Studies conducted by psychologists have consistently illustrated how human beings have difficulty with correctly integrating multiple sources of information. Even when factors can be combined in a linear function, human experts across disparate fields such as law and medicine fail to perform as well as a simple regression model. This problem becomes especially prevalent when dealing with convex or non-linear problems. William Sharpe won the Nobel Prize for simplifying an otherwise highly counterintuitive quadratic solution (brought forth by Harry Markowitz) into a linear framework. This model is known to many as the CAPM, and unfortunately the model required too many simplifying assumptions to make it work. Subsequent research showed that several of these assumptions did not appear to hold true in capital markets. The greatest violation was the assumption of a positive expected linear relationship between beta and future returns (systematic risk). In practice, research showed that beta was either negatively related or had no clear relationship to future returns and displayed more of a non-linear profile.

The original Markowitz (MPT) framework is very difficult to conceptualize, and leads to portfolios that would otherwise not appear to be logical. Several counter-intuitive properties exist, here are two interesting ones: 1) when the sharpe of most portfolios are high, adding assets that reduce portfolio volatility will increase the sharpe regardless of their returns 2) when the sharpe of most portfolios are close to zero, adding assets with a positive return will increase the sharpe regardless of their volatility. If a human being were to form a portfolio using judgment it is highly unlikely that they would account for these properties. This is where discretionary managers get into trouble– they may have a good understanding of how to forecast returns or generate possible scenarios, but integrating this information is not as straightforward as it appears. This is where portfolio math tends to have most of its value.

Despite the strengths of MPT , it is also important to understand where the math can go wrong. Primarily these flaws stem from the difficulty in estimating noisy time series data and the exacerbation of error that occurs as a function of generating “optimal” solutions. MPT optimization can become highly concentrated and inadvertently maximize allocation mistakes as a function of the degree of instability with inputs such as returns, correlations, and volatilities. However, the math remains functionally correct and is closed related to the math underlying multiple regression models. In the next post, I will show how the different optimization algorithms are related. Most share a common theme that is not clearly discussed in the research.

Even within such periods such as roaring bull markets of the 1990s that were less kind to long-term moving average systems, there were highly predictable short-term and even intra-day trends. The reverse has been true of the last several years, where short-term trends and intra-day trends have either been mean-reverting or very noisy and difficult to trade. The problem lies with our tendency to think of the market as operating in one particular time frame. But this is dangerous not just for trading, but also for generating any statistical input for factor models or optimization as well. Financial time series data is so noisy that the risk of ignoring multiple time frame information is even more significant.

The reality of time series data is that it shares much in common with fractals that can appear very different as you look at smaller or larger pictures. A fractal chart can have near infinite total length which is a bounded only by the divisibility of time frames for trading. A trend is therefore in the eye of the observer: if I consider the coastline of Britain to represent a fractal chart, my impression of the shape of Britain depends on whether I look up close or from afar. Assuming that there are several thousand scales from which I could observe the coastline, if I was placed randomly in only one scale (or time frame) I could mistakenly conclude that the next bend would be to the right versus to the left by extrapolating from my own narrow point of view. The probability that I would make a correct guess would be nearly random. However, if I could place different observers to looks dozens of scales at once and simultaneously, with proper co-ordination I could make an informed judgement that would be better than random. If those different scales contain variable degrees of noise, then different scales will be more informative than others. The meta-optimized integration of scale information will then further improve my odds of success especially if scale noise in non-stationary.

If this example seems a touch philosophical, I would urge you to think deeper and consider the implications of what this means for trading and investing. At the very least to me it implies that we must all trade multiple time frames, and be prepared to favor some more than others differently at different times. It also means that statistical inputs should contain numerous time frames for measurement spanning from high-frequency to daily, two-day, weekly etc. If we make no a priori assumptions about time frame preference then we should set up measurements like returns,volatility, and correlations for example to be parameterless and straddle a wide range of possibilities to avoid overfitting.

