Active Risk Budgeting In Action: Understanding Hedge Fund Performance by Kent A Clark and Kurt Winkelmann

Active Risk Budgeting In Action: Understanding Hedge Fund Performance by Kent A Clark and Kurt Winkelmann

I. A Simple Framework for All Asset Classes 
Any portfolio’s return and risk can be decomposed into two parts. The first part derives from the
asset class in which the portfolio is invested, and the second part draws from the manager’s views. 
Asset class risk and return can usually be obtained from passive investments, or indexing of the asset
class. The asset class is typically defined by some benchmark index like the MSCI-World equity
index or the Lehman Aggregate Bond Index. These indices offer a few very attractive characteristics.
They are known in advance, are investible, and are widely accepted as being representative of their
asset class, for example large capitalization global equities in the case of the MSCI-World index. The
indices provide a neutral set of positions, so an active manager can easily set portfolio weights with
reference to the neutral index weights. There is typically a well-defined process for coming up with
the index constituents and their weights.
The active component of risk and return is what we seek when allowing managers to deviate from their
assigned benchmark. Hedge funds are an extreme case in which the manager is completely free of a
passive asset class benchmark portfolio – there is no neutral set of positions for a hedge fund
manager. Nevertheless, recognizing that any portfolio combines passive and active risks, hedge
funds are really not very different from other components of our investment portfolios. As
implementation vehicles for managers’ views, and ideally as vehicles for pure active risk (i.e., active
risk that is uncorrelated with market risk), hedge funds represent something familiar in our
portfolios – active risk – but with little or no passive asset class risk attached. 
The framework for thinking about active and passive risk is, at this point, quite well accepted and
well defined. The following formula captures the main ideas:
Rp = Rf + Beta x (Rm - Rf) + Alpha
We start with the idea of portfolio return, Rp, deriving from the risk-free rate of return, Rf, and
compensation for bearing risk. The latter term can itself be divided into two pieces: the first of these
is passive, or asset class, return and is given by [Beta x (Rm - Rf)] (beta measures market risk, and
Rm is the return on the market index). The second compensation for bearing risk is alpha. Alpha is
a measure of the return derived from skill-based deviations from market (or asset class) returns.
There are a few important observations from this formula:
• First, we are interested in accounting for market risk when evaluating an active portfolio
manager since we expect to be paid for taking this risk. We can evaluate our decision to allocate
to the asset class by comparing the passive asset class return Rm to reasonable foregone
alternative opportunities, such as the risk-free rate. 

• Second, each portfolio may have a different level of mandated market risk (e.g., a different level
of beta), and therefore a different expected risk premium. In fact, depending upon the
investment mandate, the amount of both alpha and market risk may be choices the manager
makes. If this is the case, then the framework allows us to measure the effect of deviating from
the mandated market risk as well. 
• Finally, alpha measures the average return to non-benchmark risk taken. We can evaluate our
decision to allocate to the manager by analyzing alpha.
Alpha is the return to skill-based strategies. Some examples of skill-based strategies include security
selection (e.g., long and short positions in specific securities) and sector rotation (e.g., long and
short positions in particular sectors). Interestingly, the timing decision can also be viewed as an
application of a skill-based strategy. In this case, the manager’s skill lies in choosing when to
deviate from a long-term beta: when positive returns are expected, then the manager should
increase their beta relative to the long-term beta and vice versa. From the perspective of portfolio
construction, the key consideration for alpha is that it is uncorrelated with market performance. This
property becomes important as we begin to assess how to estimate hedge fund returns.
In any period, alpha is the difference between portfolio return and return attributable to the market. 
Alpha = Rp - [Rf + Beta x (Rm - Rf)]
We can evaluate the value proposition of investing in an active manager by assessing the amount of
active return received per unit of active risk. This is typically summarized by the Information Ratio
(IR), calculated as the ratio of average alpha to residual risk. Residual risk is measured as the
standard deviation of alpha over time. 
We can therefore restate that alpha = IR x residual risk, to reflect the economic reality that alpha
derives from the manager’s investment skill as measured by IR, and the amount of active risk the
manager assumes. This allows us to more clearly decompose returns as:
Rp = Rf + Beta x (Rm - Rf) + IR x Residual Risk
With hedge funds, there is no externally imposed guideline or restriction dictating the amount of
market risk taken. Consequently, we typically combine expected market returns and active returns
in the risk premium to create an expected return for the manager. That is:
Rp = Rf + risk premium
Importantly, if we expect the manager to take some steady state amount of market risk, we will
reflect that in the expected risk premium. The framework also allows us the ability to debate the
relative merits of our expected risk premium based on a few well-defined inputs. 
It would be unreasonable to expect an active manager to deliver exactly the expected alpha in
every period. Therefore, in addition to a single estimate of expected return for the manager, we can
use our measures of residual risk to develop a reasonable range of alphas to be expected from the
manager. Residual risk simply captures the dispersion of alpha over time, as measured by the
standard deviation of alpha. Consequently, we can use residual volatility to determine whether
realized alphas are within expectations.
Assuming that alphas (and residual returns) are normally distributed, we would expect a manager to
deliver alpha that is within one residual volatility above or below expected alpha in two out of every
three years. Moreover, in one out of twenty years, we would expect to see alpha less than expected alpha
minus two standard deviations or greater than expected alpha plus two standard deviations. 

Active Risk Budgeting In Action: Understanding Hedge Fund Performance by Kent A Clark and Kurt Winkelmann