Risk-Adjusted Performance Rankings | NickJoanRisk-Adjusted Performance Rankings | NickJoan
Core Idea
Risk-Adjusted Performance Rankings is a multi-asset comparison dashboard designed to rank up to 15 symbols by how efficiently they convert recent price movement into risk-adjusted return. Instead of looking only at raw price performance, the indicator evaluates three classic performance measures: Sharpe, Sortino and Omega over a user-defined lookback window and organizes the results into a table.
The script can be used in two ways:
• As a metrics table, where all three risk-adjusted values are shown side by side for each asset.
• As a ranking tool, where the symbols are sorted by Sharpe, Sortino, Omega, or a composite Z-Score score.
Calculation Logic
The indicator works by taking the percentage return of each symbol over the selected period and then building three separate statistics from that same return stream.
1. Return calculation
For each symbol, the script first calculates the one-bar rate of change. This creates a rolling return series that acts as the base input for all three risk-adjusted metrics.
2. Sharpe ratio
The Sharpe calculation measures average return relative to total return volatility.
• The script calculates the mean of returns over the selected lookback.
• It calculates the standard deviation of those returns.
• It divides mean return by standard deviation.
• It then multiplies by the square root of the lookback length to create a rolling-style scaled value.
In practical terms, a higher Sharpe reading means the asset has produced more return for each unit of total volatility.
3. Sortino ratio
The Sortino ratio is similar to Sharpe, but it only penalizes downside volatility.
• The script collects only negative returns from the lookback window.
• It computes the standard deviation of those downside returns.
• It divides mean return by that downside deviation.
• It then scales the result by the square root of the lookback.
This means Sortino rewards assets that may have volatile upside moves but relatively controlled downside behavior.
4. Omega ratio
The Omega calculation compares total gains to total losses over the selected window.
• All positive returns are summed as gains.
• All negative returns are converted to positive values and summed as losses.
• Omega is computed as the ratio of total gains to total losses.
A value above 1 suggests gains outweigh losses, while a value below 1 suggests the opposite.
Ranking Logic
The indicator supports several ranking modes, and each one uses the same asset list but applies a different sort key.
Metrics Table
In Metrics Table mode, the script shows:
• The ticker name.
• Sharpe.
• Sortino.
• Omega.
This mode is the most direct view if you want to inspect each asset’s raw values without sorting.
Sharpe / Sortino / Omega ranking
When one of these modes is selected:
• The table sorts the assets by that chosen metric.
• The highest values appear at the top.
• The table becomes a direct performance leaderboard.
Z-Score ranking
The Z-Score mode is a composite ranking system.
• The script first computes the mean and standard deviation of each metric across all 15 assets.
• It then converts each asset’s Sharpe, Sortino, and Omega into z-scores.
• Those three standardized values are averaged into one composite score.
• Assets are sorted by that final score.
This allows apples-to-apples comparison even when the raw metrics live on different numeric scales.
What the Colors Mean
The script uses color thresholds to make the table easier to read at a glance.
Sharpe colors
Sharpe cells are colored according to the input range defined by:
• Sharpe Min
• Sharpe Max
Values below the minimum are treated as weak.
Values between the lower zone and upper zone are shown as progressively stronger.
Values above the upper threshold are treated as strong.
Sortino colors
Sortino uses the same idea, but with its own range:
• Sortino Min
• Sortino Max
This allows the heatmap to reflect downside-adjusted performance independently from Sharpe.
Omega colors
Omega is especially important because it is naturally centered around 1.0.
• Values below the lower threshold are weak.
• Values between the band limits gradually improve.
• Values above the upper threshold are strong.
Z-Score colors
The Z-Score mode uses a standardized color logic:
• Strongly negative values are weak.
• Slightly negative values are mid-negative.
• Slightly positive values are mid-positive.
• Strongly positive values are strong.
This helps show whether an asset is above or below the group average on a normalized basis.
Table Output
Metrics Table output
In this mode, the table displays:
• Column 1: ticker.
• Column 2: Sharpe.
• Column 3: Sortino.
• Column 4: Omega.
Single-metric ranking output
In Sharpe, Sortino, and Omega modes, the table displays:
• Rank number.
