Strategic Asset Allocation

Patient investors can systematically beat the market

In the penultimate dispatch, we documented strong return predictability in US equities. Specifically, we showed that the share of assets allocated to equities by US investors predicts next quarter’s stock market return. In the previous dispatch, we showed that, even though the Capital Asset Pricing Model is an empirical catastrophe, the dynamic price of market risk — conditionally expected excess return in the following quarter — can be estimated if one has excellent return-forecasting factors. That is if one has access to variables that contain significant predictive information about future returns on the systematic factor. Previously, we have seen that, according to market microstructure theory, to be an informed investor is to be more informed relative to the market-maker, usually a large securities broker-dealer like JPMorgan or Goldman Sachs. It is clear how an investor could be more informed about the future price of a specific firm’s security than the dealers. But how can one be more informed about systematic risk than the dealers? After all, systematic risk is a function of the risk-bearing capacity of the dealers themselves.

The key to the resolution of the puzzle is to recognize that dealers and patient investors live at different frequencies. Patient investors don’t care about risk-offs that last for days, weeks, or months, as long as the prices of risk assets revive eventually. Dealers have to care about higher frequency fluctuations because they compute the value of risk on their balance sheets as a function of daily volatility. This means that when things are awful for dealers, they are sort of wonderful for patient investors. More precisely, major market risk-offs, when dealers are scrambling to obtain insurance in the VIX futures market, present a significant buying opportunity for patient investors. During such market events, risk premiums widen and assets can be bought up at bargain-basement prices — think of March 2020. Surely, it must be possible for a patient investor to systematically exploit such opportunities to make superior risk-adjusted returns over time? But in order to do so, they must be able to identify periods when asset prices are undervalued. That is, they need a reliable barometer of the dynamic risk premium.

Since we have the ingredients in place, we take a stab at strategic asset allocation. Is it possible to exploit dynamic models of risk premia to beat the buy-and-hold strategy? We demonstrate proof of concept with a highly conservative asset allocation strategy. Specifically, we model the strategy of an unleveraged, long-only patient investor’s decision making problem. The patient investor is constrained to choose what portion of her investment funds to allocate to the market portfolio of equities, with the remainder allocated to the 10-year Treasury note. So after observing the risk premia through her dynamic pricing model in the current quarter, she has to decide how much to allocate to equities and bonds for the next quarter.

Moreover, we restrict the strategy further in two ways. First, she is not allowed to make leveraged bets — equity or bond allocation cannot be less than zero or more than one. Second, the equity allocation is constrained to be 50 percent in the long run. Put another way, like the central banks targeting 2 percent inflation through the investment cycle, the mandate for our patient investor is to average a 50 percent equity allocation through the valuation cycle. The second restriction allows us to compare the performance of our strategic asset allocation against the obvious benchmark — a buy and hold portfolio with 50 percent in the market portfolio and 50 percent in the 10-year note. This allows us to make a strict comparison without loss of generality. Of course, you can do better. But for our purposes, that of demonstrating proof of concept, this highly constrained strategy is more than sufficient.

In our analysis, we have found that for dynamic pricing, the risk factor does not matter all that much — the bulk of the weight-lifting is done by the price-of-risk factors. We use the same price-of-risk features as before: global liquidity obtained from the BIS, and the credit spread and the aggregate equity allocation of US investors, both obtained from Fred. For the risk factor, we use the short-term interest rate. So technically we are pricing duration risk — an asset’s duration is the sensitivity of its returns to interest rate shocks. Once we obtain the price of duration risk through a 2-pass OLS estimator adapted from Adrian et al., we compute the equity valuation as a smooth function of the dynamic duration risk premium standardized to have mean zero and unit variance (ie, we use z-scores). Specifically, we let equity allocation equal 0.5+0.5*(2* Phi(z) -1), where Phi is the Gaussian cumulative distribution function and z is the z-score of the duration risk premium. Using the market return or dealer balance sheet capacity as the systematic factor yields comparable results. The next figure displays the estimated strategic equity allocation.

Does this simplistic systematic asset allocation strategy beat the benchmark? It does indeed. The next figure displays the cumulative returns on the benchmark and the strategic portfolio. One dollar systematically reinvested in accordance with our strategic asset allocation beginning in 1986Q1 would’ve cumulated to $200 by 2020Q2. Meanwhile, the 50-50 benchmark would’ve cumulated to $118. The 50-50 returned 14.72%, the strategic portfolio returned 16.45%, a strategic premium of 1.73%. That's a lot of premium if ask an asset manager.

We also check the result starting at different times. The results are comparable. Strategic asset allocation delivers systematically superior returns relative to the benchmark.

What you need to systematically beat the market is iron-clad discipline and a good estimate of the prevailing risk premia. With these two ingredients, even the simplest strategic allocation should allow you to beat the buy-and-hold benchmark, as we have shown.