AIMA

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Alternative Investment Management Association Representing the global hedge fund industry

Risk estimation in an 'information semi-vacuum'

Alexander Rudin

Julius Baer Financial Markets, LLC.

Q3 2006

 

In what follows we suggest a way to estimate hedge fund market risk in the absence of full portfolio information. The method starts with a typical exposure profile available from a fund manager and then makes a range of general but reasonable assumptions regarding individual instruments and their interactions within the fund portfolio. The method estimates fund volatility by capturing the two main contributions to the latter: pure market beta risk and idiosyncratic risk of individual stocks exacerbated by portfolio leverage.


Detecting strategy drift
 

One of the basic tasks of a fund of hedge funds risk manager is to estimate and track market risk of underlying funds. Usually the easiest way to do it is to monitor hedge funds’ historical performance. Indeed, it is often argued that for structural reasons, hedge fund historical volatility is a reasonably good estimator of future volatility. The problem with relying entirely on performance information is that when fund risk profile for some reason quickly changes, it takes a while (in fact, many months!) until that strategy drift surfaces in the performance statistics. To counter this problem and complement the ‘top-down’ historical performance studies, more and more hedge fund institutional investors collect and analyse position information of the underlying funds.

The main hurdle with analysing the hedge fund position information is a well-publicised unwillingness of hedge fund managers to give external investors access to their portfolios. The transparency varies widely by fund, and most importantly by fund strategy. There are, however, certain standards that managers are expected to follow if they wish to secure capital from the medium-to-large size institutional investors. These standards are the results of a compromise between hedge fund managers’ confidentiality concerns and the needs of an institutional investor to have enough information on the underlying funds to make informed judgements on the level and dynamics of fund market risk. Fund leverage and net exposure, largest positions, and ‘Greeks’ are usually communicated. In the case of equity hedge funds, information on the portfolio split by stock industry, region, and capitalisation class is often given. Global macro/CTAs supply gross/net exposure for various classes of FX, fixed income, equity, and commodity futures, and so on.

In other words, an FoF risk manager usually operates in an ‘information semi-vacuum’: basic exposure characteristics of underlying hedge funds are known, while the exact fund positioning is not available. As a result, a standard risk manager toolkit that proved to be so useful in the capital markets industry over the years is not immediately applicable. In particular, precise position-based estimates of fund volatility or, by the same token, Value-at-Risk are hard to get unless provided by the hedge fund manager himself. Unfortunately, even in those cases the fund-to-fund risk comparison remains difficult due to the widespread variations in fund risk management methodologies and lack of information on the latter.

In what follows we suggest a way to estimate hedge fund market risk volatility in the absence of full portfolio information for a fund. We will use an equity long/short example as a guinea pig. However, the approach is equally suitable for global macro/CTAs and other strategies with low inherent optionality. The suggested method starts with the typical hedge fund exposure profile and then makes a range of assumptions regarding individual instruments and their interactions within the portfolio. The method, while being not exact by design, captures the two main contributions to the fund volatility: pure market beta risk and idiosyncratic risk of individual stocks exacerbated by portfolio leverage.

Volatility estimate
 

A simple case
Let us start by introducing notation. Return of a long/short hedge fund portfolio at time t, rPt, can be expressed as:

 

[insert equation 1]
 

where [equation A]

and NL(S) are the weights and total number of instruments on the long (short) sides, and

[equation B]

are instrument returns. Our ultimate goal is to estimate variance of the portfolio (we omit t for brevity,) σP2=

[equation C]].

The way we proceed from this point depends on how we decide to model the fund portfolio.

