We all know that finding alpha is tough. But managing a portfolio of alpha sources is also trickier than it seems. Many assume that a hedge fund manager’s idiosyncratic risk has a stable relationship with his beta exposures (which is unsatisfactory); and that idiosyncratic risk is normally-distributed and, by definition, non-correlated with other idiosyncratic risks (which is potentially disastrous). Very few have made significant progress beyond these assumptions, but it should come as no surprise that one of those few is fund of hedge funds Caliburn Capital Partners - because building portfolios of alpha is its raison d’être.

“If you pay hedge fund manager fees, you want to be pay for alpha,” says CEO Jeremy Rowlands. “Where is active management more likely to work? In the least efficient markets.”

That principle has been at the heart of Rowlands’ career since 1992, when he co-founded Bayard Partners, one of the very first long/short European equity shops. “Shorting was still illegal in at least one European jurisdiction,” he recalls. “The same perspective - seeking out the most inefficient markets - informed our fund of funds concept in 2005. The starting point is not managers, but where in the matrix of economic activity we want to focus our activity.”

That sends Caliburn after some weird and wonderful stuff, such as active trading in Nord Pool energy contracts, Chinese non-performing loans, or relative-value trading of metals contracts between Shanghai and London.

“Risk managing that is a nightmare,” says Rowlands. “You have to engage with what qualitative analysis can bring to an essentially quantitative framework. Going through the fund of funds due diligence process with Bayard I saw that much of it was either qualitative to the point of being unstructured, or excessively quantitative.”

By combining qualitative and quantitative analysis, Caliburn creates profiles of all of its underlying managers’ beta risks, residual (alpha) risk and tail risks. Establishing the beta factor risks that describe most of a manager’s return could be derived by simple in-sample multivariate regressions, but Caliburn aims for a bespoke model that has utility out-of-sample and that is where qualitative insights come in.

Head of quantitative research, Apostolos Katsaris, takes an industrial metals specialist as an example. When Caliburn invested with that manager in June 2006 the standard factor models would have found industrial metals explaining most of his returns. If you were looking for an alpha manager in industrial metals he’d have seemed ideal - until January 2007, when the manager severely underperformed industrial metals. The chances are you’d have assumed that was negative alpha, redeemed - and missed a healthy 2007 and a banner year in 2008.

“Why didn’t we redeem?” asks Katsaris. “Our qualitative analyst noticed that they talked a lot about deferred copper and aluminium, and we wrote a paper looking at how commodity curves have ‘anchor points’ that move much less than other points because the market participants are so different - basically, financial players at the front, industrial players at the back.”

Caliburn digs beyond the ‘easy’ risk factors, using more than 3,500 time series - including whole curves for the entire commodity complex. “We figured that aluminium 24 months out and copper 36 months out explained this manager - and an out-of-sample expectation from that model in June 2006 explained 80% of the January 2007 losses. The fact that his losses matched that prediction gave us more confidence in him.”

The second step is assessing the manager’s alpha - his tracking error against this tailored beta model. This is important because alpha can be negative. “Reducing beta risk is not the same as reducing total risk,” as Katsaris puts it.

Out-of-sample residual data points exist for that alpha, but how should they be used to calculate risk? Caliburn’s answer is “residual risk-adjusted VaR”: it takes the VaR number from the beta model and uses that as the centre for the distribution of residual risk data points - effectively adding the alpha distribution onto the left tail of the beta distribution - changing the weight of each distribution according to the out-of-sample R2, or predictive power, of the beta model. How you respond depends on your reason for investing with the manager - if it’s purely about maximising alpha, you may want to increase his risk budget as the R2 falls, but if you are targeting a specific risk level from him and his total residual risk-adjusted VaR is going up, you may want to dial him down.

But what if the predictive power of the beta model has broken down completely - as in the case of the metals specialist, who was smart enough to anticipate the commodities crash and totally switch his book? “Another manager, in long/short European equities, showed significant commodity exposure at one point, and it turned out that they had a 20% position in a Nordic smelting company,” recalls Katsaris. “That’s the ‘master of the universe’ approach to things, predicted on the belief that hedge fund managers can achieve absolute positive returns in all environments. Our approach is to find specialists that provide exposure targeted for a strategic asset allocation perspective.”

There are other ways in which the predictive power of the beta model can break down. This is tail risk, and it is most pronounced with managers showing very little exposure to traditional risks and little volatility of expected returns: directional strategies in illiquid niche markets or market-neutral arbitrage strategies, for example. This is where the qualitative analysts come into their own. Every quarter they complete a questionnaire detailing their understanding of the key risk exposures for each manager. These insights are reviewed monthly by the risk committee.

“If these risks change we need to start discussing a change to the model - especially if the model still appears to fit the manager,” says Katsaris. The qualitative research identifies the tail risks, the distributions of which are then added to the residual risk-adjusted distribution: just as the residual risk distribution is centred around the market VaR number, so the tail risk distribution is centred around the residual risk-adjusted VaR number - again, pushing out the left tail.

“In effect, we are saying that returns will come either from market risk, residual risk, tail risk or all three combined with changing probability,” Katsaris explains. “The weightings for each distribution change across time: you go from market risk in good times to residual risk in bad and tail risk when things are really bad.”

Why is it so important to establish these more robust VaR numbers? They obviously give Caliburn a better idea of the downside risk of individual positions, but they are also necessary for portfolio risk management if, like Caliburn, one acknowledges that idiosyncratic risks can become correlated: they make it possible to model scenarios where alphas correlate, instead of just assuming this can never happen. Moreover, defining alpha this rigorously enables Caliburn’s portfolio construction to enhance rather than erode its alpha exposures - making the case for added value in the fund of funds structure.

“Every month we run a principal component analysis to find out how many risk factors we need to explain the full variability of returns,” says Katsaris. “If that number goes down, residual risks must be correlating - you could say that we pick up an emerging risk factor before it becomes too pronounced. It also means that investors can see if we are sourcing enough alpha. If not, why would you want to pay us?”