Most hedge funds claim to produce positive absolute returns. The reality is sobering: most strategies still largely depend on stock market performance and those not incorporating equities haven't kept their promises either. Excuses for negative returns are quick at hand: the markets have changed, liquidity has dried up or volatility is too high / low, to name a few.

So what can investors do to predictably achieve positive absolute returns?

Although a strategy's historical return may not necessarily predict future returns, there is predictive power in a strategy's return distribution, i.e. by selecting strategies with distinct return distributions it is possible to build a portfolio which will be far more likely to produce positive absolute returns in the future.

When choosing an asset manager or an investment one has only one return assumption, that is, it is expected to achieve consistent 'positive absolute returns' in the long run. Twenty years ago the panacea was to 'buy-and-hold.' Spoilt from high success ratios, investors awakened after the turn of the century when the one way road came to an end. Long/short hedge funds blossomed and a new financially astute elite emerged. Nevertheless, the consistency of returns eroded. Since one can never be sure to grasp the difference between skill and luck (or in academic terms, between alpha and beta), the question arises whether there are methodologies to overcome the uncertainty of investing and translate the intricacies of investment decisions into a more quantitative approach.

When building portfolios, investors focus almost solely on the mean and variance of returns. According to the Modern Portfolio Theory, this mathematical approach appears to work well as long as historical correlations between asset classes remain stable. In times of crisis, however, that is not always the case, leaving clients predictably distraught when their expected returns are offset by major negative market events or black swan events, such as the dot-com bust, the credit crisis, or the political swoon when handling the Euro crisis in 2011. By only focusing on mean return and variance, investors may not be factoring in important, measurable and robust historical information. More quantitative precision is therefore needed in order to make a statement with predictive value.

A historical return stream of an investment (instrument or strategy) delivers a more precise DNA of the asset class or strategy if the higher moments are taken into account as well, i.e. next to the mean and variance of return data (first and second moment) the third and forth moment add very decisive statistical value that cannot be observed visually from the cumulative equity curve. The third moment (skewness) measures the degree to which a pattern of returns is symmetric around the mean. The best visual representation is to plot the returns in a histogram and a symmetric distribution is one in which the two "halves" of the histogram appear as mirror-images of one another. For skewed distributions, it is quite common to have one tail of the distribution considerably longer or drawn out relative to the other tail. An investment with negative skewness could be a high-yield bond which pays out a constant stream of coupon income, but when a crisis hits relatively large losses may occur, producing a long left tail of its return distribution.

The fourth moment (kurtosis) is a measure of extreme observations. How likely are the returns to be extreme, either positive or negative? Though the sign of skewness is enough to tell something about the data, kurtosis is often expressed relative to that of a normal distribution. Data that has more kurtosis than the normal is sometimes called fat-tailed, because its extremes extend beyond that of the normal. It is a way to identify where the risk comes from since it reveals whether the risk is more likely to hit all at once or if losses are more likely be seen in small increments over time.

Empirical research has shown that investors prefer high odd moments and low even moments, that is, they are seeking a strategy with high returns, low volatility, occasionally large gains and possibly no return outliers. This sounds like wishful thinking and no asset class is known that in the long run will fit all of these requirements. The next level of sophistication is then to seek an asset allocation strategy that by virtue of statistical properties comes closest to the desired characteristics. Instead of calculating optimal portfolios and dealing with the implications of non-normality of asset returns*, a process of reverse engineering is employed. This is the key to transform uncertain outcomes into well defined statistical measures. The uncertainty of unknown results and unknown distribution of results can statistically be transformed into unknown results but known distribution of results.With all this statistical munition at hand, how is it possible to construct a strategy which will - with great likelihood - produce a long-term positive return stream, irrespective of the stock market behaviour or a looming black swan event?