In the simplest case, there is only one factor that is relevant for all stocks in the portfolio. We call this factor ‘market’. Under this assumption

 

[insert equation 2],

where

{equation D]

and are

[equation E]

the market return and stock beta coefficient, and is an error term of a corresponding single factor regression model (

[equation F]). Single factor model also postulates independence of error terms between each other (

[equation G]). Substitution of (2) into (1) and calculation of the portfolio variance yields
 

[insert equation 3]


Here

[equation H]

is the variance of i-th error term, and

[equation I]

is the portfolio market beta or, adopting the fund of hedge funds terminology, the ‘beta-adjusted net exposure’ of the equity long/short fund. In this formulation the portfolio variance has two contributors. The first term in the Eq. (3) represents the straightforward ‘market exposure’. The second term is more interesting: it represents risks caused by the price deviations of individual securities from the ‘market crowd’, or, in other words, the idiosyncratic risk of long/short investing.

Let us simplify Eq. (3) further. Assuming equally sized positions,

[equation J], and denoting average error term variance as

[equation K], we can shrink the result to: 
 

[insert equation 4]

 
Here we introduced net and gross ( ) exposures of the portfolio. The first term is the market exposure that is proportional to net (or ‘beta’) of the portfolio squared and multiplied by the market variance. The second term represents idiosyncratic risks of individual securities. It reduces when the number of stocks in the portfolio increases and grows together with the portfolio leverage.

For a typical equity long/short fund portfolio, the two contributions are of the same order of magnitude. Indeed, comparison of market volatility to error term volatility for relevant stock universe yields . Given that the net/gross levels for equity hedge space are usually around 0.3/2.0, and managers typically have around 30-40 stocks on each side ( ), the ratio of market to idiosyncratic contributions to the overall portfolio volatility
 

([insert equation 5]
is of the order of one.

As Equations (3)-(4) demonstrate, one can express portfolio expected volatility in terms of limited information available to a fund of funds manager by making certain assumptions about the missing data. The assumptions may be arbitrarily complex and are limited only by the amount of quantitative and qualitative information available to an investor.

Volatility estimate
 

A realistic equity long/short case
 

Let us illustrate our approach with a more realistic case, when net and gross exposures are available on the industry sector level . This level of transparency is typical for an equity long/short fund with a U.S.or European focus. Though notation becomes more cumbersome, the essential results remain unchanged.

First we express return of the individual stock via returns of the corresponding industry benchmark:

[insert equation 6].


The industry returns are correlated to each other with correlation coefficients . The error terms are assumed to be uncorrelated to industry returns and with each other. Portfolio variance is again a sum of two contributions, ‘market’ and ‘non-market’:
 

[insert equation 7].

The ‘market’ contribution is related to volatility and correlations of industry benchmarks (M in total):

[insert equation 8],
 

where we introduced portfolio beta exposures (or ‘industry sector nets’) with respect to those benchmarks,

[equation L]. The ‘non-market’ or idiosyncratic contribution is

[insert equation 9].
 
As before, it is expressed in terms of position sizes and volatility of error terms, which now vary by the industry.

Portfolio industry net exposures are deemed available from the hedge fund manager, which makes evaluation of

[equation M]

very straightforward. Equation (9) contribution can also be estimated by assuming equal position sizing, w, and introducing average error volatilities

[equation N]. Portfolio variance then takes the form similar to Equation. (4):

[insert equation 10]

 
where Gross(m) is a fund gross exposure to the (m) industry, in our case also deemed available from the hedge fund manager.

Conclusion
 

The suggested approach reduces risk estimation of a equity long/short fund to four steps: (1) collecting available gross/net/sizing information from a hedge fund manager, (2) identifying industry (or other) sector benchmarks and tabulating their volatilities and correlations, (3) estimating typical volatility of regression error terms by studying representative stock peer groups, and (4) estimating portfolio variance from all of the above using Equations (7)-(10).

The approach captures both main contributions to the portfolio risk – market exposure and leverage. In our opinion, the continuous estimation of portfolio variance from limited position information available from the hedge fund manager is a useful addition to any performance-based risk analysis. It takes into account rapid changes in the exposure profile of a dynamic hedge fund portfolio. It also helps put different hedge funds on equal footing in terms of risk and capital allocation comparison.

Note:
The views expressed in this paper are those of the author and do not necessarily reflect those of Julius Baer Financial Markets LLC.

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