One of the famous approaches that Jack was known for was to fire the least productive employees in his workforce. In fact, he chose to let go roughly 10% of his workforce each year. His philosophy was slightly more nuanced, and there is a good clip in wikipedia http://en.wikipedia.org/wiki/Vitality_curve that
covers his theory in more detail. Here is a key excerpt:

“Jack Welch’s vitality model has been described as a “20-70-10″ system. The “top 20″ percent of the workforce is most productive, and 70% (the “vital 70″) work adequately. The other 10% (“bottom 10″) are nonproducers and should be fired. “Rank-and-yank” advocates credit Welch’s rank-and-yank system with a 28-fold increase in earnings (and a 5-fold increase in revenue) at GE between 1981 and 2001.
In Straight from the Gut, Welch says that he asked “each of the GE’s businesses to rank all of their top executives”. Specifically (in accordance with the 20-70-10 model) the top executives were divided into “A”, “B”, and “C” players. Welch admitted that the judgments were “not always precise”.

Essentially “A” executives were in the top 20% and considered a key value center for the company, “B” employees were the middle 70% and were considered vital but not extraordinary, and 10% were considered to be of little value—”non-producers” in Jack parlance. If there is truth to the theory that this heuristic was critical for GE’s success during his tenure, then there are some lessons to be drawn for portfolio management. The most obvious is that historical performance is predictive of future performance, and thus momentum or relative-strength investing should be effective. Of course this is well-supported in the academic literature. But what is interesting to me is the concept of “firing” C players–or the bottom 10%, and also the concept of considering the B players to be vital to the organization. What this implies is that we should “cut our losers”–a concept validated by “trend-following” and many of the greatest traders of all-time. But the concept of keeping the B players is counter-intuitive, and yet for portfolio management this implies that one should keep most of the middle-performing holdings as a base of diversification to support the top 20%. One can easily see how this can be applied with several different variations as a portfolio algorithm.

As but one of many examples, suppose you started with a diversified basket of 100 stocks. You could overweight the top 20 by 1-year returns (50% of the portfolio), keep a smaller weight in the middle 70 by 1-year returns (50% of the portfolio), and simply cut the remaining 10 stocks at each rebalancing period- say every quarter (0% of the portfolio). Suppose one repeated this process until they were left with 10 stocks or fewer, at this point one could start again with 100 stocks. In theory this method could also function as a “follow-the-leader” algorithm in keeping with the last post. This variant might look at the cumulative performance or a combination of cumulative and rolling performance until you ended up with a handful of stocks. This method of “force-feeding” winners in your portfolio with capital is an approach long-heralded by William O’Neill and other trading legends. While I have not yet tested these variants, I expect to put this simple yet intuitive heuristic algorithm to the test.

Whether we think of Gold or Apple computer, the key question is how we could have invested most of our money in such stocks by following their trends as they evolved? The answer to this question is that we must seek to track the winners not exclusively on a rolling window basis (like most RS strategies), but rather from the inception or start period of our backtest. Furthermore, we must continuously monitor the leaders and weight our portfolio according to their cumulative return. Finally, to ensure we don’t miss new leaders that start moving during other points in the backtest period, we must repeat this process with multiple start dates. The CSSA SFTL (“S” stands for simple) algorithm works as follows:

1) Inception: track the compound return from the start of the backtest for each asset and each month weight the asset according to their weighted proportion of CAGR with non-negative weights. (asset CAGR / sum of non-zero asset CAGR)

2) Multiple Inception Periods: repeat the same process every 3 months and record a separate set of weights for each inception period

3) Note that you will have a set of asset weights for each inception period that changes every month as the weights change.

4) Use a weighted moving average that weights the oldest periods more than recent periods to ensure that we give more weight to tracking the best asset as recorded since the beginning of the backtest. ie for this month’s period use a weighted average of each of the current weights for all of the recorded inception periods. This is the weight applied to each stock/asset. If one was invariant to the best asset by inception period, you could use a simple moving average that would not favor any one inception period.

