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01 June 2006 12:00AM

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In the second of the series on trading strategies, Jim Hanly and John Cotter* ask, how effective are hedging strategies?
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The terms risk management and hedging are often used
together. Hedging is a component of risk management as it is
one of the methods available to control risk, and there are
many hedging tools and strategies that may be used to try and
engineer an efficient hedging outcome. Hedging1 whereby the
underlying spot asset is hedged by the corresponding futures
contract is an important tool in the management of risk.

This article examines the hedging effectiveness of different
hedging strategies in risk management. It details and compares
a number of risk measures that can be used to measure the
effectiveness of different hedging strategies. A key issue is
the extent to which hedging reduces the volatility of investors
positions. Since hedging can be interpreted as a form of
insurance, it is worth considering how effective that insurance
is in terms of risk reduction, and it is this issue we focus
our attention on.

Risk measures and hedging performance metrics

While risk management tends to mean the implementation of
strategies designed to reduce risk, an important consideration
is the measure that is used to define risk. We examine three
commonly applied measures of risk in terms of their attributes,
and their

suitability as risk measures in the context of evaluating
hedging strategies from the perspective of risk
reduction.

Variance and the standard deviation

The use of standard deviation2 is widespread in terms of
measuring risk. Moreover, it is extensively used by hedgers
following Ederington (1979), who suggests that the main purpose
of hedging is to minimise the variance associated with the
hedge, referred to as the Minimum Variance Hedge Ratio (MVHR).
However, this measure has a number of shortcomings.

Firstly, it is not an intuitive measure, as it deals with
manipulating deviations by first squaring them and then taking
the square root of the outcomes. More importantly, the standard
deviation cannot distinguish between positive and negative
returns and therefore it does not provide an accurate measure
of risk for asymmetric distributions (non-normal)3. Given
asymmetry, hedging effectiveness metrics that cannot
distinguish between tail probabilities may be inaccurate in
terms of risk measurement. Also, since it cannot measure the
left and right tails of the distribution, it fails as a risk
measure to differentiate in terms of hedging effectiveness
between short and long hedgers4. Where asset return
distributions are asymmetric as is generally the case, the
standard deviation will over or underestimate tail risk. It is
therefore not an adequate measure of risk for hedgers except in
the event that the return distribution is symmetric (normal).
Even in this case the semi-variance is more appropriate5.

Value at Risk (VaR)

Recently VaR has become a very popular market risk measure. We
can use it as an objective function in hedging when the user
tries to minimise the VaR associated with their hedge. VaR is
essentially a quantile of a loss distribution6 and is widely
used in financial risk management and the evaluation of the
effectiveness of hedge strategies7. In particular, unlike the
variance, it is estimated separately for upside and downside
risk (see figure 1 for downside VaR). VaR has become popular
despite a number of limitations as a risk measure. Its most
serious theoretical shortcoming is that it is not a coherent
measure of risk, as it is not sub-additive. A risk measure,
r(.) is sub-additive if r(X+Y)<r(X) + r(Y) implying that
aggregating risk does not increase the risk of the portfolio
over the sum of the risks of the constituent sub-portfolios.
The fact that VaR is not sub-additive leads to strange
'negative' diversification effects in the context of portfolio
theory. Also, in practice, two portfolios may have the same VaR
but exhibit very different potential losses. In other words,
the VaR cannot tell us what the likely losses will be in the
event that the VaR is exceeded (see figure 1). It is of limited
use therefore as a valid measure of risk to use in the
evaluation of hedge strategies in situations where hedging is
concerned with protecting against extreme losses such as those
associated with tail events in excess of the VaR. These
shortcomings can be addressed by the use of the Conditional
Value at Risk (CVaR) measure that has the property of
sub-additivity.

CVaR

CVaR is the expected loss conditional that we have exceeded the
VaR, which is essentially a weighted average of the losses that
exceed the VaR. CVaR is preferable to the VaR because it
estimates not only the probability of a loss, but also the
magnitude of a possible loss. Furthermore, CVaR exhibits the
sub-additive property and is thus coherent. Risk measures such
as CVaR are increasingly being incorporated into risk
management systems as an additional tool that may be viewed in
conjunction with a VaR statement, to give not only the
probability of a tail loss, but also some indication of the
potential losses that may arise from a tail event (see figure
1). We can use CVaR as an alternative objective function to VaR
where the hedger tries to minimise the CVaR associated with the
hedging strategy.

Hedging effectiveness

Having examined these three different risk measures that a
hedging strategy may attempt to reduce, we now consider the
effectiveness of various hedging strategies in terms of their
ability to reduce these risk measures, and to examine whether
there are differences between different hedging strategies in
terms of hedging effectiveness. We illustrate our results for
the Nymex8 crude oil futures contract that is much in demand at
present given uncertain energy prices.

