Risk Management Analytics

Portfolio Risk Measures

Investment portfolios contain multiple sources of risk. Some risks, like "systematic" or market risks are taken intentionally with the expectation of a return premium.  Additional risk may be introduced into a portfolio as a result of a portfolios actual asset allocation differing from the stated Policy target weights.  This allocation mismatch may increase or decrease a plan's total risk, but it will always increase a funds tracking error vs. its stated Policy Benchmark.  Additional risks within a portfolio may be attributable to what is commonly referred to as Benchmark Mismatch. This risk results from the weighted average of the manager benchmarks within an asset class differing (sometimes substantially) from the overall asset class benchmark.  The other remaining source of risk inherent in many institutional portfolios is active management risk. Active management risk is taken based on the belief that it will offer a return premium, or Alpha, relative to a passive investment alternative.

The Wilshire Compass provides Risk Management Summary Reports that allow fund sponsors to measure and better understand all of these risks which are inherent in large institutional portfolios.  Shown below are samples of these reports along with a brief explanation of the risks being depicted.

The below graphically illustrates a Sample Funds' strategic asset allocation investment policy target weights and how those allocations contribute to the Fund's systematic or market risk.  Interestingly in the example below, while public equity investments represent 60% of the portfolio by weight, they contribute over 95% of the Fund's total systematic risk!

The top of the next page shows similar information but this time it is based upon the funds "actual" asset allocation as of a point in time.  In addition the lower section of this page provides insight into all of the Fund's sources of Total Risk and Tracking Error.

The third page of the report shows what the actual allocation mismatches are, i.e. overweight non-US equity 5.0% and underweight fixed income by 6.0% and the impact on both Total Risk and Tracking Error.

The fourth page of the report provides a granular view of Benchmark Mismatch at both Total Risk, and Tracking Error level.  Notice how the totals of each of these graphs 1.68% and 1.82% ties back to the Page 2, Benchmark Mismatch for Total Risk and Tracking Error respectively.

The final page of the report provides details regarding where the most active management risk is being taken.

Additional 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 December 31, 2009.

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 Small-Cap Value equity managers vs. the Wilshire Small 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.

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