This method will invariably track the best asset in hindsight that one could have chosen during the backtest while also providing the opportunity to track the best asset from a variety of inception periods. It is a fairly simple but stable FTL method that could be developed into something more powerful.

This philosophy extends to all industries, and especially those that are driven by intense competition, technology and innovation. Of course, quantitative investing fits in perfectly within this category. So what can we learn from Steve Jobs? He was a man that wasn’t fond of rules or the status quo. Jobs would run his business based on his vision of how technology would evolve in the future rather than how it actually was in the present. He was willing to risk everything in order to best shape his products with this vision.  If he were in finance he would quickly recognize that greatest rewards will accrue to those that can create innovative algorithms or technology. It is very easy to imagine him seeing the value in a quantitative approach to investing.  Furthermore, Jobs would spend less time studying what others are doing in the field and focus on taking a completely novel approach. He would hire talent and promote risk-taking at every level of the organization. Furthermore he would invest extensively in research and development and avoid using a management accounting approach to evaluating its budget.

In the world of “quant” investing today,there are several major barriers to duplicate this approach: 1) a  true lack of diverse and creative talent 2)a lack of  consistent commitment to an ongoing research and development 3) embedded philosophical barriers to innovation .  The first problem is driven by the type of “left-brained” people that are attracted to and consistently employed in finance:  math, engineering and physics. This makes sense because of the high intellectual and technical barriers that exist in modern quantitative finance. However, the saturation of Phds and math wizards creates a talent pool that often lacks both diversity and creativity. While it is true that creativity can come from any background, it is certainly less likely to come from those that have cognitive wiring that is the polar opposite of those people that are typically artistic and creative.

Another challenge is that it is much more difficult to tangibly measure the value of financial innovation unless one is committed to the process. It is easy to measure the value of programmers or the mathematicians that create core programs. In contrast, adding alpha requires incrementally longer time frames to evaluate accurately as the trading frequency becomes lower. However, evaluation is a critical part of business decisions to increase R&D expenditures. That explains why hedge funds,high frequency firms and investment banks continue to hire top scientists while the rest of the investment industry fails to invest in talent.

A final achilles heel resides in the psychological, political, and philosophical barriers to innovation. In all areas of finance, the cost of miscalculation or being “wrong” is so high that human nature causes us to seek out those who are less likely to screw up the math. Having worked with many Phds and other bright individuals, the fear of being wrong or even doing math that is not conventional is so strong and pervasive that they are psychologically unwilling to break from convention. Of course, the very essence of the creative  process requires risking being incredibly wrong in order to find a better way to do something. This can mean that a quant can lose their job for introducing a novel idea that doesn’t pan out, but will probably keep their job if they use GARCH or Fama-French and mess up. Clearly between the type of employee that gets hired, fear of math mistakes, and  the obvious politics involved, innovation has many hurdles to overcome.

We need to stop worrying about being wrong— in a competitive game there is no alpha in  being conventional and avoiding mistakes. There is no such thing as the “right” way to do anything anymore. In quantum physics we are continually exposed to how little concrete information we truly possess. Why should a vastly more unpredictable field be any different? Determinism and mathematical proofs are rapidly losing their value in finance. There is no fixed reality, and the highly dimensional nature financial problems today require both tremendous statistical skills but also the unique and artistic insights that drive the hypotheses to be tested. The new brand of quant firms that will succeed will integrate both approaches under one roof.

