Strategy Stats [presentTrading]Hello! it's another weekend. This tool is a strategy performance analysis tool. Looking at the TradingView community, it seems few creators focus on this aspect. I've intentionally created a shared version. Welcome to share your idea or question on this.
█ Introduction and How it is Different
Strategy Stats is a comprehensive performance analytics framework designed specifically for trading strategies. Unlike standard strategy backtesting tools that simply show cumulative profits, this analytics suite provides real-time, multi-timeframe statistical analysis of your trading performance.
Multi-timeframe analysis: Automatically tracks performance metrics across the most recent time periods (last 7 days, 30 days, 90 days, 1 year, and 4 years)
Advanced statistical measures: Goes beyond basic metrics to include Information Coefficient (IC) and Sortino Ratio
Real-time feedback: Updates performance statistics with each new trade
Visual analytics: Color-coded performance table provides instant visual feedback on strategy health
Integrated risk management: Implements sophisticated take profit mechanisms with 3-step ATR and percentage-based exits
BTCUSD Performance
The table in the upper right corner is a comprehensive performance dashboard showing trading strategy statistics.
Note: While this presentation uses Vegas SuperTrend as the underlying strategy, this is merely an example. The Stats framework can be applied to any trading strategy. The Vegas SuperTrend implementation is included solely to demonstrate how the analytics module integrates with a trading strategy.
⚠️ Timeframe Limitations
Important: TradingView's backtesting engine has a maximum storage limit of 10,000 bars. When using this strategy stats framework on smaller timeframes such as 1-hour or 2-hour charts, you may encounter errors if your backtesting period is too long.
Recommended Timeframe Usage:
Ideal for: 4H, 6H, 8H, Daily charts and above
May cause errors on: 1H, 2H charts spanning multiple years
Not recommended for: Timeframes below 1H with long history
█ Strategy, How it Works: Detailed Explanation
The Strategy Stats framework consists of three primary components: statistical data collection, performance analysis, and visualization.
🔶 Statistical Data Collection
The system maintains several critical data arrays:
equityHistory: Tracks equity curve over time
tradeHistory: Records profit/loss of each trade
predictionSignals: Stores trade direction signals (1 for long, -1 for short)
actualReturns: Records corresponding actual returns from each trade
For each closed trade, the system captures:
float tradePnL = strategy.closedtrades.profit(tradeIndex)
float tradeReturn = strategy.closedtrades.profit_percent(tradeIndex)
int tradeType = entryPrice < exitPrice ? 1 : -1 // Direction
🔶 Performance Metrics Calculation
The framework calculates several key performance metrics:
Information Coefficient (IC):
The correlation between prediction signals and actual returns, measuring forecast skill.
IC = Correlation(predictionSignals, actualReturns)
Where Correlation is the Pearson correlation coefficient:
Correlation(X,Y) = (nΣXY - ΣXY) / √
Sortino Ratio:
Measures risk-adjusted return focusing only on downside risk:
Sortino = (Avg_Return - Risk_Free_Rate) / Downside_Deviation
Where Downside Deviation is:
Downside_Deviation = √
R_i represents individual returns, T is the target return (typically the risk-free rate), and n is the number of observations.
Maximum Drawdown:
Tracks the largest percentage drop from peak to trough:
DD = (Peak_Equity - Trough_Equity) / Peak_Equity * 100
🔶 Time Period Calculation
The system automatically determines the appropriate number of bars to analyze for each timeframe based on the current chart timeframe:
bars_7d = math.max(1, math.round(7 * barsPerDay))
bars_30d = math.max(1, math.round(30 * barsPerDay))
bars_90d = math.max(1, math.round(90 * barsPerDay))
bars_365d = math.max(1, math.round(365 * barsPerDay))
bars_4y = math.max(1, math.round(365 * 4 * barsPerDay))
Where barsPerDay is calculated based on the chart timeframe:
barsPerDay = timeframe.isintraday ?
24 * 60 / math.max(1, (timeframe.in_seconds() / 60)) :
timeframe.isdaily ? 1 :
timeframe.isweekly ? 1/7 :
timeframe.ismonthly ? 1/30 : 0.01
🔶 Visual Representation
The system presents performance data in a color-coded table with intuitive visual indicators:
Green: Excellent performance
Lime: Good performance
Gray: Neutral performance
Orange: Mediocre performance
Red: Poor performance
█ Trade Direction
The Strategy Stats framework supports three trading directions:
Long Only: Only takes long positions when entry conditions are met
Short Only: Only takes short positions when entry conditions are met
Both: Takes both long and short positions depending on market conditions
█ Usage
To effectively use the Strategy Stats framework:
Apply to existing strategies: Add the performance tracking code to any strategy to gain advanced analytics
Monitor multiple timeframes: Use the multi-timeframe analysis to identify performance trends
Evaluate strategy health: Review IC and Sortino ratios to assess predictive power and risk-adjusted returns
Optimize parameters: Use performance data to refine strategy parameters
Compare strategies: Apply the framework to multiple strategies to identify the most effective approach
For best results, allow the strategy to generate sufficient trade history for meaningful statistical analysis (at least 20-30 trades).
