def VolatilityRegimeAdjustment(ret,
forcast_volitility,
half_life=90,
forcast_num=21):
BiasStats = pd.Series(np.nan, index=forcast_volitility.index)
for i, iDate in enumerate(forcast_volitility.index):
iInd = (ret.index <= iDate).sum() - 1
if forcast_num > 0:
if ret.shape[0] >= iInd + forcast_num + 1:
iRet = (1 +
ret.iloc[iInd + 1:iInd + forcast_num + 1]).prod() - 1
else:
continue
else:
if i == forcast_volitility.shape[0] - 1:
continue
else:
iNextDate = forcast_volitility.index[i + 1]
iNextInd = (ret.index <= iNextDate).sum() - 1
iRet = (1 + ret.iloc[iInd + 1:iNextInd + 1]).prod() - 1
iTemp = (iRet / forcast_volitility.loc[iDate])**2
BiasStats.loc[iDate] = iTemp.sum() / pd.notnull(iTemp).sum()
BiasStats = BiasStats[pd.notnull(BiasStats)]
Weight = getExpWeight(ret.shape[0], half_life=half_life, is_unitized=False)
Weight.reverse()
Weight = pd.Series(Weight, index=ret.index)
Weight = Weight[BiasStats.index] / Weight[BiasStats.index].sum()
return (Weight * BiasStats**2).sum()**0.5
def estimateSampleCovMatrix_EWMA(ret, forcast_num=1, half_life=np.inf):
Weight = np.flipud(np.array(getExpWeight(ret.shape[0], half_life)))
Weight = np.repeat(np.reshape(Weight, (ret.shape[0], 1)),
ret.shape[1],
axis=1)
Mask = (~np.isnan(ret))
Weight = Weight * Mask
WeightSqrt = Weight**0.5
ret = np.copy(ret)
ret[~Mask] = 0.0
ret = ret * WeightSqrt
TotalWeight = np.dot(WeightSqrt.T, WeightSqrt)
TotalWeight[TotalWeight == 0] = np.nan
BiasAdjust = (TotalWeight**2 - np.dot(Weight.T, Weight))
BiasAdjust[BiasAdjust == 0] = np.nan
BiasAdjust = TotalWeight**2 / BiasAdjust
AvgRet1 = np.dot(ret.T, WeightSqrt) / TotalWeight
AvgRet2 = np.dot(WeightSqrt.T, ret) / TotalWeight
CovMatrix = (np.dot(ret.T, ret) / TotalWeight -
AvgRet1 * AvgRet2) * BiasAdjust
Vol = np.diag(CovMatrix)**0.5
Temp = (
(np.dot((ret**2).T, Mask) / TotalWeight - AvgRet1**2) *
(np.dot(Mask.T, ret**2) / TotalWeight - AvgRet2**2))**0.5 * BiasAdjust
Temp[Temp == 0] = np.nan
CovMatrix = (CovMatrix / Temp * Vol).T * Vol
return (CovMatrix.T + CovMatrix) / 2 * forcast_num
def estimateCovMatrix(ret,
forcast_num=21,
auto_corr_num=10,
half_life=480,
calc_cov=True):
if forcast_num > auto_corr_num + 1:
N = auto_corr_num
else:
N = forcast_num - 1
Weight = np.flipud(np.array(getExpWeight(ret.shape[0], half_life)))
if calc_cov:
CovMatrix = pd.DataFrame(np.nan,
index=ret.columns,
columns=ret.columns)
for j, jCol in enumerate(ret.columns):
for kCol in ret.columns[j:]:
jRet = ret[jCol].values
kRet = ret[kCol].values
Covs = np.zeros(N * 2 + 1)
Coefs = np.zeros(N * 2 + 1)
for Delta in range(-N, N + 1):
Coefs[Delta + N] = N + 1 - np.abs(Delta)
Covs[Delta + N] = calcCovariance(jRet, kRet, Weight, Delta)
CovMatrix[jCol][kCol] = np.nansum(Coefs * Covs)
CovMatrix[kCol][jCol] = CovMatrix[jCol][kCol]
else:
Columns = ret.columns
CovMatrix = np.zeros(ret.shape[1]) + np.nan
ret = ret.values
for j in range(ret.shape[1]):
jRet = ret[:, j]
Covs = np.zeros(N * 2 + 1)
Coefs = np.zeros(N * 2 + 1)
for Delta in range(-N, N + 1):
Coefs[Delta + N] = N + 1 - np.abs(Delta)
Covs[Delta + N] = calcCovariance(jRet, jRet, Weight, Delta)
CovMatrix[j] = np.nansum(Coefs * Covs)
CovMatrix = pd.Series(CovMatrix, index=Columns)
CovMatrix = CovMatrix * forcast_num / (N + 1)
return CovMatrix