sig-pub/internal/trading/backtest/backtest_stats.go

package backtest

import (
	"math"
	"sig-pub/pkg/trade"
	"sig-pub/pkg/types/ta"
	"sig-pub/pkg/utils/collect"
	"sort"
)

// SharpeRatio computes an annualized Sharpe ratio based on closed trades.
// rfAnnual is the annual risk-free rate expressed as a decimal (e.g. 0.01 for 1%).
// Method:
// - For each closed trade, we compute a period return = trade.Pnl / initialCash.
// - Period lengths are derived from successive trade close timestamps (ms).
// - Excess returns = periodReturn - rfAnnual * periodYears.
// - Sharpe = mean(excess) / stddev(excess) * sqrt(periodsPerYear)
// This provides a reasonable approximation when equity snapshots are not available.
func (a *TradingPlanBacktester) sharpeRatio(rfAnnual float64) float64 {
	if a.account.initialCash <= 0 {
		return 0
	}
	n := len(a.account.closeTrades)
	if n < 2 {
		return 0
	}

	trades := make([]*trade.TradeOrder, 0, n)
	for _, tid := range a.account.closeTrades {
		if order, ok := a.account.orders[tid]; ok {
			trades = append(trades, order)
		}
	}
	collect.SortAsc(trades, func(trd *trade.TradeOrder) int64 { return trd.TradeId })

	// 年化每笔收益方法：
	// 对每笔平仓交易，先计算该笔收益相对于初始资金的返回率（profit / initialCash），
	// 再根据该笔持仓时长（以毫秒为单位，使用 t.Ctime - t.EntryTime）将收益年化：
	// annualizedReturn = return * (secsYear / dtSec)
	// 然后计算超额收益 = annualizedReturn - rfAnnual
	// 最后 Sharpe = mean(excess) / stddev(excess)
	const secsYear = 365.0 * 24.0 * 3600.0
	excess := make([]float64, 0, n)
	for _, t := range trades {
		ret := t.Profit / a.account.initialCash
		// holding time in seconds
		dtSec := float64(t.Ctime-t.EntryTime) / 1000.0
		if dtSec <= 0 {
			dtSec = 1.0
		}
		annualized := ret * (secsYear / dtSec)
		excess = append(excess, annualized-rfAnnual)
	}
	if len(excess) <= 1 {
		return 0
	}
	meanEx := ta.Avg(excess)
	sd := stddev(excess)
	if sd == 0 {
		return 0
	}
	return meanEx / sd
}

// sharpeFromEquitySnapshots computes Sharpe based on equity time series snapshots.
// Method:
// - compute simple returns between consecutive snapshots: r_t = eq_t / eq_{t-1} - 1
// - compute average snapshot interval and derive periodsPerYear = secsYear / avgDt
// - rf per period = rfAnnual / periodsPerYear
// - excess = r_t - rf_per_period
// - Sharpe = mean(excess)/std(excess) * sqrt(periodsPerYear)
func sharpeFromEquitySnapshots(snapshots []*EquitySnapshot, rfAnnual float64) float64 {
	if len(snapshots) < 2 {
		return 0
	}
	// ensure sorted by timestamp
	sort.Slice(snapshots, func(i, j int) bool { return snapshots[i].Ts < snapshots[j].Ts })

	const secsYear = 365.0 * 24.0 * 3600.0
	var returns []float64
	var dts []float64
	for i := 1; i < len(snapshots); i++ {
		prev := snapshots[i-1].Equity
		cur := snapshots[i].Equity
		if prev <= 0 {
			continue
		}
		returns = append(returns, cur/prev-1)
		dt := float64(snapshots[i].Ts-snapshots[i-1].Ts) / 1000.0
		if dt <= 0 {
			dt = 1.0
		}
		dts = append(dts, dt)
	}
	if len(returns) <= 1 {
		return 0
	}
	sum := 0.0
	for _, d := range dts {
		sum += d
	}
	avgDt := sum / float64(len(dts))
	periodsPerYear := secsYear / avgDt
	rfPeriod := rfAnnual / periodsPerYear

	excess := make([]float64, len(returns))
	for i := range returns {
		excess[i] = returns[i] - rfPeriod
	}
	meanEx := ta.Avg(excess)
	sd := stddev(excess)
	if sd == 0 {
		return 0
	}
	return meanEx / sd * math.Sqrt(periodsPerYear)
}

// sortinoFromEquitySnapshots computes Sortino Ratio based on equity time series snapshots.
func sortinoFromEquitySnapshots(snapshots []*EquitySnapshot, rfAnnual float64) float64 {
	if len(snapshots) < 2 {
		return 0
	}
	// ensure sorted by timestamp
	sort.Slice(snapshots, func(i, j int) bool { return snapshots[i].Ts < snapshots[j].Ts })

	const secsYear = 365.0 * 24.0 * 3600.0
	var returns []float64
	var dts []float64
	for i := 1; i < len(snapshots); i++ {
		prev := snapshots[i-1].Equity
		cur := snapshots[i].Equity
		if prev <= 0 {
			continue
		}
		returns = append(returns, cur/prev-1)
		dt := float64(snapshots[i].Ts-snapshots[i-1].Ts) / 1000.0
		if dt <= 0 {
			dt = 1.0
		}
		dts = append(dts, dt)
	}
	if len(returns) <= 1 {
		return 0
	}
	sum := 0.0
	for _, d := range dts {
		sum += d
	}
	avgDt := sum / float64(len(dts))
	periodsPerYear := secsYear / avgDt
	rfPeriod := rfAnnual / periodsPerYear

	excess := make([]float64, len(returns))
	downsideSum := 0.0
	for i := range returns {
		excess[i] = returns[i] - rfPeriod
		if excess[i] < 0 {
			downsideSum += excess[i] * excess[i]
		}
	}
	meanEx := ta.Avg(excess)
	downsideDev := math.Sqrt(downsideSum / float64(len(returns)))
	if downsideDev == 0 {
		return 0
	}
	return meanEx / downsideDev * math.Sqrt(periodsPerYear)
}

func calmarRatio(annualReturn float64, maxDrawdown float64) float64 {
	if maxDrawdown == 0 {
		return 0
	}
	return annualReturn / maxDrawdown
}

func profitFactor(orders []*trade.TradeOrder) float64 {
	grossProfit := 0.0
	grossLoss := 0.0
	for _, o := range orders {
		if o.Profit > 0 {
			grossProfit += o.Profit
		} else {
			grossLoss += math.Abs(o.Profit)
		}
	}
	if grossLoss == 0 {
		if grossProfit == 0 {
			return 0
		}
		return 999.0 // Infinite
	}
	return grossProfit / grossLoss
}

func stddev(x []float64) float64 {
	if len(x) <= 1 {
		return 0
	}
	m := ta.Avg(x)
	s := 0.0
	for _, v := range x {
		d := v - m
		s += d * d
	}
	// population or sample? use sample (n-1)
	return math.Sqrt(s / float64(len(x)-1))
}