*Rev. Date November 1, 2022*

Historical Risk Statistics is an analysis block that can be added to any custom analysis template, and is also present when running comparisons on multiple investments and/or portfolios. It includes the following standard risk measures that can be used to better understand the behavior of an investment or portfolio:

**Beta to Benchmark**: The investment’s or portfolio’s sensitivity to its benchmark. Note: this metric is only available if a benchmark is selected.

**Downside Capture**: The ratio of the average returns of the investment to the average returns of the benchmark when benchmark returns were negative.

**Upside Capture**: The ratio of the average returns of the investment to the average returns of the benchmark when benchmark returns were non-negative.

**Average Down Month:** It is calculated by taking the average return of all the negative monthly return data points.

**Average Up Month: **It is calculated by taking the average return of all the positive monthly return data points.

**Downside / Upside Volatility: **Downside volatility is computed as the square root of downside semi-variance of the returns, which is the sum of the squares of the negative values of returns divided by their count. Upside volatility is computed as the square root of upside semi-variance of the returns, which is the sum of the squares of the positive values of returns divided by their count.

Where R is the historical return distribution. (In the actual implementation we assume that E[R] = 0).

Where E is the expected average, which we assume to be zero.**Batting Average: **If Relative to Benchmark is toggled off, it is the ratio of total periods that an investment posts non-negative returns. If Relative to Benchmark is toggled on, it is the ratio of total periods that an investment beats or matches its index.

**CVaR (5%): **Conditional VaR is the weighted average measure compared to the “point estimation” of VaR, which could more accurately measure the tail risk. Conditional Value at Risk (CVaR) is derived by taking the expectation of the “extreme” losses in the tail of the distribution of possible returns, beyond the VaR cutoff point.

**VaR (95%)**: The “Value at Risk” of the investment or portfolio is the estimated maximum amount the investment or portfolio might lose over a one month period based on historical returns at a 95% confidence level.

**VaR (97.5%):** The “Value at Risk” of the investment or portfolio is the estimated maximum amount the investment or portfolio might lose over a one month period based on historical returns at a 97.5% confidence level.

**VaR (99%): **The “Value at Risk” of the investment or portfolio is the estimated maximum amount the investment or portfolio might lose over a one month period based on historical returns at a 99% confidence level.

**Skewness**: The degree of asymmetry in the distribution of returns for an investment or portfolio. For example, if the distribution had more values in the right side of the distribution (compared to a normal distribution), the investment or portfolio will have a negative skewness.

**Kurtosis**: The degree of extreme values in the distribution of returns for an investment or portfolio. For example, if the distribution had more values in the tails of the distribution (relative to a normal distribution), it will have a positive kurtosis.

**Sortino Ratio**: A risk-adjusted performance measure calculated by dividing the excess arithmetic annualized return for the investment or portfolio (relative to the risk-free rate) by its annualized downside volatility, or volatility when excess returns were negative.[1]

**Calmar Ratio**: A risk-adjusted performance measure calculated by dividing the geometric annualized return for the investment or portfolio by its absolute value of the maximum drawdown over the most recent 3 year period.

**Autocorrelation**: Autocorrelation represents the degree of correlation between two successive time intervals. It is a measure of how the lagged version of a value along a time-series relates to its previous value.

where:

series = the time series from which we are calculating correlation

lag = the lagged interval

**Downside Correlation: **Downside correlation represents the correlation between the given return stream and the benchmark for all periods where both returns are negative.

[1] The risk-free rate is the average 3 month sovereign benchmark yield in the user’s base currency area.

*This document highlights certain aspects of this feature. As an overview, it does not discuss all material facts or assumptions. Please see **Important Disclosure and Disclaimer Information**.*