Finding the optimal lookback length on an adaptive basis is a worthwhile idea that is not the subject of this post. What is more interesting is whether the optimal lookback is a function of a persistent cycle length or whether the optimal lookback is simply an artifact of predictable fractal behavior. In other words, do the onset of significant rallies or drawdowns behave as a catalyst for change in the relative strength cycle?  It is plausible for example that a significant drawdown in a bull market would “reset the clock” for industry group relative strength with new leaders replacing the old ones in such circumstances. It stands to reason that any significant drawdown or rally can  1) change risk-seeking/risk-avoiding behavior 2) can be caused by perceptions of economic health that will favor certain sectors over others 3) ignite or deflate critical volume liquidity for a given issue that will tend to reinforce trends in both directions.

If this is true, then having fixed rolling lookbacks such as 3 months or 9 months will be less effective than creating an “anchored” relative strength measure that works off of a fixed point of origin. For example, one could measure the relative strength from the bottom point of a significant drawdown after it has re-established new highs as the basis for identifying the strongest groups. Furthermore, one can also measure the relative strength from the breakout point in the previous situation. Alternatively, one could measure the relative strength from the top of a significant rally after it establishes new lows and also at the breakout point as well.  One could also measure relative strength from the bottom of a major rally (ie like the march  low in 2009). There are numerous possibilities using this angle, and the key is to compare such effectiveness of such  methods to  rolling lookbacks so that it can be determined whether they add statistically significant value over a simpler appoach. My theory is that while anchored relative strength may not consistently beat rolling relative strength, there may be some event patterns (such as those mentioned above) that do have relevance. Furthermore, this may be especially true in volatile markets versus consistently trending markets.  Of course, the opposite could be true as well. It is up to the diligent system developer to explore…………

It is conventional wisdom that gold  should not have a risk premium, and historically this has been true though this is a separate debate. What is more important is that gold carries a negative correlation to other assets, and thus in a low or zero interest rate environment it does not need to have much of an expected return in order to improve portfolio risk-adjusted returns. Consider that holding standard deviation constant,  an asset with a -.5 correlation reduces portfolio risk by 50%. That means that gold returns can be up to 50% lower than all other asset returns and still improve the portfolio sharpe.  The same principle holds true for all assets that have low or negative correlations to equities.  This  substantially increases the pool of assets that would qualify for inclusion in a properly diversified portfolio. The lower the correlation, and the lower the expected return of equities, the lower the expected return hurdle for assets without risk premiums need to be to improve risk-adjusted performance.  This means that expected returns that are zero or even negative can potentially qualify such assets for an efficient portfolio.  Of course, this is a “special situation” that occurs in the rare circumstances where interest rates are near zero. Thus the conventional approach of focusing only on assets that have a risk premium in all environments is a flawed approach. A superior approach would consider the dynamics of interest rates and all asset correlations along with a possible range of expected returns.

Furthermore to say that the Global Alpha fund was a high-speed computerized fund is a complete misnomer. Such behemoth hedge funds that trade for outside investors almost always run strategies that appear somewhat “conventional” (tactical asset allocation, buying undervalued securities, engaging in complicated over the counter derivative and fixed income strategies) and have modest turnover that is enhanced high speed execution.  In contrast, the strategies run internally are almost certainly higher frequency and built on tremendous structural edges gained from trading for and on behalf of clients.   To me, the closure of “Global Alpha”  highlights several points: 1) the markets are in the midst of tremendous global financial mess where conventional historical relationships have been severely disrupted by highly unpredictable movements in different assets—this was probably one of the reasons why Goldman had trouble especially since it is trading the Global Alpha with a lower frequency of trading 2) it is no longer  desirable for economic and practical reasons to trade scalable quantitative strategies on behalf of investors— their capital is not truly required for a firm like Goldman and investors are disruptive by exposing them to greater legal risk and unwanted transparency 3) the best talent (aside from the internal GS trading group) is rapidly shifting to proprietary trading and high-frequency firms where it is most beneficial.

Things are changing in the investment industry, and something tells me that this is a historic event that many will point to in the future as a turning point. The  jury is still out yet as to what these changes will be, but my intuition suggests that we are entering a new and different era for investment management. True “alpha” is quickly becoming a privatized business.