The first step is to identify specific investments (instruments or strategies) with typical and predictable return distribution characteristics. This procedure already excludes a large number of potential investment choices. An actively managed stock portfolio, for example, has highly unpredictable return streams because of beta-dependence and an unknown alpha, i.e. investment performance depends on stock market behaviour and the skills of the asset manager. A long/short equity fund can potentially produce long-term positive returns and its distribution can be positively skewed but this has to be viewed in light of the 2008 events when most products were still positively correlated to the stock market and therefore lost their positive skew. A stock index ETF, on the other hand, has a more predictable return distribution, i.e. negative skew and a left fat tail.

The next step is to select those predictable distributions with very pronounced moments. Combining only two of those 'extreme' known distributions can lead to highly consistent return streams with very favourable properties. One example is the combination of two investment strategies with the following characteristics:

Strategy 2 has the properties of a 'managed Option Writing' investment and profits from being short volatility. Over time a managed Option Writing strategy exhibits similar characteristics to selling insurance, as steady premiums are garnered most of the time, punctuated by periodic losses, leading to a negative skew. The safer variation of a pure insurance strategy is to sell both puts and calls, leading to higher premiums but meaning that losses can occur both in a falling market (akin to an insurance catastrophe) and also when prices rise. However, the option positions will offset each other to some extent, as market movements which hurt one leg of the strategy as the options move into-the-money will benefit the other as they move out-of-the-money. The skill in managing the strategy is derived from understanding market technicals, including seasonal effects, as well as fundamentals, which allow the option legs to be repositioned according to observed market action or expected future price paths and the overall 'Greek' exposure to be kept within accepted bounds. In the wake of a loss event, however, premiums expand and the option writer accelerates the rate at which the loss is recouped and goes on to collect higher profits. Returns are highest in the aftermath of market volatility.

Strategy 1 represents a typical 'systematic Managed Futures' investment and profits from being long volatility. The reason for its typical return distribution lies in the nature of the trading programs used. Most Managed Futures programs use disciplined, trend-following trading strategies which are designed to capture a majority of the price movement in long and intermediate-term trends while systematically using stop-loss orders to try to exit bad trades before the losses mount. Consequently, these trading programs tend to produce more "big winners" than "big losers", hence the positive skew of returns. Because Managed Futures programs can hold both long and short exposure in many different financial and commodity markets around the world, they can exploit opportunities not available to traditional portfolios. Managed Futures programs also maintain very attractive liquidity characteristics, so they can quickly reverse direction when and if appropriate. This kind of flexibility-not shared by traditional stock and bond fund investments-is particularly important during financial crises, when "cash is king." During a crisis, investors typically seek and store liquidity, withdrawing from risky asset markets. This causes market volatility to rise and price trends to become exaggerated. Trend-following programs that systematically cut losses early and let profits run tend to have unusually good returns and a negative correlation to traditional investments during times of stress.

The profit and loss profile of both strategies can best be visualized by the following two graphs:

The combined strategy takes advantage of the opposing profit and loss properties of both strategies: when volatility is rising, Managed Futures will shine with great likelihood, offsetting the possible losses in the Option Writing strategy. When volatility is low, Managed Futures may realize many small losses which with great likelihood are more than compensated by the premiums of the Option Writing strategy. The individual return distributions below clearly exhibit quite different shapes resulting from their unique return drivers. As a result, the green area which represents the return distribution of the combined strategy displays a much more normal distribution of returns; in particular, the undesired left tail and negative skew disappear.

This approach has greater predictive value than the fallible extrapolation of historical returns of any given strategy into the future. The likelihood of achieving the desired combined results is greatest if the trading logic of the underlying long and short volatility strategies is maintained consistently and no attempts to predict market direction or volatility are made. Whether volatility is rising or falling, whether it is high or low, the uncertainty of surprise losses should disappear almost 'by definition'. The equity curve above right displays the exemplary result of such a strategy.

*see for example: *The Impact of Skewness and Fat Tails on the Asset Allocation Decision*, James X. Xiong and Thomas M. Idzorek, Financial Analysts Journal, Volume 67, Number 2

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.