/**
* Ulcer Index
* Measures downside volatility and risk by focusing on drawdowns from recent highs
*/
/**
* Calculate Ulcer Index
* @param closes Array of closing prices
* @param period Period for calculation (default 14)
* @returns UlcerIndexData object
*/
export function calculateUlcerIndex(closes, period = 14) {
// Minimum 3 data points required
if (closes.length < 3) {
return null;
}
// Use adaptive period for small datasets
const effectivePeriod = Math.min(period, closes.length);
// Find the maximum price in the period for each point
const maxPrices = [];
for (let i = 0; i < closes.length; i++) {
const startIndex = Math.max(0, i - effectivePeriod + 1);
const periodPrices = closes.slice(startIndex, i + 1);
maxPrices.push(Math.max(...periodPrices));
}
// Calculate drawdowns
const drawdowns = [];
let maxDrawdown = 0;
for (let i = 0; i < closes.length; i++) {
const drawdown = ((maxPrices[i] - closes[i]) / maxPrices[i]) * 100;
drawdowns.push(drawdown);
maxDrawdown = Math.max(maxDrawdown, drawdown);
}
// Calculate Ulcer Index: Square root of average of squared drawdowns
const recentDrawdowns = drawdowns.slice(-effectivePeriod);
const squaredDrawdowns = recentDrawdowns.map(d => d * d);
const averageSquaredDrawdown = squaredDrawdowns.reduce((sum, d) => sum + d, 0) / effectivePeriod;
const ulcerIndex = Math.sqrt(averageSquaredDrawdown);
// Current drawdown
const currentDrawdown = drawdowns[drawdowns.length - 1];
// Assess risk level
let riskLevel = 'low';
if (ulcerIndex > 20) {
riskLevel = 'extreme';
}
else if (ulcerIndex > 15) {
riskLevel = 'high';
}
else if (ulcerIndex > 10) {
riskLevel = 'moderate';
}
// Determine trend (improving vs deteriorating)
let trend = 'stable';
if (drawdowns.length >= effectivePeriod * 2) {
const currentPeriodAvg = recentDrawdowns.reduce((sum, d) => sum + d, 0) / effectivePeriod;
const previousPeriodDrawdowns = drawdowns.slice(-effectivePeriod * 2, -effectivePeriod);
const previousPeriodAvg = previousPeriodDrawdowns.reduce((sum, d) => sum + d, 0) / effectivePeriod;
if (currentPeriodAvg < previousPeriodAvg * 0.9) {
trend = 'improving';
}
else if (currentPeriodAvg > previousPeriodAvg * 1.1) {
trend = 'deteriorating';
}
}
// Calculate signal strength based on Ulcer Index level
const strength = Math.min(100, ulcerIndex * 5);
// Calculate risk-adjusted return (if we have enough data)
let riskAdjustedReturn = null;
if (closes.length >= effectivePeriod * 2) {
const startPrice = closes[closes.length - effectivePeriod * 2];
const endPrice = closes[closes.length - 1];
const totalReturn = ((endPrice - startPrice) / startPrice) * 100;
riskAdjustedReturn = ulcerIndex > 0 ? totalReturn / ulcerIndex : totalReturn;
}
// Generate trading signal
let signal = 'neutral';
if (riskLevel === 'extreme' && trend === 'deteriorating') {
signal = 'sell'; // High risk, deteriorating conditions
}
else if (riskLevel === 'low' && trend === 'improving') {
signal = 'buy'; // Low risk, improving conditions
}
// Assess market stress
let marketStress = 'low';
if (ulcerIndex > 25) {
marketStress = 'crisis';
}
else if (ulcerIndex > 18) {
marketStress = 'high';
}
else if (ulcerIndex > 12) {
marketStress = 'moderate';
}
return {
ulcerIndex,
currentDrawdown,
maxDrawdown,
period: effectivePeriod,
riskLevel,
trend,
strength,
riskAdjustedReturn,
signal,
marketStress
};
}
/**
* Calculate Ulcer Index for multiple periods
* @param closes Array of closing prices
* @param periods Array of periods to calculate Ulcer Index for
* @returns Array of UlcerIndexData objects
*/
