Study on real data

Asset allocation

We make difficult choices while allocating assets. Investors tend to adjust their strategic asset allocation (SAA) based on recent fads, fashion and conventional wisdom. The allocation to hedge funds and other alternative assets like commodities or private equities are recent examples. But this has occurred repetitively, for example allocation to Nifty Fifty stocks in the 60s and 70s, to Japanese equities in the 80s, or to internet stocks in the 90s are other examples. More recently, the industry has been increasingly allocating to risk premia, factors and other so-called alternative betas.

The breadth of potential investment choices has grown larger and larger. Regulators have responded to this development by requiring extensive skills and experience from members of governing bodies such as investment committees and boards of directors. We talked about the paradox of choice under the Technology chapter. Taking the right decisions on asset allocation is a typical stressful situation, where paralysis can be felt as a consequence of the breadth of choices and respective arguments in favor and against, all to be considered. Then, there is a high likelihood regret will be felt, as in hindsight the choices which were made might have been better. AGNOSTIC is precious support in such situations.

Let’s consider a typical investment universe for a Swiss Institutional investor: government and corporate bonds, equities and real estate, diversified by geography, i.e. other than domestic Swiss: US, EU, emerging markets, further diversified by the addition of commodities and hedge funds as alternatives. Unconstrainted, what would AGNOSTIC have recommended given these choices?

AGNOSTIC is true to its promise. It does almost as well as the best asset and by timing its allocation wisely, is able to produce a performance that even beats the best asset.

The reservations are quite evident though. Driven by its objective to narrowly match the performance of the best performing asset, AGNOSTIC is literally careless about diversification. For example, at one point it has no hesitation about recommending to allocate near to 100% of the assets to emerging market equities. This is why we developed an extension to allow the introduction of constraints on the allocations AGNOSTIC can choose from. Please note that although not used here, constraints on minimum allocation can be mixed together with constraints on maximum allocation. In the below illustration, we have constrained AGNOSTIC’s allocation choices as follows:

  • up to 50% in any geographical area,
  • up to 50% in equities in all areas,
  • up to 30% in real estate in all areas,
  • up to 30% in other alternative assets (commodities and hedge funds together).

For comparison purposes, the original extent of achievable performance with no constraint (as above) appears in grey. The turquoise area delimits achievable performance accounting for the constraints.

AGNOSTIC does better than the best possible static allocation allowed within the constraints. In this particular case, it even manages to match the performance of the best asset notwithstanding any constraint. Of particular note, AGNOSTIC operates immediately, starting from day one by observing underlying asset returns and working out recommended allocations day after day, from amongst the choice of possible asset allocations. What you see in the above graph is the performance you would have obtained had you entrusted AGNOSTIC with your allocation from the very first day.

By extension, clients should consider adding their own tools alongside the possible assets AGNOSTIC can recommend an allocation to, like for instance tactical asset allocation (TAA) decision tools based on:

  • fundamental or macro-economic models,
  • technical indicators, or quantitative strategies,
  • output from an investment commitee.

In so doing, by delivering allocation recommendations, AGNOSTIC will implicitely be indicating the relative merit of each investment opportunity and pointing out how to come close to matching the best of them. Your most valued tools, capable of exploiting information from the markets, even temporarily, should be added to the possible choices for AGNOSTIC.

Factors & smart betas

There has been a growing appetite from Institutional investors to invest in factor-based products. There are numerous reasons behind this trend: diversification benefits in combination with traditional asset classes and performance, being the main ones. Their availability and number has multiplied. Factors are nothing else than rule-based investment strategies. When based on prices and accounting values alone, the number of potential factors is large. Including alternative datasets, e.g. shopping mall parking lot occupancy pictured from satellites or statistics from specific mobile apps, as a way to forecast sales, etc. Possibilities have become extremely large.

How to choose? AGNOSTIC is here for choice, as it was developed to assist investors facing a large number of choices. AGNOSTIC can be a precious tool for investors seeking to invest in factors.

Below, we cover the specific case of traditional value factor HML. We focus on choosing countries where the HML factor can be put to work in a productive way. The original academic literature on the HML factor was grounded on US stocks. Subsequently, other countries were tested leading to the conclusion that the factor was significant in almost all of them. While valuable information per se, those papers are not actionable. Questions remain:

  • The variability of performance from one country to another?
  • Reason for some countries underperforming the expectations per the original research on US stocks?

AGNOSTIC solves the problem by making recommendations pertaining to application of the HML factor to each country, weighting allocations to the different countries accordingly. The worst performing country is avoided, while the algorithm’s performance tends to match the performance of the best countries.

AQR High minus Low (HML) factor, country by country

Trading strategies

One area where AGNOSTIC shines is definitely the allocation to and timing of trading strategies, since that was the reason for its development. In this respect, it is worth noting an important observation. AGNOSTIC performs best with inputs that have a higher signal to noise ratio and finds it extremely difficult to productively allocate to typical base investments like individual stocks, bonds, commodities or currencies. AGNOSTIC requires that information is filtered. The most basic example is an index, where covariance helps reduce noise. A more sophisticated filter is a trading strategy, formalized as an investment model. Those will do the job of sorting between signal and noise. How do you choose between the different indexing methodologies and trading strategies? AGNOSTIC is your delegate for choice if you wish to come closest to performance of the one which will come out best.