• Ticker.
• Chosen metric.
This keeps the interface minimal while still showing the full ranked order.
Z-Score output
In this mode, the table displays:
• Rank number.
• Ticker.
• Sharpe Z.
• Sortino Z.
• Omega Z.
• Average score.
This view is useful when you want a compact, relative ranking rather than raw values.
Inputs
The indicator has four main input groups.
Calculation
• Period: defines the lookback window used for all metric calculations.
Table
• Display Mode: chooses between Metrics Table, Sharpe, Sortino, Omega, and Z-Score.
• Table Position: controls where the table is placed on the chart.
Color Scale
• Sharpe Min / Max: controls the heatmap thresholds for Sharpe.
• Sortino Min / Max: controls the heatmap thresholds for Sortino.
• Omega Min / Max: controls the heatmap thresholds for Omega.
Colors
• Strong: the strongest positive color.
• Mid +: the intermediate positive color.
• Mid -: the intermediate negative color.
• Weak: the weakest negative color.
Tickers
The script includes 15 symbol inputs, allowing you to compare a basket of assets at once. This makes it suitable for crypto rotation, watchlist comparison, or broad performance ranking across a selected universe.
How to Use It
This indicator is best used as a relative strength and quality filter, not as a standalone entry signal.
Trend selection
Use the ranking table to see which assets are showing the best risk-adjusted behavior over the chosen period.
Rotation analysis
If you track a basket of coins or market leaders, the indicator can help identify which names are improving in risk-adjusted terms and which ones are losing momentum.
Risk control
A raw gain is not always useful if it comes with excessive volatility or poor downside behavior. This script helps highlight assets with better return efficiency, not just bigger movement.
Multi-factor comparison
Because Sharpe, Sortino, and Omega emphasize different aspects of return quality, the script gives a more balanced view than a single metric alone.
Practical Interpretation
Here is a simple way to read the results:
• High Sharpe: efficient return relative to total volatility.
• High Sortino: strong return with less downside volatility.
• High Omega: gains outweigh losses over the lookback window.
• High Z-Score average: strong performance relative to the rest of the selected universe.
If an asset scores well across all three, it usually represents a stronger and more stable candidate than one that only looks good on one metric.
Best Use Cases
Typical uses include:
• Crypto basket comparison.
• Top-asset ranking.
• Risk-adjusted momentum filtering.
• Rotation watchlists.
• Regime-aware asset selection.
It is especially useful when you want to compare many symbols quickly without manually calculating which ones are actually performing best on a quality-adjusted basis.
Notes
The metric table is only as good as the selected lookback period and asset set.
• Shorter periods react faster but can be noisier.
• Longer periods smooth the results but may lag recent shifts.
• The Z-Score mode is relative to the selected group, so its meaning depends on the symbols you include. Indicator
Sortino Ratio Oscillator [MarkitTick]💡 The Sortino Ratio Oscillator introduces a sophisticated, risk-adjusted performance metric typically reserved for portfolio analysis, adapting it into a highly responsive momentum oscillator. By strictly penalizing downside volatility while rewarding upside momentum, it provides a much clearer picture of market strength compared to traditional oscillators that treat all volatility equally.
✨ Originality and Utility
Standard momentum indicators measure the velocity of price movement based on general variance. However, traditional models penalize both upside and downside volatility. A massive bullish breakout creates "high volatility," which standard indicators often misinterpret as an overextended or risky market condition.
This script resolves that inherent flaw by migrating the academic Sortino Ratio into a technical trading framework. It isolates "bad" volatility (price drops) from "good" volatility (price gains). The utility here is immense: traders can identify trends where the price action is genuinely supported by positive risk-adjusted returns, filtering out noisy markets where the downside deviation is too high. Furthermore, this tool features an integrated divergence detection engine, dynamic histogram coloring, and built-in webhook alert formatting, making it a comprehensive suite for algorithmic and discretionary traders alike.
🔬 Methodology and Concepts
The core engine of this indicator relies on continuously assessing the bar-to-bar percentage return of the asset.
First, it calculates the raw percentage return between the current close and the previous close.
