PortfolioMetrics

General

Start Date

The start date of historical data available for all assets, used for backtesting.

End Date

The end date of historical data available for all assets, used for backtesting.

Risk-free Rate

The risk-free rate is the theoretical rate of return of an investment with zero risk. It represents the interest an investor would expect from an absolutely risk-free investment.

Link: Investopedia

Performance Metrics

Cumulative Return

The cumulative return on an investment is the aggregate amount that the investment has gained or lost over time, independent of the amount of time involved.

The cumulative return can be expressed as a simple return using arithmetic average or as a compounded return using geometric average. We measure the cumulative return with the compounding effect, assuming the profits are reinvested. Different from CAGR, this value is not annualized.

Formula:

where is the return for period .

where the End Value is expressed using compounded return.

Link: Investopedia

CAGR

The compound annual growth rate (CAGR) is the rate of return that would be required for an investment to grow from its beginning balance to its ending balance, assuming the profits were reinvested at the end of each period of the investment’s life span. Different from the cumulative compounded return, this value is expressed in annual terms.

Formula:

where is the number of years.

Link: Investopedia

Annual Return

The annual return averages the end-of-year returns for an investment over a series of years. The return can be expressed as a simple return using arithmetic average or as a compounded return using geometric average. We measure the return with the compounding effect, assuming the profits are reinvested.

Monthly Return

The monthly return averages the end-of-month returns for an investment over a series of months. The return can be expressed as a simple return using arithmetic average or as a compounded return using geometric average. We measure the return with the compounding effect, assuming the profits are reinvested.

Daily Return

The daily return averages the daily returns for an investment. The return can be expressed as a simple return using arithmetic average or as a compounded return using geometric average. We measure the return with the compounding effect, assuming the profits are reinvested.

Sharpe Ratio

The Sharpe ratio measures risk-adjusted performance of an investment by comparing the excess returns with the total standard deviation of the portfolio returns. The excess returns are returns above the risk-free rate of return. The Sharpe ratio above 1 is considered good.

Formula:

where is the portfolio return, is the risk-free rate, and is the standard deviation of the portfolio return.

Link: Investopedia

Sortino Ratio

The Sortino ratio is a variation of the Sharpe ratio that compares the excess returns with the standard deviation of negative portfolio returns, instead of the total standard deviation of the portfolio returns.

Formula:

where is the portfolio return, is the risk-free rate, and is the standard deviation of negative portfolio returns.

Link: Investopedia

Omega Ratio

The Omega ratio compares investment's gains relative to its losses. It is a variation of the Sharpe ratio that additionally considers the third and fourth momentum effect, i.e., skewness and kurtosis.

Formula:

where is the probability of positive returns and is the probability of negative returns.

Calmar Ratio

The Calmar ratio compares the CAGR of the portfolio with its maximum drawdown.

Formula:

where CAGR is the compound annual growth rate, and Max Drawdown is the maximum loss from a peak to a trough in the portfolio value.

Link: Investopedia

Best Day

The highest single-day return achieved by the portfolio during the analyzed period.

Worst Day

The lowest single-day return experienced by the portfolio during the analyzed period.

Best Month

The highest monthly return achieved by the portfolio during the analyzed period.

Worst Month

The lowest monthly return experienced by the portfolio during the analyzed period.

Best Year

The highest annual return achieved by the portfolio during the analyzed period.

Worst Year

The lowest annual return experienced by the portfolio during the analyzed period.

MTD Return

The month-to-date return represents the cumulative return of an investment from the beginning of the current month up to the present date, capturing returns for the ongoing month.

Formula:

where is the return for day of the current month.

3M Return

The three months return represents the cumulative return of an investment over the past three months, measuring the percentage change in value during this quarterly period.

Formula:

where is the return for month .

6M Return

The six months return represents the cumulative return of an investment over the past six months, measuring the percentage change in value during this semi-annual period.

Formula:

where is the return for month .

YTD Return

The year-to-date return represents the cumulative return of an investment from the beginning of the current calendar year up to the present date, capturing returns for the ongoing year.

