Risk Summary Portfolio Statistics

Risk

The Risk row gives the predicted risk for the value date on an annualized basis. For the Fund and Benchmark columns, this is understood as the annualized standard deviation of the distribution of returns for the Value Date. The Risk row gives the total calculated risk associated with certain choices of security-level weights assuming the data in the risk model. For the Fund and Benchmark columns, it gives the risks associated with their respective choice of open weights. For the Active column it is the risk associated with the active security-level weights or the differences between the Fund weights and Benchmark weights.

The precise computations are described in the Risk Decomposition section. The Active column risk is equal to the tracking error, and is found in the Risk Decomposition section of the Portfolio Summary sheet. The Fund and Benchmark columns are calculated identically except that one uses the fund and benchmark weights, respectively, as the input into the calculations.

Beta

Beta is a measurement of the volatility of a fund compared to the volatility of the market. A beta greater than one means a fund is more volatile with respect to the market, and a beta less than one means a fund is less volatile with respect to the market. The market has a beta of one.

We denote beta by β.

The portfolio-level beta is calculated by taking the weighted average of the security-level betas. It is calculated as follows.

Here, we are denoting portfolio-level beta by β.

Exposure

The Exposure row breaks down the long and short weights of noncash instruments separately. Note that this row does not appear when Auto/Long Short Report Mode is not selected.

where w_Cash is the weight of cash in the fund. For the Long Fund Column, we have the following formula.

where w⁺_Cash is the weight of cash if it is positive and zero otherwise. Similarly, for the Short Fund column we consider only negative weights.

where w^-_Cash is the weight of cash if it is negative and zero otherwise.

Leverage

Another statistic that appears in the long/short report is leverage. The leverage is simply the sum of the absolute values of the noncash weights:

Market Value (x Cash)

This gives the total market value of the Fund at the beginning of the period, excluding cash. It is calculated by summing the security-level market values and subtracting the market value of cash.

VaR (Value at Risk)

VaR stands for Value at Risk, and gives the estimated maximum value loss of the portfolio over a time period chosen by the user at a user-chosen confidence level. For example, if the report is run for a one-month period, VaR will give the estimated maximum loss for that month (up to the given confidence level). Note that since all risk numbers are annualized, in the below calculation for VaR, we must “scale” risk to the appropriate time period.

The default confidence level is 95%, which has a corresponding normal-based critical value of 1.645. That is, there is a 95% probability that a standard normal random variable is less than 1.645. VaR is calculated as follows.

Cash Weight

The Cash Weight is simply the percentage of the portfolio comprised of cash at the beginning of the period:

Cash Value

The Cash Value is the total market value of cash held in the fund at the beginning of the period. The value is converted to the reporting currency if necessary.

Securities in Model

The final row of the Portfolio Statistics section lists the percentage of securities whose risk exposures were available in the risk model. In this example, 87 of the 88 Fund holdings, or 98.86%, had risk exposures listed in the data. Similarly, 483 of the 489 benchmark holdings, or 98.77%, had their risk exposures listed in the data. Securities whose exposures are not in the data have are not used in risk calculations. The list of exactly which securities do not appear in the model can be found on the Fund Holdings - Exceptions and Benchmark Holdings - Exceptions sheets.