█ Default Settings
The default settings have been carefully calibrated for cryptocurrency markets:
Performance Tracking:
Time periods: 7D, 30D, 90D, 1Y, 4Y
Statistical measures: Return, Win%, MaxDD, IC, Sortino Ratio
IC color thresholds: >0.3 (green), >0.1 (lime), <-0.1 (orange), <-0.3 (red)
Sortino color thresholds: >1.0 (green), >0.5 (lime), <0 (red)
Multi-Step Take Profit:
ATR multipliers: 2.618, 5.0, 10.0
Percentage levels: 3%, 8%, 17%
Short multiplier: 1.5x (makes short take profits more aggressive)
Stop loss: 20%
Sortino
Sharpe and Sortino Ratios with Date RangeThis indicator calculates the Sharpe and Sortino ratios using a chart symbol's periodic price returns.
I added the ability to calculate SORTINO and Sharpe based on CUSTOM DATES within the option menu.
It builds on the script here: by adding this feature.
A little about the Sortino Ratio.
www.nasdaq.com
I want equity market returns, but I don’t want equity market volatility. This is the sentiment many investors naturally feel. This sentiment often grows stronger as one approaches or is in the phase where they desire distributions from their savings to improve lifestyle. This is why there is a need for active management in the investment arena. The desire to control downside volatility, but also participate in the upside growth is a very fundamental human desire. The Sortino Ratio measures how well a particular investment meets this fundamental human desire.
There is the old adage, “volatility is the price you pay for returns.” However, what if we could measure the historical performance of an investment and see if it has given above average returns compared to the downside volatility. This is a simple division problem. It will tell us if the volatility “price we are paying for returns” is good. We can then compare that to other investments to see how they compare.
Let us take the return and subtract the risk-free interest rate and then simply divide that by the downside movement from the average. A basic division problem yielding a number that measures a very basic human desire: How well did this investment do compared to the downside risk it experienced.
In the world of financial analysis and investment management, ratios are abundant. There are many ratios that are truly important to a particular analysis. However, the sheer abundance of ratios that are available often overwhelms the casual investor, leading them to disregard ratios altogether. I would argue for those investors that desire a way to rank an investment by its ability to satisfy this very fundamental human desire, the Sortino Ratio is the number they need to consider.
Disappointing in the marketplace for research, the Sortino Ratio is not featured prominently. It is much easier to find the inflows a particular ETF has experienced than the Sortino Ratio. Inflows are important. They measure how much people are investing into an ETF. However, they are mostly only important to the fund manager, not the investor. What investors care about is the Risk-Adjusted Return. This is the Sortino Ratio.
Dynamic Risk-Adjusted Performance Ratios with TableWith this indicator, you have everything you need to monitor and compare the Sharpe ratio, Sortino ratio, and Omega ratio across multiple assets—all in one place. This tool is designed to help save time and improve efficiency by letting you track up to 15 assets simultaneously in a fully customizable table. You can adjust the lookback period to fit your trading strategy and get a clearer picture of how your assets perform over time. Instead of switching between charts, this indicator puts all the critical information you need at your fingertips.
Sharpe Ratio -
Helps evaluate the overall efficiency of investments by comparing the average return to the total risk (measured by the standard deviation of all returns). Essentially, it tells you how much excess return you’re getting for each unit of risk you’re taking. A higher Sharpe ratio means you’re getting better risk-adjusted performance—something you’ll want to aim for in your portfolio.
Sortino Ratio -
Goes a step further by focusing only on downside risk—because let’s face it, no one worries about positive volatility. This ratio is calculated by dividing the average return by the standard deviation of only the negative returns. Perfect for those concerned about avoiding losses rather than chasing extreme gains. It gives you a sharper view of how well your assets are performing relative to the risks you’re trying to avoid.
Omega Ratio -
Offers a unique perspective by comparing the sum of positive returns to the absolute sum of negative returns. It’s a straightforward way to see if your wins outweigh your losses. A higher Omega ratio means your positive returns significantly exceed the downside, which is exactly what you want when building a strong, reliable portfolio.
