diff --git a/calculate/metrics.go b/calculate/metrics.go new file mode 100644 index 0000000..33c8a70 --- /dev/null +++ b/calculate/metrics.go @@ -0,0 +1,110 @@ +package calculate + +import ( + "math" + + "gonum.org/v1/gonum/floats" + "gonum.org/v1/gonum/stat" + "gonum.org/v1/gonum/stat/distuv" +) + +func DownsideVolatility(values []float64, periodsPerYear float64) float64 { + negative := make([]float64, 0, len(values)) + negative = negativeValues(negative, values) + for i := range negative { + negative[i] = math.Pow(negative[i], 2) + } + x := stat.Mean(negative, nil) + return math.Sqrt(x) * math.Sqrt(periodsPerYear) +} + +func SortinoRatio(portfolio, riskFree []float64, downsideVol, periodsPerYear float64) float64 { + pr := AnnualizedArithmeticReturn(portfolio, periodsPerYear) + rr := AnnualizedArithmeticReturn(riskFree, periodsPerYear) + return (pr - rr) / downsideVol +} + +func MaxDrawdown(values []float64) (float64, int) { + retained := retainedAfterDrawdown(values) + i := floats.MinIdx(retained) + ret := retained[i] + return 1 - ret, i +} + +func CalmarRatio(portfolio, riskFree []float64, maxDrawdown, periodsPerYear float64) float64 { + pr := AnnualizedArithmeticReturn(portfolio, periodsPerYear) + rr := AnnualizedArithmeticReturn(riskFree, periodsPerYear) + return (pr - rr) / maxDrawdown +} + +func UlcerIndex(values []float64, periodsPerYear float64) float64 { + retained := retainedAfterDrawdown(values) + for i := range retained { + retained[i] = math.Pow(retained[i], 2) + } + x := stat.Mean(retained, nil) + return math.Sqrt(x) * math.Sqrt(periodsPerYear) +} + +func TrackingError(excessReturns []float64, periodsPerYear float64) float64 { + return stat.PopStdDev(excessReturns, nil) * math.Sqrt(periodsPerYear) +} + +func InformationRatio(portfolio, benchmark []float64, periodsPerYear float64) float64 { + pr := AnnualizedTimeWeightedReturn(portfolio, periodsPerYear) + br := AnnualizedTimeWeightedReturn(benchmark, periodsPerYear) + er := pr - br + + excess := make([]float64, len(portfolio)) + floats.SubTo(excess, portfolio, benchmark) + te := TrackingError(excess, periodsPerYear) + + return er / te +} + +func BetaToBenchmark(portfolio, benchmark []float64) float64 { + _, slope := stat.LinearRegression(benchmark, portfolio, nil, false) + return slope +} + +func ValueAtRisk(values []float64, portfolioValue, confidenceLevel, periodsPerYear float64) float64 { + normal := distuv.Normal{ + Mu: 0, + Sigma: 1.0, + } + zScore := normal.Quantile(confidenceLevel) + return portfolioValue * zScore * AnnualizeRisk(stat.PopStdDev(values, nil), periodsPerYear) +} + +func negativeValues(out, in []float64) []float64 { + for _, v := range in { + if v < 0 { + out = append(out, v) + } + } + return out +} + +func retainedAfterDrawdown(values []float64) []float64 { + cum := make([]float64, len(values)) + for i := range values { + if i == 0 { + cum[i] = 1 + values[i] + } else { + cum[i] = cum[i-1] * (1 + values[i]) + } + } + retained := make([]float64, len(values)) + for i := range cum { + if i == 0 { + retained[i] = 1 + continue + } + x := floats.Max(cum[0:i]) + if x < 1 { + x = 1 + } + retained[i] = cum[i] / x + } + return retained +} diff --git a/calculate/metrics_test.go b/calculate/metrics_test.go new file mode 100644 index 0000000..2e02a51 --- /dev/null +++ b/calculate/metrics_test.go @@ -0,0 +1,120 @@ +package calculate + +import ( + "bytes" + "encoding/csv" + "errors" + "io" + "os" + "path/filepath" + "strconv" + "testing" + + "github.com/stretchr/testify/assert" + "github.com/stretchr/testify/require" + "gonum.org/v1/gonum/floats" +) + +func