. In order to do so, we carry out expanding window PLS. Second, also in real time, we rescale the signal to have range [0, 1], where 0 denotes that financial conditions are tighter than ever before (since the beginning of the sample in 1997) and 1 denotes that they are looser than ever before. Finally, we allow 100 weeks of burn-in to initialize the model.
The next figure displays our signal. We have marked out the dot-com crash in 2000, 9/11, the collapse of Bear Sterns and Lehman, Draghi’s ‘Whatever it takes’ comment that ended the eurozone crisis, and the onset of the coronapanic. Our metric for the global financial cycle tracks all these market events. We can also see the so-called ‘Trump reflation trade,’ which began before the election but really took off in the hours after Trump won. There is also the familiar pattern of the three cycles since the financial crisis. The graph also shows the ultra-loose financial conditions prevailing during the dot-com bubble that came to grief in 2000, and the financial boom that caused the global financial crisis.
We can also examine the impact of QE on global financial conditions. The dotted lines mark weeks in which the Fed was buying upwards of $50 billion in bonds. We can see that QE worked in easing financial conditions.
So, the signal is highly informative. Having solved the signal extraction problem, we design our strategic allocation strategy as follows. We model the simple problem of an investor choosing between a safe asset, which we take to be the 3-month bill, and a risky asset, which we take to be the SP500/SPX. The investor’s problem is to strategically choose exposure to the risky asset for the next week after observing the signal this week. The solution we propose is the simplest possible: the investor chooses to allocate a fraction of her portfolio to SPX that is equal to the signal (which, recall, sits on the unit interval). The logic is that the investor reckons that if risk appetite is high, next week’s market return will be high; conversely, if risk appetite is low, next week’s market returns will be low.
How well does this strategic rebalancing strategy do relative to the buy-and-hold benchmark?
We first look at the relative performance over the whole sample. Suppose that you had invested a dollar in each of these strategies on Feb 28, 1999. The buy-and-hold strategy dollar would’ve cumulated to $2.48, as of the end of March 2021. Meanwhile, the strategic asset allocation portfolio would’ve cumulated to $4.29. The cumulative rate of return are 4.2 percent for the buy-and-hold strategy and 6.8 percent for strategic asset allocation.
Table 1 displays the summary statistics for the two strategies. Note that the mean in the table is the arithmetic mean, while the one quoted above is the (correct) geometric mean. We can see that not only does strategic asset allocation yield higher returns, it comes with lower risk — both as measured by the dispersion of returns (std) and the skew (SPX returns are more skewed to the left). The Sharpe ratio of the strategic portfolio is 2.57 times that of the SPX benchmark!
The next figure displays skew-Normal densities fit to the two return series. We can see that SPX returns are dramatically more dispersed than the returns on strategic asset allocation.
Looking at the distributions, it seems that strategic asset allocation not only has more attractive moments, but seems to second-order stochastically dominate the market benchmark. What that implies is that not only do you make more money (the location of the distribution is to the right) for less risk (the scale of the distribution is smaller), the probability mass to the left of any point to the left of the cross-over point is smaller than that for the market — the probability of bad outcomes is strictly lower no matter what threshold we choose for defining a bad outcome.
We test this hypothesis using the following theorem: one distribution second-order stochastically dominates another if the integral of the difference in the quantile distributions is positive for every quantile. We compute the integral for all percentiles. The next figure graphs it against the quantiles. We can see that it is positive throughout. So even though your returns are bounded point wise (for each week) by the returns on the SP500, the former still second-order stochastically dominates the latter.
In order to understand why our systematic strategy works so well, we compare the returns of the two strategies. The market return is on the X axis, the return on strategic asset allocation portfolio is on the Y axis. The diagonal line is 45 degrees. We can see that the returns on the strategic portfolio are capped by the market portfolio — since the strategic portfolio is weighted portfolio of the SPX and the Bill. But look at what happens around the origin: when market returns are negative, the strategic portfolio returns are also negative but not as bad as market returns — they are above the 45 degree line. And when market returns are positive, the strategic portfolio returns are also positive, but not as high as market returns — they are below the 45 degree line.
So, strategic asset allocation works because the signal allows you to reduce your exposure to risk assets as they start falling, and increase exposure as they start rising. As I mentioned on Twitter, the signal is god. Everything else is secondary. If you can isolate the signal for risk appetite in real time, you can beat the market while taking strictly less risk. The ultimate reason is that you are harvesting the dynamic mispricing of risk, which is what the signal is meant to capture.
The bottomline is that if you know the real time price of systematic risk, you can adjust your exposure to risk assets in a systematic way that allows you to beat the market with zero leverage (although you can lever up if you want) and strictly less risk. You can call this market timing. But it is the rational strategy for informed investors.
You can find the replication data and code on my GitHub.
Now *this* I can get into. Time to start an algo hedge fund!
Hi Anusar, any specific reason why you didn't put the dollar index in this FCI?
Many Thanks,
Dan