This indicator is perfect for traders who want to streamline their decision-making process and gain an edge. Bringing together these three critical ratios into a single user-defined table makes it easy to compare and rank assets at a glance. Whether optimizing a portfolio or looking for the best opportunities, this tool helps you stay ahead by focusing on risk-adjusted returns. The customizable lookback period lets you tailor the analysis to fit your unique trading approach, giving you insights that align with your goals. If you’re serious about making data-driven decisions and improving your trading outcomes, this indicator is a game-changer for your toolkit.
Risk Radar ProThe "Risk Radar Pro" indicator is a sophisticated tool designed to help investors and traders assess the risk and performance of their investments over a specified period. This presentation will explain each component of the indicator, how to interpret the results, and the advantages compared to traditional metrics.
The "Risk Radar Pro" indicator includes several key metrics:
● Beta
● Maximum Drawdown
● Compound Annual Growth Rate (CAGR)
● Annualized Volatility
● Dynamic Sharpe Ratio
● Dynamic Sortino Ratio
Each of these metrics is dynamically calculated using data from the entire selected period, providing a more adaptive and accurate measure of performance and risk.
1. Start Date
● Description: The date from which the calculations begin.
● Interpretation: This allows the user to set a specific period for analysis, ensuring that all metrics reflect the performance from this point onward.
2. Beta
● Description: Beta measures the volatility or systematic risk of the instrument relative to a reference index (e.g., SPY).
● Interpretation: A beta of 1 indicates that the instrument moves with the market. A beta greater than 1 indicates more volatility than the market, while a beta less than 1 indicates less volatility.
● Advantages: Unlike classic beta, which typically uses fixed historical intervals, this dynamic beta adjusts to market changes over the entire selected period, providing a more responsive measure.
3. Maximum Drawdown
● Description: The maximum observed loss from a peak to a trough before a new peak is achieved.
● Interpretation: This shows the largest single drop in value during the specified period. It is a critical measure of downside risk.
● Advantages: By tracking the maximum drawdown dynamically, the indicator can provide timely alerts when significant losses occur, allowing for better risk management.
4. Annualized Performance
● Description: The mean annual growth rate of the investment over the specified period.
● Interpretation: The Annualized Performance represents the smoothed annual rate at which the investment would have grown if it had grown at a steady rate.
● Advantages: This dynamic calculation reflects the actual long-term growth trend of the investment rather than relying on a fixed time frame.
5. Annualized Volatility
● Description: Measures the degree of variation in the instrument's returns over time, expressed as a percentage.
● Interpretation: Higher volatility indicates greater risk, as the investment's returns fluctuate more.
● Advantages: Annualized volatility calculated over the entire selected period provides a more accurate measure of risk, as it includes all market conditions encountered during that time.
6. Dynamic Sharpe Ratio
● Description: Measures the risk-adjusted return of an investment relative to its volatility.
● Choice of Risk-Free Rate Ticker: Users can select a ticker symbol to represent the risk-free rate in Sharpe ratio calculations. The default option is US03M, representing the 3-month US Treasury bill.
● Interpretation: A higher Sharpe ratio indicates better risk-adjusted returns. This ratio accounts for the risk-free rate to provide a comparison with risk-free investments.
● Advantages: By using returns and volatility over the entire period, the dynamic Sharpe ratio adjusts to changes in market conditions, offering a more accurate measure than traditional static calculations.
7. Dynamic Sortino Ratio
● Description: Similar to the Sharpe ratio, but focuses only on downside risk.
Interpretation: A higher Sortino ratio indicates better risk-adjusted returns, focusing solely on negative returns, which are more relevant to risk-averse investors.
● Choice of Risk-Free Rate Ticker: Similarly, users can choose a ticker symbol for the risk-free rate in Sortino ratio calculations. By default, this is also set to US03M.
● Advantages: This ratio's dynamic calculation considering the downside deviation over the entire period provides a more accurate measure of risk-adjusted returns in volatile markets.
Comparison with Basic Metrics
● Static vs. Dynamic Calculations: Traditional metrics often use fixed historical intervals, which may not reflect current market conditions. The dynamic calculations in "Risk Radar Pro" adjust to market changes, providing more relevant and timely information.
● Comprehensive Risk Assessment: By including metrics like maximum drawdown, Sharpe ratio, and Sortino ratio, the indicator provides a holistic view of both upside potential and downside risk.
● User Customization: Users can customize the start date, reference index, risk-free rate, and table position, tailoring the indicator to their specific needs and preferences.
Conclusion
The "Risk Radar Pro" indicator is a powerful tool for investors and traders looking to assess and manage risk more effectively. By providing dynamic, comprehensive metrics, it offers a significant advantage over traditional static calculations, ensuring that users have the most accurate and relevant information to make informed decisions.