Next, it isolates the downside returns. If a return is positive, it is ignored for the risk calculation (treated as zero). If it is negative, it is squared to emphasize larger drawdowns, following standard variance practices.
The script then computes the Simple Moving Average of these squared negative returns over a user-defined lookback window, calculating the square root to determine the final Downside Deviation.
Simultaneously, the Simple Moving Average of the raw returns is calculated to find the mean return over the same period.
The final Sortino Ratio is produced by dividing the mean return by the downside deviation.
To smooth the output and generate actionable crossovers, a secondary Signal Line is derived by applying an average to the raw Sortino Ratio.
To enhance the analytical depth, the script incorporates a robust divergence engine that scans for pivot highs and lows over a customizable lookback window. By comparing price action pivots with the oscillator's momentum peaks and troughs, it systematically maps out both regular and hidden divergences.
🎨 Visual Guide
The visual presentation is meticulously structured to provide instant clarity on risk-adjusted momentum states.
• The Sortino Histogram
The core oscillator is plotted as a multi-colored histogram. It utilizes a four-state coloring system to indicate momentum shifts:
Solid Bull Color: The ratio is above zero and rising, indicating accelerating positive risk-adjusted returns.
Transparent Bull Color: The ratio is above zero but falling, suggesting positive momentum is decelerating.
Solid Bear Color: The ratio is below zero and falling, indicating accelerating downside risk.
Transparent Bear Color: The ratio is below zero but rising, showing that downside risk is waning.
• Signal Line and Cloud Fill
A highlighted Signal Line tracks the moving average of the Sortino Ratio. The space between the Sortino histogram and the Signal Line is filled with a dynamic cloud, helping traders easily spot shifts in immediate trend strength.
• Threshold Lines
Dashed lines represent the Overbought and Oversold thresholds. A solid gray line marks the Zero Level, acting as the primary baseline for positive versus negative risk-adjusted states.
• Divergence Mapping
Regular Bullish (RB): Displayed as a solid line connecting price lows to oscillator lows, complete with a label below the candle.
Hidden Bullish (HB): Displayed as a dashed line, indicating trend continuation.
Regular Bearish (RD): Displayed as a solid line connecting price highs to oscillator highs.
Hidden Bearish (HD): Displayed as a dashed line.
• Candle Coloring
When enabled, the price chart's candles are painted to match the four-state color logic of the Sortino Histogram, linking the oscillator's data directly to the price action on the main chart.
📖 How to Use
Traders can interpret the Sortino Ratio Oscillator through several distinct frameworks depending on their trading style.
• Zero-Line Crossovers
A baseline shift occurs when the histogram crosses the zero line. A cross into positive territory confirms that the average returns now outweigh the downside deviation, signaling a structurally sound bullish environment. Conversely, a drop below zero warns that downside volatility is dominating the asset's behavior.
• Signal Line Interactions
Watch for the histogram to cross the Signal Line. When the Sortino Ratio spikes above its signal line, momentum is expanding. When it crosses below, it often precedes a consolidation or a reversal, as highlighted by the cloud fill changing colors.
• Extremes and Reversals
The Overbought and Oversold threshold lines act as exhaustion markers. An asset sustaining a Sortino Ratio above the Overbought level is exhibiting unusually high, unpenalized upside movement. While strong, traders should watch for the histogram to peak and cross back below the Signal Line as an early warning of a pullback.
• Trading Divergences
Divergences are perhaps the most powerful signals generated by this tool. Look for Regular Bullish Divergences when the price makes a lower low, but the Sortino Ratio makes a higher low. This indicates that despite the price drop, the underlying downside volatility is shrinking relative to the mean return, hinting at a bottom. Hidden Divergences are excellent for trading pullbacks in the direction of the macro trend.
⚙️ Inputs and Settings
• Sortino Settings
Lookback Length: Defines the period used to calculate the mean return and downside deviation. A shorter length is highly reactive, while a longer length provides macroscopic trend stability.
Signal Length: Adjusts the smoothness of the Signal Line.
Overbought / Oversold Levels: Customizes the threshold lines for extreme readings.
• Candle Coloring
A simple toggle to enable or disable the dynamic coloring of the main chart price candles based on the oscillator's state.
