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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