The "Risk Radar Pro" indicator provides analytical tools and metrics for informational purposes only. It is not intended as financial advice. Users should conduct their own research and consider their individual risk tolerance and investment objectives before making any investment decisions based on the indicator's outputs. Trading and investing involve risks, including the risk of loss. Past performance is not indicative of future results.
Sharpe and Sortino Ratios█ OVERVIEW
This indicator calculates the Sharpe and Sortino ratios using a chart symbol's periodic price returns, offering insights into the symbol's risk-adjusted performance. It features the option to calculate these ratios by comparing the periodic returns to a fixed annual rate of return or the returns from another selected symbol's context.
█ CONCEPTS
Returns, risk, and volatility
The return on an investment is the relative gain or loss over a period, often expressed as a percentage. Investment returns can originate from several sources, including capital gains, dividends, and interest income. Many investors seek the highest returns possible in the quest for profit. However, prudent investing and trading entails evaluating such returns against the associated risks (i.e., the uncertainty of returns and the potential for financial losses) for a clearer perspective on overall performance and sustainability.
The profitability of an investment typically comes at the cost of enduring market swings, noise, and general uncertainty. To navigate these turbulent waters, investors and portfolio managers often utilize volatility , a measure of the statistical dispersion of historical returns, as a foundational element in their risk assessments because it provides a tangible way to gauge the uncertainty in returns. High volatility suggests increased uncertainty and, consequently, higher risk, whereas low volatility suggests more stable returns with minimal fluctuations, implying lower risk. These concepts are integral components in several risk-adjusted performance metrics, including the Sharpe and Sortino ratios calculated by this indicator.
Risk-free rate
The risk-free rate represents the rate of return on a hypothetical investment carrying no risk of financial loss. This theoretical rate provides a benchmark for comparing the returns on a risky investment and evaluating whether its excess returns justify the risks. If an investment's returns are at or below the theoretical risk-free rate or the risk premium is below a desired amount, it may suggest that the returns do not compensate for the extra risk, which might be a call to reassess the investment.
Since the risk-free rate is a theoretical concept, investors often utilize proxies for the rate in practice, such as Treasury bills and other government bonds. Conventionally, analysts consider such instruments "risk-free" for a domestic holder, as they are a form of government obligation with a low perceived likelihood of default.
The average yield on short-term Treasury bills, influenced by economic conditions, monetary policies, and inflation expectations, has historically hovered around 2-3% over the long term. This range also aligns with central banks' inflation targets. As such, one may interpret a value within this range as a minimum proxy for the risk-free rate, as it may correspond to the minimum rate required to maintain purchasing power over time. This indicator uses a default value of 2% as the risk-free rate in its Sharpe and Sortino ratio calculations. Users can adjust this value from the "Risk-free rate of return" input in the "Settings/Inputs" tab.
Sharpe and Sortino ratios
The Sharpe and Sortino ratios are two of the most widely used metrics that offer insight into an investment's risk-adjusted performance . They provide a standardized framework to compare the effectiveness of investments relative to their perceived risks. These metrics can help investors determine whether the returns justify the risks taken to achieve them, promoting more informed investment decisions.
Both metrics measure risk-adjusted performance similarly. However, they have some differences in their formulas and their interpretation:
1. Sharpe ratio
The Sharpe ratio , developed by Nobel laureate William F. Sharpe, measures the performance of an investment compared to a theoretically risk-free asset, adjusted for the investment risk. The ratio uses the following formula:
Sharpe Ratio = (𝑅𝑎 − 𝑅𝑓) / 𝜎𝑎
Where:
• 𝑅𝑎 = Average return of the investment
• 𝑅𝑓 = Theoretical risk-free rate of return
• 𝜎𝑎 = Standard deviation of the investment's returns (volatility)
A higher Sharpe ratio indicates a more favorable risk-adjusted return, as it signifies that the investment produced higher excess returns per unit of increase in total perceived risk.
2. Sortino ratio
The Sortino ratio is a modified form of the Sharpe ratio that only considers downside volatility , i.e., the volatility of returns below the theoretical risk-free benchmark. Although it shares close similarities with the Sharpe ratio, it can produce very different values, especially when the returns do not have a symmetrical distribution, since it does not penalize upside and downside volatility equally. The ratio uses the following formula:
Sortino Ratio = (𝑅𝑎 − 𝑅𝑓) / 𝜎𝑑
Where:
• 𝑅𝑎 = Average return of the investment
• 𝑅𝑓 = Theoretical risk-free rate of return
• 𝜎𝑑 = Downside deviation (standard deviation of negative excess returns, or downside volatility)
The Sortino ratio offers an alternative perspective on an investment's return-generating efficiency since it does not consider upside volatility in its calculation. A higher Sortino ratio signifies that the investment produced higher excess returns per unit of increase in perceived downside risk.