• Divergence Settings
Enable Divergence: Master toggle for the divergence engine.
Show Regular / Hidden: Independent toggles to filter specific divergence types.
Pivot Lookback Left / Right: Determines the strictness of the pivot point detection. Higher values require more significant peaks and troughs to form a valid pivot, filtering out noise.
• Webhook Action Names
Customizable string inputs allowing algorithmic traders to map specific script events directly to JSON payloads for automated execution platforms.
🔍 Deconstruction of the Underlying Scientific and Academic Framework
The Sortino Ratio, developed by Dr. Frank A. Sortino, is a vital modification of the Sharpe Ratio. In Modern Portfolio Theory, the Sharpe Ratio evaluates the performance of an investment by adjusting for its risk, defined universally as the standard deviation of its returns. However, standard deviation measures total volatility, treating an unexpected positive gain exactly the same as a negative loss.
This oscillator resolves that mathematical paradox by isolating downside deviation. The scientific framework dictates that a minimum acceptable return—in this script's case, zero—must be established. Only returns falling strictly below this threshold are aggregated and squared to calculate the downside variance. By exclusively measuring the standard deviation of negative asset returns, the formula effectively removes the penalty for upside volatility.
In a purely academic sense, a high Sortino Ratio mathematically proves that the asset is generating its returns without suffering significant, erratic drawdowns. Translated into technical analysis, when the indicator rises, it mathematically proves that the ratio of upward momentum relative to downward variance is expanding. This makes it an incredibly robust statistical measure, completely immune to the standard look-around bias of typical mathematical oscillators that collapse under the weight of sudden, positive price shocks.
⚠️ Disclaimer
All provided scripts and indicators are strictly for educational exploration and must not be interpreted as financial advice or a recommendation to execute trades. I expressly disclaim all liability for any financial losses or damages that may result, directly or indirectly, from the reliance on or application of these tools. Market participation carries inherent risk where past performance never guarantees future returns, leaving all investment decisions and due diligence solely at your own discretion. Indicator
Relative Performance Analyzer [AstrideUnicorn]Relative Performance Analyzer (RPA) is a performance analysis tool inspired by the data comparison features found in professional trading terminals. The RPA replicates the analytical approach used by portfolio managers and institutional analysts who routinely compare multiple securities or other types of data to identify relative strength opportunities, make allocation decisions, choose the most optimal investment from several alternatives, and much more.
Key Features:
Multi-Symbol Comparison: Track up to 5 different symbols simultaneously across any asset class or dataset
Two Performance Calculation Methods: Choose between percentage returns or risk-adjusted returns
Interactive Analysis: Drag the start date line on the chart or manually choose the start date in the settings
Professional Visualization: High-contrast color scheme designed for both dark and light chart themes
Live Performance Table: Real-time display of current return values sorted from the top to the worst performers
Practical Use Cases:
ETF Selection: Compare similar ETFs (e.g., SPY vs IVV vs VOO) to identify the most efficient investment
Sector Rotation: Analyze which sectors are showing relative strength for strategic allocation
Competitive Analysis: Compare companies within the same industry to identify leaders (e.g., APPLE vs SAMSUNG vs XIAOMI)
Cross-Asset Allocation: Evaluate performance across stocks, bonds, commodities, and currencies to guide portfolio rebalancing
Risk-Adjusted Decisions: Use risk-adjusted performance to find investments with the best returns per unit of risk
Example Scenarios:
Analyze whether tech stocks are outperforming the broader market by comparing XLK to SPY
Evaluate which emerging market ETF (EEM vs VWO) has provided better risk-adjusted returns over the past year
HOW DOES IT WORK
The indicator calculates and visualizes performance from a user-defined starting point using two methodologies:
Percentage Returns: Standard total return calculation showing percentage change from the start date
Risk-Adjusted Returns: Cumulative returns divided by the volatility (standard deviation), providing insight into the efficiency of performance. An expanding window is used to calculate the volatility, ensuring accurate risk-adjusted comparisons throughout the analysis period.