Formula:

where is the return for day of the current year.

1Y Return

The one year return represents the cumulative return of an investment over the past twelve months, measuring the percentage change in value during this annual period.

Formula:

where is the return for month .

3Y Return (ann.)

The three years annualized return represents the compound annual growth rate (CAGR) of an investment over the past three years.

Formula:

5Y Return (ann.)

The five years annualized return represents the compound annual growth rate (CAGR) of an investment over the past five years.

Formula:

10Y Return (ann.)

The ten years annualized return represents the compound annual growth rate (CAGR) of an investment over the past ten years.

Formula:

Risk Metrics

Annualized Volatility

The annualized volatility is the standard deviation of the portfolio price on an annualized basis.

Formula:

where is the standard deviation of returns, and is the number of periods per year (e.g., 252 for daily returns).

Max Drawdown

The maximum drawdown (MDD) is the maximum observed loss from a peak to a trough of a portfolio, before a new peak is attained.

Formula:

where the Peak Value is the highest portfolio value, and the Trough Value is the lowest portfolio value during a drawdown period.

Link: Investopedia

Longest Drawdown

The longest drawdown, also known as the maximum drawdown duration, is the longest time it has taken for a portfolio to recover losses.

Link: Investopedia

Value at Risk

The Value at Risk (VaR) quantifies the maximum potential loss of a portfolio at a specified confidence level. This VaR value is computed using the Variance-Covariance method at 95% confidence level. Other possible methods are historical method and the Monte Carlo method.

Formula:

where is the expected portfolio return, is the portfolio standard deviation, and is the z-score corresponding to the desired confidence level.

Link: Investopedia

CVaR

The Conditional Value at Risk (CVaR), also known as the expected shortfall, measures the risk for the worst-case scenario of a portfolio. CVaR is derived by taking a weighted average of the “extreme” losses in the tail of the distribution of possible returns, beyond the Value at Risk (VaR) cutoff point.

Link: Investopedia

Risk of Ruin

The probability that an investment strategy or trading system will result in a complete loss of capital.

Link: Investopedia

Kelly Criterion

A formula used to determine the optimal size of a series of bets or investments to maximize long-term growth rate.

Link: Investopedia

Recovery Factor

The recovery factor measures how fast the strategy recovers from drawdowns.

Ulcer Index

The Ulcer Index (UI) measures both the depth and duration of drawdowns, providing a measure of risk that considers both the magnitude and duration of losses.

Link: Investopedia

Serenity Ratio

The Serenity ratio (SR) is a variation of the Sharpe ratio that compares the excess returns with the risk measure based on Conditional Value at Risk and the Ulcer Index, instead of the total standard deviation of the portfolio returns.

Benchmark Comparison Metrics

Alpha

Alpha represents the excess return of the portfolio beyond what would be expected based on its beta and the benchmark (market) return.

Formula:

where is the portfolio actual return, is the benchmark (market) return, and is the portfolio beta.

Link: Investopedia

Beta

Beta compares the volatility of the portfolio with the volatility of the benchmark (market). A beta of 1 implies the portfolio moves in line with the market, while a beta greater than 1 indicates higher volatility, and a beta less than 1 indicates lower volatility compared to the market.

Formula:

where is the portfolio return and is the benchmark (market) return.

Link: Investopedia

Correlation

Correlation measures how a portfolio's returns align with a benchmark, ranging from -1 to +1. High positive correlation (values closer to +1) means the investment closely follows the benchmark, while negative correlation (values closer to -1) suggests the investment tends to move in the opposite direction of the benchmark.

Information Ratio

The Information Ratio (IR) is a variation of Sharpe ratio that uses benchmark returns instead of the risk-free rate.

Formula:

where is the portfolio return, is the benchmark return, and is the standard deviation of the tracking error.

Link: Investopedia

Treynor Ratio

The Treynor ratio compares the excess returns with the investment's beta, representing systematic risk.

Formula:

where is the portfolio return, is the risk-free rate, and is the beta of the portfolio.

Link: Investopedia