The risk-free rate (𝑅𝑓) in the numerator of both ratio formulas acts as a baseline for comparing an investment's performance to a theoretical risk-free alternative. By subtracting the risk-free rate from the expected return (𝑅𝑎−𝑅𝑓), the numerator essentially represents the risk premium of the investment.
Comparison with another symbol
In addition to the conventional Sharpe and Sortino ratios, which compare an instrument's returns to a risk-free rate, this indicator can also compare returns to a user-specified benchmark symbol , allowing the calculation of Information ratios .
An Information ratio is a generalized form of the Sharpe ratio that compares an investment's returns to a risky benchmark , such as SPY, rather than a risk-free rate. It measures the investment's active return (the difference between its returns and the benchmark returns) relative to its tracking error (i.e., the volatility of the active return) using the following formula:
𝐼𝑅 = (𝑅𝑝 − 𝑅𝑏) / 𝑇𝐸
Where:
• 𝑅𝑝 = Average return on the portfolio or investment
• 𝑅𝑏 = Average return from the benchmark instrument
• 𝑇𝐸 = Tracking error (volatility of 𝑅𝑝 − 𝑅𝑏)
Comparing returns to a benchmark instrument rather than a theoretical risk-free rate offers unique insights into risk-adjusted performance. Higher Information ratios signify that the investment produced higher active returns per unit of increase in risk relative to the benchmark. Conventional choices for non-risk-free benchmarks include major composite indices like the S&P 500 and DJIA, as the resulting ratios can provide insight into the effectiveness of an investment relative to the broader market.
Users can enable this generalized calculation for both the Sharpe and Sortino ratios by selecting the "Benchmark symbol returns" option from the "Benchmark type" dropdown in the "Settings/Inputs" tab.
It's crucial to note that this indicator compares the charts symbol's rate of change (return) to the rate of change in the benchmark symbol. Consequently, not all symbols available on TradingView are suitable for use with these ratios due to the nature of what their values represent. For instance, using a bond as a benchmark will produce distorted results since each bar's values represent yields rather than prices, meaning it compares the rate of change in the yield. To maintain consistency and relevance in the calculated ratios, ensure the values from the compared symbols strictly represent price information.
█ FEATURES
This indicator provides traders with two widely used metrics for assessing risk-adjusted performance, generalized to allow users to compare the chart symbol's price returns to a fixed risk-free rate or the returns from another risky symbol. Below are the key features of this indicator:
Timeframe selection
The "Returns timeframe" input determines the timeframe of the calculated price returns. Users can select any value greater than or equal to the chart's timeframe. The default timeframe is "1M".
Periodic returns tracking
This indicator compounds and collects requested price returns from the selected timeframe over monthly or daily periods, similar to how the Broker Emulator works when calculating strategy performance metrics on trade data. It employs the following logic:
• Track returns over monthly periods if the chart's data spans at least two months.
• Track returns over daily periods if the chart's data spans at least two days but not two months.
• Do not track or collect returns if the data spans less than two days, as the amount of data is insufficient for meaningful ratio calculations.
The indicator uses the returns collected from up to a specified number of periods to calculate the Sharpe and Sortino ratios, depending on the available historical data. It also uses these periodic returns to calculate the average returns it displays in the Data Window.
Users can control the maximum number of periods the indicator analyzes with the "Max no. of periods used" input in the "Settings/Inputs" tab. The default value is 60 periods.
Benchmark specification
The "Benchmark return type" input specifies the benchmark type the indicator compares to the chart symbol's returns in the ratio calculations. It features the following two options:
• "Risk-free rate of return (%)": Compares the price returns to a user-specified annual rate of return representing a theoretical risk-free rate (e.g., 2%).
• "Benchmark symbol return": Compares the price returns to a selected benchmark symbol (e.g., "AMEX:SPY) to calculate Information ratios.
When comparing a chart symbol's returns to a specified benchmark symbol, this indicator aligns the times of data points from the benchmark with the times of data points from the chart's symbol to facilitate a fair comparison between symbols with different active sessions.
Visualization and display
• The indicator displays the periodic returns requested from the specified "Returns timeframe" in a separate pane. The plot includes dynamic colors to signify positive and negative returns.
• When the "Returns timeframe" value represents a higher timeframe, the indicator displays background highlights on the main chart pane to signify when a new value is available and whether the return is positive or negative.
• When the specified benchmark return type is a benchmark symbol, the indicator displays the requested symbol's returns in the separate pane as a gray line for visual comparison.