export function calculateMultipleUlcerIndex(closes, periods = [14, 28, 90]) {
return periods
.map(period => calculateUlcerIndex(closes, period))
.filter((ulcer) => ulcer !== null);
}
/**
* Get Ulcer Index interpretation
* @param ulcer UlcerIndexData object
* @returns Human-readable interpretation
*/
export function getUlcerIndexInterpretation(ulcer) {
const { ulcerIndex, riskLevel, trend, marketStress, signal } = ulcer;
let interpretation = `Ulcer Index: ${ulcerIndex.toFixed(2)}`;
interpretation += ` - ${riskLevel} risk, ${trend} trend`;
if (marketStress !== 'low') {
interpretation += ` (${marketStress} market stress)`;
}
if (signal !== 'neutral') {
interpretation += ` - ${signal.toUpperCase()} signal`;
}
return interpretation;
}
/**
* Analyze risk-adjusted performance
* @param ulcer UlcerIndexData object
* @param returns Array of returns for comparison
* @returns Risk-adjusted performance analysis
*/
export function analyzeRiskAdjustedPerformance(ulcer, returns) {
if (returns.length === 0) {
return {
sharpeRatio: null,
sortinoRatio: null,
ulcerPerformance: 'fair',
riskEfficiency: 50
};
}
const avgReturn = returns.reduce((sum, r) => sum + r, 0) / returns.length;
const volatility = Math.sqrt(returns.reduce((sum, r) => sum + Math.pow(r - avgReturn, 2), 0) / returns.length);
// Sharpe Ratio (assuming 0% risk-free rate)
const sharpeRatio = volatility > 0 ? avgReturn / volatility : null;
// Sortino Ratio (downside deviation only)
const downsideReturns = returns.filter(r => r < 0);
const downsideDeviation = downsideReturns.length > 0 ?
Math.sqrt(downsideReturns.reduce((sum, r) => sum + Math.pow(r, 2), 0) / downsideReturns.length) : 0;
const sortinoRatio = downsideDeviation > 0 ? avgReturn / downsideDeviation : null;
// Ulcer Performance assessment
let ulcerPerformance = 'fair';
const ui = ulcer.ulcerIndex;
if (ui < 5) {
ulcerPerformance = 'excellent';
}
else if (ui < 10) {
ulcerPerformance = 'good';
}
else if (ui > 20) {
ulcerPerformance = 'poor';
}
// Risk efficiency score
const riskEfficiency = Math.max(0, Math.min(100, 100 - ui * 2));
return { sharpeRatio, sortinoRatio, ulcerPerformance, riskEfficiency };
}
/**
* Calculate Ulcer Index trend analysis
* @param closes Array of closing prices
* @param periods Number of periods to analyze
* @returns Trend analysis for risk assessment
*/
export function analyzeUlcerIndexTrend(closes, periods = 60) {
if (closes.length < periods + 14) {
return {
overallRiskTrend: 'stable',
riskMomentum: 0,
recommendedPositionSize: 100,
marketCondition: 'normal'
};
}
const ulcerData = calculateMultipleUlcerIndex(closes, [14, 28, 90]);
if (ulcerData.length === 0) {
return {
overallRiskTrend: 'stable',
riskMomentum: 0,
recommendedPositionSize: 100,
marketCondition: 'normal'
};
}
// Analyze risk trend
const avgUlcer = ulcerData.reduce((sum, u) => sum + u.ulcerIndex, 0) / ulcerData.length;
let overallRiskTrend = 'stable';
let riskMomentum = 0;
if (avgUlcer < 8) {
overallRiskTrend = 'decreasing';
riskMomentum = Math.max(0, 10 - avgUlcer);
}
else if (avgUlcer > 15) {
overallRiskTrend = 'increasing';
riskMomentum = Math.min(10, avgUlcer - 15);
}
// Recommended position size based on risk
const recommendedPositionSize = Math.max(10, Math.min(100, 100 - avgUlcer * 3));
// Market condition assessment
let marketCondition = 'normal';
if (avgUlcer < 5) {
marketCondition = 'calm';
}
else if (avgUlcer > 20) {
marketCondition = 'crisis';
}
else if (avgUlcer > 12) {
marketCondition = 'volatile';
}
return { overallRiskTrend, riskMomentum, recommendedPositionSize, marketCondition };
}