HOW TO USE
Setup Your Comparison: Enable up to 5 assets and input their symbols in the settings
Set Analysis Period: When you first launch the indicator, select the start date by clicking on the price chart. The vertical start date line will appear. Drag it on the chart or manually input a specific date to change the start date.
Choose Return Type: Select between percentage or risk-adjusted returns based on your analysis needs
Interpret Results
Use the real-time table for precise current values
SETTINGS
Assets 1-5: Toggle on/off and input symbols for comparison (stocks, ETFs, indices, forex, crypto, fundamental data, etc.)
Start Date: Set the initial point for return calculations (drag on chart or input manually)
Return Type: Choose between "Percentage" or "Risk-Adjusted" performance. Indicator
Best MA Finder: Sharpe/Sortino ScannerThis script, Best MA Finder: Sharpe/Sortino Scanner, is a tool designed to identify the moving average (SMA or EMA) that best acts as a dynamic trend threshold on a chart, based on risk-adjusted historical performance. It scans a wide range of MA lengths (SMA or EMA) and selects the one whose simple price vs MA crossover delivered the strongest results using either the Sharpe ratio or the Sortino ratio. Reading it is intuitive: when price spent time above the selected MA, conditions were on average more favorable in the backtest; below, less favorable. It is a trend and risk gauge, not an overbought or oversold signal.
What it does:
- Runs individual long-only crossover backtests for many MA lengths across short to very long horizons.
- For each length, measures the total number of trades, the annualized Sharpe ratio, and the annualized Sortino ratio.
- Uses the chosen metric value (Sharpe or Sortino) as the score to rank candidates.
- Applies a minimum trade filter to discard statistically weak results.
- Optionally applies a local stability filter to prefer a length that also outperforms its close neighbors by at least a small margin.
- Selects the optimal MA and displays it on the chart with a concise summary table.
How to use it:
- Choose MA type: SMA or EMA.
- Choose the metric: Sharpe or Sortino.
- Set the minimum trade count to filter out weak samples.
- Select the risk-free mode:
Auto: uses a short-term risk-free rate for USD-priced symbols when available.
Manual: you provide a risk-free ticker.
None: no risk-free rate.
- Optionally enable stability controls: neighbor radius and epsilon.
- Toggle the on-chart summary table as needed.
On-chart output:
- The selected optimal MA is plotted.
- The optional table shows MA length, number of trades, chosen metric value annualized, and the annual risk-free rate used.
Key features:
- Risk-adjusted optimization via Sharpe or Sortino for fair, comparable assessment.
- Broad MA scan with SMA and EMA support.
- Optional stability filter to avoid one-off spikes.
- Clear and auditable presentation directly on the chart.
Use cases:
- Traders who want a defensible, data-driven trend threshold without manual trial and error.
- Swing and trend-following workflows across timeframes and asset classes.
- Quick SMA vs EMA comparisons using risk-adjusted results.
Limitations:
- Not a full trading strategy with position sizing, costs, funding, slippage, or stops.
- Long-only, one position at a time.
- Discrete set of MA lengths, not a continuous optimizer.
- Requires sufficient price history and, if used, a reliable risk-free series.
This script is open-source and built from original logic. It does not replicate closed-source scripts or reuse significant external components.
Indicator
Custom Performance TableThis script generates a table designed to provide a concise yet highly customizable overview of the performance of multiple financial instruments, displayed directly on the chart. The table can include up to 40 tickers, each individually configurable, with values updated in real time based on either the current chart timeframe or a specific user-selected timeframe.
NOTE : The update frequency of the table values depends on the refresh rate of the chart's main ticker to which the indicator is applied. To ensure a consistent and reliable data feed, especially when monitoring heterogeneous instruments, it is recommended to apply the indicator to a highly liquid and continuously traded asset, such as BTCUSD.
PERFORMANCE CALCULATION MODES
You can choose from three different performance calculation modes:
1) Change % (Percentage Change)
Displays the percentage change of the current price compared to the previous candle within the selected timeframe.
(Current Price - Previous Price) / Previous Price * 100
This mode provides an immediate and straightforward measure of each instrument's percentage movement, useful for quick visual comparisons of relative strength among assets.
2) Z-Score
The Z-Score measures how much the current price variation deviates from the historical average variation, relative to the standard deviation of those variations.