• Within the separate pane, the indicator displays a single-cell table that shows the base period it uses for periodic returns, the number of periods it uses in the calculation, the timeframe of the requested data, and the calculated Sharpe and Sortino ratios.
• The Data Window displays the chart symbol and benchmark returns, their periodic averages, and the Sharpe and Sortino ratios.
█ FOR Pine Script™ CODERS
• This script utilizes the functions from our RiskMetrics library to determine the size of the periods, calculate and collect periodic returns, and compute the Sharpe and Sortino ratios.
• The `getAlignedPrices()` function in this script requests price data for the chart's symbol and a benchmark symbol with consistent time alignment by utilizing spread symbols , which helps facilitate a fair comparison between different symbol types. Retrieving prices from spreads avoids potential information loss and data misalignment that can otherwise occur when using separate requests from each symbol's context when those symbols have different sessions or data times.
• For consistency, the `getAlignedPrices()` function includes extended hours and dividend adjustment modifiers in its data requests. Additionally, it includes other settings inherited from the chart's context, such as "settlement-as-close" preferences for fair comparison between futures instruments.
• This script uses the `changePercent()` function from our ta library to calculate the percentage changes of the requested data.
• The newly released `force_overlay` parameter in display-related functions allows indicators to display visuals on the main chart and a separate pane simultaneously. We use the parameter in this script's bgcolor() call to display background highlights on the main chart.
Look first. Then leap.
RiskMetrics█ OVERVIEW
This library is a tool for Pine programmers that provides functions for calculating risk-adjusted performance metrics on periodic price returns. The calculations used by this library's functions closely mirror those the Broker Emulator uses to calculate strategy performance metrics (e.g., Sharpe and Sortino ratios) without depending on strategy-specific functionality.
█ CONCEPTS
Returns, risk, and volatility
The return on an investment is the relative gain or loss over a period, often expressed as a percentage. Investment returns can originate from several sources, including capital gains, dividends, and interest income. Many investors seek the highest returns possible in the quest for profit. However, prudent investing and trading entails evaluating such returns against the associated risks (i.e., the uncertainty of returns and the potential for financial losses) for a clearer perspective on overall performance and sustainability.
One way investors and analysts assess the risk of an investment is by analyzing its volatility , i.e., the statistical dispersion of historical returns. Investors often use volatility in risk estimation because it provides a quantifiable way to gauge the expected extent of fluctuation in returns. Elevated volatility implies heightened uncertainty in the market, which suggests higher expected risk. Conversely, low volatility implies relatively stable returns with relatively minimal fluctuations, thus suggesting lower expected risk. Several risk-adjusted performance metrics utilize volatility in their calculations for this reason.
Risk-free rate
The risk-free rate represents the rate of return on a hypothetical investment carrying no risk of financial loss. This theoretical rate provides a benchmark for comparing the returns on a risky investment and evaluating whether its excess returns justify the risks. If an investment's returns are at or below the theoretical risk-free rate or the risk premium is below a desired amount, it may suggest that the returns do not compensate for the extra risk, which might be a call to reassess the investment.
Since the risk-free rate is a theoretical concept, investors often utilize proxies for the rate in practice, such as Treasury bills and other government bonds. Conventionally, analysts consider such instruments "risk-free" for a domestic holder, as they are a form of government obligation with a low perceived likelihood of default.
The average yield on short-term Treasury bills, influenced by economic conditions, monetary policies, and inflation expectations, has historically hovered around 2-3% over the long term. This range also aligns with central banks' inflation targets. As such, one may interpret a value within this range as a minimum proxy for the risk-free rate, as it may correspond to the minimum rate required to maintain purchasing power over time.
The built-in Sharpe and Sortino ratios that strategies calculate and display in the Performance Summary tab use a default risk-free rate of 2%, and the metrics in this library's example code use the same default rate. Users can adjust this value to fit their analysis needs.
Risk-adjusted performance
Risk-adjusted performance metrics gauge the effectiveness of an investment by considering its returns relative to the perceived risk. They aim to provide a more well-rounded picture of performance by factoring in the level of risk taken to achieve returns. Investors can utilize such metrics to help determine whether the returns from an investment justify the risks and make informed decisions.
The two most commonly used risk-adjusted performance metrics are the Sharpe ratio and the Sortino ratio.
1. Sharpe ratio
The Sharpe ratio , developed by Nobel laureate William F. Sharpe, measures the performance of an investment compared to a theoretically risk-free asset, adjusted for the investment risk. The ratio uses the following formula:
Sharpe Ratio = (𝑅𝑎 − 𝑅𝑓) / 𝜎𝑎
Where:
• 𝑅𝑎 = Average return of the investment
• 𝑅𝑓 = Theoretical risk-free rate of return
• 𝜎𝑎 = Standard deviation of the investment's returns (volatility)
A higher Sharpe ratio indicates a more favorable risk-adjusted return, as it signifies that the investment produced higher excess returns per unit of increase in total perceived risk.
