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Risk Management Analytics

Risk
Measures
All
of the analytics within the Asset and Manager modules give users the
option of choosing one of three statistical risk measures: standard
deviation, downside risk, and target shortfall. The most commonly
used risk measure, standard deviation, reflects the degree to which
an individual value in a probability distribution tends to vary from
the mean of the distribution. Standard deviation can be thought of as
the average dispersion from the mean within an observed sample or
population. Since most capital market return series are approximately
normal or lognormally distributed over long time periods, standard
deviation provides a fairly good and understandable description of
return volatility over time.
The
graph below plots the return and standard deviation (risk level) of
several indexes over the ten-year period ended April 30, 2004.
Downside risk or
semivariance is a statistical measure, which considers only those
deviations that fall below the mean, and is important to investors
who are concerned only about returns that are below the average.
Intuitively, downside risk is a reasonable measure and some portfolio
theories have been developed using it. However, when return series
are normally distributed downside risk is proportional to variance.
In these cases, the downside risk measure provides no greater insight
as to the relative riskiness of different assets or portfolios than
does the more easily understood standard deviation measure.
The graph below, shows
the same indexes but uses semivariance as the risk measure. As can be
seen the relative relationships between the market indexes is similar using
both risk measures.

Target Shortfall
is a statistical risk measure calculated in a similar fashion to
downside risk. Whereas downside risk takes into account only those
observations that fall below the mean, the target shortfall risk
measure is concerned only with those observations which fall below
a user defined and specified return.
Excess
Risk Measures
Compass allows
users to analyze another form of risk known as relative or excess
risk. Excess risk is defined as the volatility of excess return which
is defined as the difference between the portfolio return and the
return of some pre-specified standard such as a market index or peer
group. Common measures of excess risk are Tracking Error and Residual
Risk. Tracking Error is defined as variability of the total difference in returns
between an index and a manager's portfolio and it reflects all risks
associated with an active investment strategy. Residual Risk is a
narrower concept and generally refers to that portion of tracking
error that is not correlated with the index.
Tracking Error
can be calculated using a number of different analytics in Compass.
The Manager Consistency graph shown below plots Excess Return and
Excess Risk (Tracking Error) for several large value equity managers
vs. the Wilshire Large Cap Value Index.

Tracking Error
gives investors insights into the level of active management risk
being assumed by the investment manager. In the graph above, products
with lower
excess risk would be expected to track their
benchmark more closely. In contrast, the other products would not
be expected to track the index as closely given their higher Tracking Error.
Residual Risk
can be calculated in Compass using either the single factor CAPM
model or the multiple factor attribution model. The CAPM model uses a market
index as the sole factor while the multiple factor attribution model uses
several different style factors to calculate residual risk.
Portfolio
Risk Measures
Total fund risk
can be analyzed in Compass using two analytical tools, Portfolio
Simulation and Value at Risk (VAR). The Portfolio Simulation tool
allows users to calculate the distribution of returns of one or more
multi-asset portfolios over a user-defined time interval. The
distribution of portfolio returns and the accompanying percentile
values gives users insights into the potential volatility or
riskiness of different asset mixes based on user-specified capital
market assumptions. The Portfolio Simulation output can also be used
to calculate the probabilities of attaining required return levels.
The Portfolio
Simulation graph below illustrates the distribution of returns for
three different portfolio asset mixes over a ten-year time horizon.
The degree of dispersion around the mean indicates the expected
volatility or riskiness of a given asset mix. In the example below,
Portfolio C has a wider dispersion of returns around its mean than
does Portfolio A or B and, therefore, it would be viewed as riskier.
Investors must then decide whether the greater "upside"
offered by Portfolio C is adequate compensation for this greater risk.

The VAR model
uses manager-specific inputs to calculate a popular risk measure
known as Value at Risk. Banks and other financial institutions
developed VAR models as a means to better measure, understand and
control financial market risks over short time horizons. Value at
risk is defined as the maximum dollar amount a portfolio is expected
to lose over a specified time interval, under normal market
conditions, with a certain level of confidence. VAR can be calculated
on an absolute basis (i.e. absolute loss vs. initial starting value)
or on a relative basis (relative to an expected return, a liability
stream, or any other custom benchmark).
VAR analysis is
a good short-term risk management tool and when used in conjunction
with broader evaluation methods is an excellent method for evaluating
the impact short-term risk management decisions have on the potential
long-term value of the fund. However, because VAR analysis focuses
exclusively on the "lower tail" of portfolio outcomes, it
may needlessly discourage investors from accepting systematic market
risks that ultimately reward investors with longer investment horizons.
In the graph
below, we calculate the absolute and relative VARs for a $1,000,000
portfolio over several time periods with 95% confidence. Notice that
the maximum expected loss or absolute VAR relative to today's
$1,000,000 billion starting value is $65.7M over three months and
$91.9M over twelve months.

The VAR Analysis
model in Compass can also be used to calculate VARs for different
portfolio mixes over a single time period. In the graph below, we
compute VARs for four different asset mixes over a twelve-month time
interval. Based on the analysis, Portfolio 4 has the lowest VAR of
$57.2M and Portfolio 1 has the highest VAR of $91.9 over a
twelve-month period, assuming 95% confidence.

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