TestMetrics(t *testing.T) { + data, err := loadTestdataReturns(filepath.FromSlash("testdata/metrics.tsv"), 3) + require.NoError(t, err) + cash, portfolio, benchmark := data[0], data[1], data[2] + assert.Len(t, cash, 10_000) + assert.Len(t, portfolio, 10_000) + assert.Len(t, benchmark, 10_000) + + // Downside Volatility 13.03% =SQRT(AVERAGE(K2:K10001))*SQRT($N$1) + t.Run("Downside Volatility", func(t *testing.T) { + result := DownsideVolatility(portfolio, PeriodsPerYear) + assert.InDelta(t, 0.1303, result, 0.0001) + }) + + // Sortino Ratio 0.17 =(N6-N5)/N12 + t.Run("Sortino Ratio", func(t *testing.T) { + downsideVol := DownsideVolatility(portfolio, PeriodsPerYear) + result := SortinoRatio(portfolio, cash, downsideVol, PeriodsPerYear) + assert.InDelta(t, 0.17, result, 0.01) + }) + + // Calmar Ratio 0.06 =N7/N17 + t.Run("Calmar Ratio", func(t *testing.T) { + maxDrawdown, _ := MaxDrawdown(portfolio) + result := CalmarRatio(portfolio, cash, maxDrawdown, PeriodsPerYear) + assert.InDelta(t, 0.059, result, 0.001) + }) + + // Ulcer Index 13.82 =SQRT(AVERAGE(I2:I10001))*SQRT(N1) + t.Run("Ulcer Index", func(t *testing.T) { + result := UlcerIndex(portfolio, PeriodsPerYear) + assert.InDelta(t, 13.82, result, 0.01) + }) + + // Max Drawdown 37.38% =1-MIN(H2:H10001) + t.Run("Max Drawdown", func(t *testing.T) { + result, _ := MaxDrawdown(portfolio) + assert.InDelta(t, 0.3738, result, 0.0001) + }) + + // Tracking Error 6.27% =STDEV.P(F2:F10001)*SQRT(N1) + t.Run("Tracking Error", func(t *testing.T) { + excess := make([]float64, len(portfolio)) + floats.SubTo(excess, portfolio, benchmark) + result := TrackingError(excess, PeriodsPerYear) + assert.InDelta(t, 0.0627, result, 0.0001) + }) + + // Information Ratio 0.06 =N9/N10 + t.Run("Information Ratio", func(t *testing.T) { + result := InformationRatio(portfolio, benchmark, PeriodsPerYear) + assert.InDelta(t, 0.06, result, 0.01) + }) + + // Beta to Benchmark 0.75 =SLOPE(D2:D10001,E2:E10001) + t.Run("Beta to Benchmark", func(t *testing.T) { + result := BetaToBenchmark(portfolio, benchmark) + assert.InDelta(t, 0.748, result, 0.001) + }) + + // VaR (5% Confidence) (2,148.94) =N18*N11*N2 + t.Run("Value at Risk aka VaR", func(t *testing.T) { + const ( + portfolioValue = 10_000.00 + confidenceLevel = 0.95 + ) + result := ValueAtRisk(portfolio, portfolioValue, confidenceLevel, PeriodsPerYear) + assert.InDelta(t, 2148.94, result, 0.01) + }) +} + +func loadTestdataReturns(fileName string, columns int) ([][]float64, error) { + buf, err := os.ReadFile(fileName) + if err != nil { + return nil, err + } + r := csv.NewReader(bytes.NewBuffer(buf)) + r.FieldsPerRecord = columns + r.Comma = '\t' + r.ReuseRecord = true + r.TrimLeadingSpace = true + data := make([][]float64, columns) + for i := 0; ; i++ { + line, err := r.Read() + if err != nil { + if errors.Is(err, io.EOF) { + break + } + return nil, err + } + if i < 1 || len(line) != 3 { + continue + } + for j := range line { + f, err := strconv.ParseFloat(line[j], 64) + if err != nil { + return nil, err + } + data[j] = append(data[j], f) + } + } + return data, nil +} diff --git a/calculate/testdata/metrics.tsv b/calculate/testdata/metrics.tsv new file mode 100644 index 0000000..e6dab7d --- /dev/null +++ b/calculate/testdata/metrics.tsv @@ -0,0 +1,10001 @@ +U.S. Cash Portfolio Benchmark +-0.000002 0.007084 0.011167 +0.000026 0.000323 0.000131 +-0.000611 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