2. Sortino ratio
The Sortino ratio is a modified form of the Sharpe ratio that only considers downside volatility , i.e., the volatility of returns below the theoretical risk-free benchmark. Although it shares close similarities with the Sharpe ratio, it can produce very different values, especially when the returns do not have a symmetrical distribution, since it does not penalize upside and downside volatility equally. The ratio uses the following formula:
Sortino Ratio = (𝑅𝑎 − 𝑅𝑓) / 𝜎𝑑
Where:
• 𝑅𝑎 = Average return of the investment
• 𝑅𝑓 = Theoretical risk-free rate of return
• 𝜎𝑑 = Downside deviation (standard deviation of negative excess returns, or downside volatility)
The Sortino ratio offers an alternative perspective on an investment's return-generating efficiency since it does not consider upside volatility in its calculation. A higher Sortino ratio signifies that the investment produced higher excess returns per unit of increase in perceived downside risk.
█ CALCULATIONS
Return period detection
Calculating risk-adjusted performance metrics requires collecting returns across several periods of a given size. Analysts may use different period sizes based on the context and their preferences. However, two widely used standards are monthly or daily periods, depending on the available data and the investment's duration. The built-in ratios displayed in the Strategy Tester utilize returns from either monthly or daily periods in their calculations based on the following logic:
• Use monthly returns if the history of closed trades spans at least two months.
• Use daily returns if the trades span at least two days but less than two months.
• Do not calculate the ratios if the trade data spans fewer than two days.
This library's `detectPeriod()` function applies related logic to available chart data rather than trade data to determine which period is appropriate:
• It returns true if the chart's data spans at least two months, indicating that it's sufficient to use monthly periods.
• It returns false if the chart's data spans at least two days but not two months, suggesting the use of daily periods.
• It returns na if the length of the chart's data covers less than two days, signifying that the data is insufficient for meaningful ratio calculations.
It's important to note that programmers should only call `detectPeriod()` from a script's global scope or within the outermost scope of a function called from the global scope, as it requires the time value from the first bar to accurately measure the amount of time covered by the chart's data.
Collecting periodic returns
This library's `getPeriodicReturns()` function tracks price return data within monthly or daily periods and stores the periodic values in an array . It uses a `detectPeriod()` call as the condition to determine whether each element in the array represents the return over a monthly or daily period.
The `getPeriodicReturns()` function has two overloads. The first overload requires two arguments and outputs an array of monthly or daily returns for use in the `sharpe()` and `sortino()` methods. To calculate these returns:
1. The `percentChange` argument should be a series that represents percentage gains or losses. The values can be bar-to-bar return percentages on the chart timeframe or percentages requested from a higher timeframe.
2. The function compounds all non-na `percentChange` values within each monthly or daily period to calculate the period's total return percentage. When the `percentChange` represents returns from a higher timeframe, ensure the requested data includes gaps to avoid compounding redundant values.
3. After a period ends, the function queues the compounded return into the array , removing the oldest element from the array when its size exceeds the `maxPeriods` argument.
The resulting array represents the sequence of closed returns over up to `maxPeriods` months or days, depending on the available data.
The second overload of the function includes an additional `benchmark` parameter. Unlike the first overload, this version tracks and collects differences between the `percentChange` and the specified `benchmark` values. The resulting array represents the sequence of excess returns over up to `maxPeriods` months or days. Passing this array to the `sharpe()` and `sortino()` methods calculates generalized Information ratios , which represent the risk-adjustment performance of a sequence of returns compared to a risky benchmark instead of a risk-free rate. For consistency, ensure the non-na times of the `benchmark` values align with the times of the `percentChange` values.
Ratio methods
This library's `sharpe()` and `sortino()` methods respectively calculate the Sharpe and Sortino ratios based on an array of returns compared to a specified annual benchmark. Both methods adjust the annual benchmark based on the number of periods per year to suit the frequency of the returns:
• If the method call does not include a `periodsPerYear` argument, it uses `detectPeriod()` to determine whether the returns represent monthly or daily values based on the chart's history. If monthly, the method divides the `annualBenchmark` value by 12. If daily, it divides the value by 365.
• If the method call does specify a `periodsPerYear` argument, the argument's value supersedes the automatic calculation, facilitating custom benchmark adjustments, such as dividing by 252 when analyzing collected daily stock returns.
When the array passed to these methods represents a sequence of excess returns , such as the result from the second overload of `getPeriodicReturns()`, use an `annualBenchmark` value of 0 to avoid comparing those excess returns to a separate rate.