Hedging strategies

We examine hedging effectiveness for three separate strategies.
First, investors may of course choose not to hedge their
exposures, that we call a No hedge strategy. Second, in the
event that hedging is considered, the simplest hedge strategy
using futures is a Naïve hedge. This strategy uses a hedge
ratio9 of 1:1 where each unit of the crude oil contract is
hedged with equivalent units in an opposite position in a
futures contract. Third, model based hedges such as moving
window Ordinary Least Squares or GARCH models have become
popular as a means of running a dynamic hedging strategy. These
strategies involve continually monitoring the hedge over time
and changing the hedge to reflect changes that may occur in the
relationship between the spot asset being hedged and the
underlying hedging instrument.

We now turn to some examples to investigate whether hedging is
as effective at reducing VaR and CVaR as it is in reducing a
more general risk measure such as the standard deviation. We
examine the three risk measures outlined to determine both the
possible losses and the hedging effectiveness based on a No
hedge, a Naïve hedge and a dynamic daily hedging
strategy10 (model hedge) as applied to crude oil exposures. The
hedging instrument used is the corresponding futures contract
and hedging effectiveness is measured not just by the standard
deviation, but also by VaR and CVaR. We also examined11 hedging
effectiveness for both symmetric and asymmetric distributions
to demonstrate how different distributional characteristics
that are found in real world hedging situations would affect
the various risk measures. Figure 2 presents estimated daily
losses as measured by the Standard Deviation, VaR and CVaR
metrics respectively.

A number of interesting points arise. Firstly, we can see that
both the VaR and CVaR risk measures are useful in that they can
distinguish performance for short hedgers from those of long
hedgers. Using these risk measures we can see that there are
significant differences in terms of the potential losses
associated with the separate tails of the distribution. For
example, the one-day CVaR figures (symmetric distribution)
using a Naïve Hedge are $37,330 for short hedgers as
compared with $29,780 for long hedgers. Secondly, we can see
that potential tail losses are quite different for symmetric as
compared with asymmetric distributions. For example, while the
estimated losses are similar for opposite tails of the
symmetric distribution, there are large differences between
left and right tails in the case of the asymmetric
distribution. This means that the estimated losses of short and
long hedgers differ significantly, and differences would become
more pronounced for the (more) skewed distributions. This
implies that hedgers who fail to use tail specific hedging
performance metrics may chose inefficient hedging strategies
that result in them being mishedged vis a vis their hedging
objectives.

Figure 3 demonstrates the benefits of hedging as compared with
leaving crude oil exposures unhedged. The percentage reductions
in the relevant risk measure are calculated using the figures
presented in figure 2. For example, a Naïve Hedge strategy
reduces the VaR for a short hedger under the symmetric
distribution by 42% (i.e. from a one-day VaR of $51,150 for No
Hedge to $29,660 for a Naïve Hedge). The model based hedge
is even better with a 46% reduction in the one-day VaR. Also
from figure 3, we can see that both the Naïve and Model
based hedges outperform a No Hedge position in all cases bar
one. This demonstrates the value of hedging as a method of
reducing risk across each of the different risk metrics
employed.

A second point relates to the hedging performance for symmetric
as compared with the asymmetric distributions. We can see that
hedging performance is significantly better for the symmetric
distribution with reductions in standard deviation of around
60% and VaR and CVaR reductions of the order of 40-50%. For the
asymmetric distribution however, the story changes with
significantly worse hedging effectiveness observed across each
risk measure. Using the case of short hedgers for example, the
Model Based Hedge will only reduce the VaR by 21% and the CVaR
by 10%. This may indicate that hedging may not be as effective
during periods of high volatility associated with asymmetric
return distributions. Thus hedgers may face the risk that their
hedges may not be as effective during periods when they most
require them. Again demonstrated are the different hedging
outcomes for short as compared with long hedgers. In this
example, the long hedgers benefit more than short hedgers as
measured by larger reductions in both VaR and CVaR. This
demonstrates the ability of the VaR and CVaR metrics to model
tail events and to differentiate between the tails of the
distribution whereas the standard deviation is limited in this
respect.

Conclusion

This article has put forward some justifications for the use of
a number of risk measures as part of an overall risk management
strategy. We have highlighted that traditional measures based
on standard deviation are not capable of measuring risk in the
same way as tail specific ones, as they cannot distinguish
between left and right tail probabilities as required by short
and long hedgers. While the VaR is tail specific, we have also
noted some potential shortcomings of the measure and put
forward an alternative measure - the CVaR which addresses some
weaknesses of VaR. The message for investors is that a number
of risk measures should be considered when designing a hedging
strategy, but more importantly, they need to decide which risk
measure they are seeking to minimise, as hedging effectiveness
may vary, depending on the risk measure used. Also, hedges may
not be as

effective at reducing risk in volatile markets that are skewed.
In hedging terms, this means that investors may face the risk
that their hedges will not fulfill their function of risk
reduction during stressful markets conditions when they are
most needed. q

References

Cotter, J & Hanly, J (2006a). Re-examining Hedging
Performance. Journal of Futures Markets.

Cotter, J & Hanly, J (2006b). Hedging Effectiveness under
Conditions of Asymmetry. Working Paper. UCD.

Ederington, L (1979). 'The Hedging Performance of the New
Futures Markets'. Journal of Finance.

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