(Current Variation - Average Variation) / Standard Deviation of Variations
The result indicates how statistically unusual a movement is:
- Values near 0 suggest normal variations.
- Values above ±2 indicate statistically significant deviations.
This is a valuable tool for identifying overbought/oversold conditions or market stress events and is often used in mean reversion strategies.
NOTE : Due to technical constraints, Z-Score can only be calculated when the selected timeframe matches the chart's timeframe exactly.
3) RAROC (Risk-Adjusted Return on Capital)
RAROC expresses an asset's performance in relation to the risk taken, measured through its volatility (standard deviation of price).
Percentage Change / Standard Deviation of Price
It allows for an assessment of return efficiency in relation to volatility.
A high RAROC value indicates a high return relative to the risk, making it a useful tool for comparing assets with different risk profiles. It is especially suitable for portfolio selection and allocation purposes.
TABLE CONFIGURATION
Each ticker can be customized with its own label, colors, and position in the table.
Each row can display the ticker name or a custom label, which, at the user's discretion, can either replace the name or be shown as an informational tooltip.
The table can be placed anywhere on the chart using horizontal and vertical offset parameters. Thanks to offset support, you can, for example, create financial market overview layouts. This can be done by completely “cleaning” the chart from price and indicators using PulseWire settings, and then displaying multiple tables simultaneously (see the example chart published here).
Advanced customization options are also available for the table's appearance, including font settings, colors, borders, and more.
CALCULATION TIMEFRAME
The indicator allows the user to force a specific timeframe (Daily, Weekly, Monthly, Yearly) when applied to intraday charts.
However, for Z-Score mode, the selected timeframe must match the chart's timeframe exactly to ensure correct computation. Otherwise, the script will halt until settings are properly adjusted.
USAGE NOTES
Custom Performance Table is a flexible and adaptable tool, suitable for both intraday operations and medium- to long-term analysis. It is designed for traders and analysts who need to compare assets based on quantitative metrics, whether simple (like percentage change) or more advanced and risk-adjusted (such as Z-Score and RAROC). Indicator
BTC Slayer 9000 - Relative Risk-adjusted performanceBTC Slayer 9000: Relative Risk-Adjusted Performance
Dear friends and fellow traders,
I am pleased to introduce the BTC Slayer 9000, a script designed to provide clear insights into risk-adjusted performance relative to a benchmark. Whether you're navigating the volatile world of cryptocurrencies or exploring opportunities in stocks, this tool helps you make informed decisions by comparing assets against your chosen benchmark.
What Does It Do?
This indicator is based on the Ulcer Index (UI), a metric that measures downside risk. It calculates the Ulcer Performance Index (UPI), which combines returns and downside risk, and compares it to a benchmark (like BTC/USDT, SPY500, or any trading pair).
The result is the Relative UPI (RUPI):
Positive RUPI (green area): The asset's risk-adjusted performance is better than the benchmark.
Negative RUPI (red area): The asset's risk-adjusted performance is worse than the benchmark.
Why Use It?
Risk vs. Reward: See if the extra risk of an asset is justified by its returns.
Customizable Benchmark: Compare any asset against BTC, SPY500, or another chart.
Dynamic Insights: Quickly identify outperforming assets for long positions and underperformers for potential shorts.
How to Use:
Inputs:
Adjust the lookback period to set the time frame for analysis. 720 Period is meant to represent 30 days. I like to use 168 period because I do not hold trades for long.
Choose your comparison chart (e.g., BTC/USDT, SPY500, AAPL, etc.).
Interpretation:
Green Area Above 0: The asset offers better risk-adjusted returns than the benchmark.
Red Area Below 0: The benchmark is a safer or more rewarding option.
Perfect for All Traders
Whether you:
Trade Cryptocurrencies: Compare altcoins to BTC.
Invest in Stocks: Compare individual stocks to indices like SPY500.
Evaluate Portfolio Options: Decide between assets like AAPL or TSLA.
This indicator equips you with a systematic way to evaluate "Is the extra risk worth it?".
The script was compiled in Collaboration with ChatGPT Indicator
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 PulseWire 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.
Indicator
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. Library