By default, these methods only calculate the ratios on the last available bar to minimize their resource usage. Users can override this behavior with the `forceCalc` parameter. When the value is true , the method calculates the ratio on each call if sufficient data is available, regardless of the bar index.
Look first. Then leap.
█ FUNCTIONS & METHODS
This library contains the following functions:
detectPeriod()
Determines whether the chart data has sufficient coverage to use monthly or daily returns
for risk metric calculations.
Returns: (bool) `true` if the period spans more than two months, `false` if it otherwise spans more
than two days, and `na` if the data is insufficient.
getPeriodicReturns(percentChange, maxPeriods)
(Overload 1 of 2) Tracks periodic return percentages and queues them into an array for ratio
calculations. The span of the chart's historical data determines whether the function uses
daily or monthly periods in its calculations. If the chart spans more than two months,
it uses "1M" periods. Otherwise, if the chart spans more than two days, it uses "1D"
periods. If the chart covers less than two days, it does not store changes.
Parameters:
percentChange (float) : (series float) The change percentage. The function compounds non-na values from each
chart bar within monthly or daily periods to calculate the periodic changes.
maxPeriods (simple int) : (simple int) The maximum number of periodic returns to store in the returned array.
Returns: (array) An array containing the overall percentage changes for each period, limited
to the maximum specified by `maxPeriods`.
getPeriodicReturns(percentChange, benchmark, maxPeriods)
(Overload 2 of 2) Tracks periodic excess return percentages and queues the values into an
array. The span of the chart's historical data determines whether the function uses
daily or monthly periods in its calculations. If the chart spans more than two months,
it uses "1M" periods. Otherwise, if the chart spans more than two days, it uses "1D"
periods. If the chart covers less than two days, it does not store changes.
Parameters:
percentChange (float) : (series float) The change percentage. The function compounds non-na values from each
chart bar within monthly or daily periods to calculate the periodic changes.
benchmark (float) : (series float) The benchmark percentage to compare against `percentChange` values.
The function compounds non-na values from each bar within monthly or
daily periods and subtracts the results from the compounded `percentChange` values to
calculate the excess returns. For consistency, ensure this series has a similar history
length to the `percentChange` with aligned non-na value times.
maxPeriods (simple int) : (simple int) The maximum number of periodic excess returns to store in the returned array.
Returns: (array) An array containing monthly or daily excess returns, limited
to the maximum specified by `maxPeriods`.
method sharpeRatio(returnsArray, annualBenchmark, forceCalc, periodsPerYear)
Calculates the Sharpe ratio for an array of periodic returns.
Callable as a method or a function.
Namespace types: array
Parameters:
returnsArray (array) : (array) An array of periodic return percentages, e.g., returns over monthly or
daily periods.
annualBenchmark (float) : (series float) The annual rate of return to compare against `returnsArray` values. When
`periodsPerYear` is `na`, the function divides this value by 12 to calculate a
monthly benchmark if the chart's data spans at least two months or 365 for a daily
benchmark if the data otherwise spans at least two days. If `periodsPerYear`
has a specified value, the function divides the rate by that value instead.
forceCalc (bool) : (series bool) If `true`, calculates the ratio on every call. Otherwise, ratio calculation
only occurs on the last available bar. Optional. The default is `false`.
periodsPerYear (simple int) : (simple int) If specified, divides the annual rate by this value instead of the value
determined by the time span of the chart's data.
Returns: (float) The Sharpe ratio, which estimates the excess return per unit of total volatility.
method sortinoRatio(returnsArray, annualBenchmark, forceCalc, periodsPerYear)
Calculates the Sortino ratio for an array of periodic returns.
Callable as a method or a function.
Namespace types: array
Parameters:
returnsArray (array) : (array) An array of periodic return percentages, e.g., returns over monthly or
daily periods.
annualBenchmark (float) : (series float) The annual rate of return to compare against `returnsArray` values. When
`periodsPerYear` is `na`, the function divides this value by 12 to calculate a
monthly benchmark if the chart's data spans at least two months or 365 for a daily
benchmark if the data otherwise spans at least two days. If `periodsPerYear`
has a specified value, the function divides the rate by that value instead.
forceCalc (bool) : (series bool) If `true`, calculates the ratio on every call. Otherwise, ratio calculation
only occurs on the last available bar. Optional. The default is `false`.
periodsPerYear (simple int) : (simple int) If specified, divides the annual rate by this value instead of the value
determined by the time span of the chart's data.
Returns: (float) The Sortino ratio, which estimates the excess return per unit of downside
volatility.
Sortino RatioFrom Wikipedia :
"The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency.
The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk."
