*Rev. Date August 18, 2023*

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. Beta to benchmark is the single OLS beta calculated by regressing the investment returns to the benchmark returns over the full analysis period. For daily returns, beta is calculated using the rolling 5-day average returns for both the investment/portfolio and benchmark to minimize the impact of market asynchronicity.

**Pairwise Correlations**

**Benchmark Correlation**shows the correlation between the investment or portfolio returns and the specified benchmark returns over the analysis period.

**Portfolio Correlations**show the pairwise correlation of investments in the portfolio.

**Downside Correlation**is the correlation between the investment or portfolio and benchmark when both returns are negative.**Relative Correlation**is the correlation between the investments’ excess returns relative to a common benchmark.**Residual Correlation**is the correlation between the investments’ residual returns.

For daily returns, all pairwise correlation metrics listed in this section are calculated using the rolling 5-day average returns for both the investment/portfolio and benchmark to minimize the impact of market asynchronicity.

**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. Kurtosis is measured relative to the kurtosis of a normal distribution, which is 3. Thus, Venn is showing the “excess” kurtosis or kurtosis over 3.

**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 (single period)

[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**.*