US sectors

The first illustration is the result of feeding AGNOSTIC with US sector performances. Though it clearly avoids the worst, AGNOSTIC does not live up to expectations. The likely explanation is that US sector returns are mostly random.

Investments based on SPDR Select Sector Fund ETFs

Now, we introduce a trading strategy for each sector, which is fed as input to AGNOSTIC. The outcome is quite extreme, as the trading strategies are in this case very efficient at exploiting information from the markets with the help of a model highly capable of distinguishing signal from noise. But let’s concentrate on the particular result of AGNOSTIC. Have you noticed how it fulfilled its part of the deal, dwarfing even the performance of the best trading strategy thanks to timing?

Investments based on trading strategies on each SPDR Select Sector Fund. For the sake of clarity, ETF tickers are carried over as denomination for sector strategies

You will have noticed we did not care for constraints in the illustration, though you may have to abide by some due to e.g. internal rules, diversification requirements, or capacity constraints. In such a situation, the plug-in developed for input of constraints will be useful, as demonstrated in the very first section related to asset allocation.

Daily momentum meets daily mean-reversion

A story follows, to illustrate the ease by which you can fall into the trap of believing what worked in the past will continue to in the future. The reality check offered by AGNOSTIC can help you either not to fall in the first place, or if you do fall, to quickly climb out of the trap with little consequence.

Imagine that you are a PhD student, back in the early 70s, with an access to daily data of the S&P 500. Over the weekend, playing with your HP-35 calculator, you discover an interesting pattern. A strategy of being long, from the close of today to the close of tomorrow, if the performance from the close of yesterday to the close of today was positive and being short when the opposite occured, had impressive returns in the past. Looking at alternative look-back periods of two, three, four or five days is not as impressive. You quickly come to the conclusion that the one day follow-through strategy is to be preferred, Sharpe Ratio and p-values confirming the fact.

Fast forward 25 years, you have become a hedge fund manager. Your quant teams have solved all the intricacies of implementing such a strategy and everything is working perfectly. Business is running smoothly and no one is really concerned with the strategy itself, resources are concentrated on the minimization of market impact. However, performance starts to deteriorate and investors complain. The strategy has been working for decades, so there is little reason why it should not continue in the future. Nevertheless, you follow your quant team that tells you recent evidence suggests a strategy based on a four or five day period could work better, Sharpe Ratio and p-values confirming the fact. Performance does not really improve. A few client full redemptions later, the situation further deteriorates in the early 2000s. Performance becomes very negative and it looks like you should actually do the opposite of what you have done in the past. Time for a change? Future will tell.

Our particular interest here is to show how AGNOSTIC’s recommendations would have fared in such a situation. As an input, trading strategies based on one to five days lookback periods are considered. Alongside, the same strategies but inverted are equally added, for consideration by AGNOSTIC. You never know, things change and you might have to actually do the opposite of what you originally believed in.

Investment strategies based on daily momentum or… daily mean-reversion

As can be seen, while the cost of adding momentum strategies with different lookback windows and their reverse (short momentum, i.e. long mean-reversion), is negligible, the diversity of strategies offered to AGNOSTIC for making recommendations has proved precious when difficulties arrived. AGNOSTIC was able to dynamically and without second-thoughts recommend switching into those strategies presenting the best prospects. Even if those switching opportunities ended up being rare, the potential requirement to do so was covered. Better evaluate alternatives and use them when needed, than stick with a strategy hoping performance returns.

Choice of parameters in trading strategies and models

Momentum on strategies

Remember, in the chapter covering History we mentioned that Encelade Capital used to rely on momentum on strategies to take advantage of persistence in the performance of trading strategies. Below, we present an illustration. One base strategy is chosen and applied to a set of US stocks. We apply the strategy for the next time step(s) to the stocks where it had the best results in the past. A number of strategy parameters can be selected: in-sample time period, quantiles of stock’s performance to consider for investment, lag to start using these stocks and out-of-sample period during which the strategy will be applied. We focus on the in-sample period. Other parameters are fixed. Lag is one day, we are long the top and short the bottom 1% of stocks and keep this position for a month. As you can see in the graph from the area of achievable performance displayed in grey, the differences in performance can be sizeable from one in-sample period length to the other. How would AGNOSTIC have fared in this case? Pretty well indeed.

Momentum on strategies

Long established factors

We now consider the historic momentum factor as per data downloaded from Kenneth French’s website.

In the following example, we define a set of investment opportunities as being long or short whatever decile of momentum. As mentioned above, being long the 10th decile and short the first is obvious once you have seen the data. One may wonder how AGNOSTIC would have fared with the choice of deciles if it had been entrusted to dynamically recommend which deciles to pick. The answer from the below plots for long and short deciles are pretty convincing. While staying open to change, AGNOSTIC manages to keep up with the best choices in hindsight, i.e the top and bottom deciles.

Fama French momentum, long deciles 1 (LOW) to 10 (HIGH)

Fama French momentum, short deciles 1 (LOW) to 10 (HIGH)