func (self SGD) addBiasToMatrix(x mat.MatrixRO) *mat.DenseMatrix {
xb := mat.Ones(x.Rows(), self.InputDims()+1)
for r := 0; r < x.Rows(); r++ {
for i := 0; i < self.InputDims(); i++ {
xb.Set(r, i, x.Get(r, i))
}
}
return xb
}
// generateReturns generates performance specifically for assets, and returns
// separately by asset class as a map
// Receiver: SimulationData
// Params: numberOfMonths int -- number of periods to model
// Returns: returnResultsByAsset
func (s *SimulationData) generateReturns(numberOfMonths int) returnResultsByAsset {
assetPerformanceData := s.AssetPerformanceData // map[string]Distribution
assetClassIds := s.assetClassIds() // []string
numberOfAssets := len(assetClassIds)
choleskyApplied := s.applyCholeskyDecomposition(numberOfMonths)
prices := goMatrix.Zeros(numberOfMonths, numberOfAssets)
for row := 0; row < prices.Rows(); row++ {
for column := 0; column < prices.Cols(); column++ {
var startingValue float64
if row == 0 {
startingValue = 0.0
} else {
startingValue = prices.Get((row - 1), column)
}
assetId := assetClassIds[column] // These are sorted alphabetically
assetStats := assetPerformanceData[assetId]
assetMeanReturn := assetStats.Mean
assetStdDev := assetStats.StdDev
b := assetMeanReturn - 0.5*math.Pow(assetStdDev, 2)
c := assetStdDev * choleskyApplied.Get(row, column)
// Can't do the exp(x) in the same step as you need to use the previous value as a starting price!
prices.Set(row, column, (startingValue + b + c))
}
}
for row := 0; row < prices.Rows(); row++ {
for column := 0; column < prices.Cols(); column++ {
basePrice := prices.Get(row, column)
expPrice := math.Exp(basePrice)
prices.Set(row, column, expPrice)
}
}
/* Convert prices to relative returns. */
// Add T=0, price=1.0
initialPrices := goMatrix.Ones(1, numberOfAssets)
augmentedPrices, _ := initialPrices.Stack(prices)
// Create base matrix
asRelativeReturns := goMatrix.Zeros(numberOfMonths, numberOfAssets)
// Each row in the prices matrix is a list of asset prices in each year - NOT
// the progression of a single asset. We'll need to grab columns for that.
for column := 0; column < augmentedPrices.Cols(); column++ {
priceValues := augmentedPrices.GetColVector(column).Array() // []float64
for periodIndex, periodPrice := range priceValues {
if periodIndex == 0 {
// Nothing to do on the first column
continue
}
lastPrice := priceValues[periodIndex-1]
pctReturn := (periodPrice - lastPrice) / lastPrice
asRelativeReturns.Set((periodIndex - 1), column, pctReturn)
}
}
/* */
results := asRelativeReturns.Arrays() // [][]float64
resultsByAsset := returnResultsByAsset{} // map[string][]float64
for _, assetClassId := range assetClassIds {
resultsByAsset[assetClassId] = make([]float64, numberOfMonths)
}
for periodIndex, resultSet := range results {
for assetIndex, returnResult := range resultSet {
assetClassId := assetClassIds[assetIndex]
resultsByAsset[assetClassId][periodIndex] = returnResult
}
}
return resultsByAsset
}