diff --git a/qlib/model/riskmodel.py b/qlib/model/riskmodel.py
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+++ b/qlib/model/riskmodel.py
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+# Copyright (c) Microsoft Corporation.
+# Licensed under the MIT License.
+
+import warnings
+import numpy as np
+import pandas as pd
+
+from typing import Union
+
+from qlib.model.base import BaseModel
+
+
+class RiskModel(BaseModel):
+    """Risk Model
+
+    A risk model is used to estimate the covariance matrix of stock returns.
+    """
+
+    MASK_NAN = 'mask'
+    FILL_NAN = 'fill'
+    IGNORE_NAN = 'ignore'
+
+    def __init__(self, nan_option: str = 'ignore', assume_centered: bool = False, scale_return: bool = True):
+        """
+        Args:
+            nan_option (str): nan handling option (`ignore`/`mask`/`fill`)
+            assume_centered (bool): whether the data is assumed to be centered
+            scale_return (bool): whether scale returns as percentage
+        """
+        # nan
+        assert nan_option in [self.MASK_NAN, self.FILL_NAN, self.IGNORE_NAN], \
+            f'`nan_option={nan_option}` is not supported'
+        self.nan_option = nan_option
+
+        self.assume_centered = assume_centered
+        self.scale_return = scale_return
+
+    def predict(self, X: Union[pd.Series, pd.DataFrame, np.ndarray],
+                return_corr: bool = False, is_price: bool = True) -> Union[pd.DataFrame, np.ndarray]:
+        """
+        Args:
+            X (pd.Series, pd.DataFrame or np.ndarray): data from which to estimate the covariance,
+                with variables as columns and observations as rows.
+            return_corr (bool): whether return the correlation matrix
+            is_price (bool): whether `X` contains price (if not assume stock returns)
+
+        Returns:
+            pd.DataFrame or np.ndarray: estimated covariance (or correlation)
+        """
+        # transform input into 2D array
+        if not isinstance(X, (pd.Series, pd.DataFrame)):
+            columns = None
+        else:
+            if isinstance(X.index, pd.MultiIndex):
+                if isinstance(X, pd.DataFrame):
+                    X = X.iloc[:, 0].unstack(level='instrument') # always use the first column
+                else:
+                    X = X.unstack(level='instrument')
+            else:
+                # X is 2D DataFrame
+                pass
+            columns = X.columns # will be used to restore dataframe
+            X = X.values
+
+        # calculate pct_change
+        if is_price:
+            X = X[1:] / X[:-1] - 1 # NOTE: resulting `n - 1` rows
+
+        # scale return
+        if self.scale_return:
+            X *= 100
+
+        # handle nan and centered
+        X = self._preprocess(X)
+
+        # estimate covariance
+        S = self._predict(X)
+
+        # return correlation if needed
+        if return_corr:
+            vola = np.sqrt(np.diag(S))
+            corr = S / np.outer(vola, vola)
+            if columns is None:
+                return corr
+            return pd.DataFrame(corr, index=columns, columns=columns)
+
+        # return covariance
+        if columns is None:
+            return S
+        return pd.DataFrame(S, index=columns, columns=columns)
+
+    def _predict(self, X: np.ndarray) -> np.ndarray:
+        """covariance estimation implementation
+
+        This method should be overridden by child classes.
+
+        By default, this method implements the empirical covariance estimation.
+
+        Args:
+            X (np.ndarray): data matrix containing multiple variables (columns) and observations (rows)
+
+        Returns:
+            np.ndarray: covariance matrix
+        """
+        xTx = np.asarray(X.T.dot(X))
+        N = len(X)
+        if isinstance(X, np.ma.MaskedArray):
+            M = 1 - X.mask
+            N = M.T.dot(M) # each pair has distinct number of samples
+        return xTx / N
+
+    def _preprocess(self, X: np.ndarray) -> Union[np.ndarray, np.ma.MaskedArray]:
+        """handle nan and centerize data
+
+        Note:
+            if `nan_option='mask'` then the returned array will be `np.ma.MaskedArray`
+        """
+        # handle nan
+        if self.nan_option == self.FILL_NAN:
+            X = np.nan_to_num(X)
+        elif self.nan_option == self.MASK_NAN:
+            X = np.ma.masked_invalid(X)
+        # centerize
+        if not self.assume_centered:
+            X = X - np.nanmean(X, axis=0)
+        return X
+
+
+class ShrinkCovEstimator(RiskModel):
+    """Shrinkage Covariance Estimator
+
+    This estimator will shrink the sample covariance matrix towards
+    an identify matrix:
+        S_hat = (1 - alpha) * S + alpha * F
+    where `alpha` is the shrink parameter and `F` is the shrinking target.
+
+    The following shrinking parameters (`alpha`) are supported:
+        - `lw` [1][2][3]: use Ledoit-Wolf shrinking parameter
+        - `oas` [4]: use Oracle Approximating Shrinkage shrinking parameter
+        - float: directly specify the shrink parameter, should be between [0, 1]
+
+    The following shrinking targets (`F`) are supported:
+        - `const_var` [1][4][5]: assume stocks have the same constant variance and zero correlation
+        - `const_corr` [2][6]: assume stocks have different variance but equal correlation
+        - `single_factor` [3][7]: assume single factor model as the shrinking target
+        - np.ndarray: provide the shrinking targets directly
+
+    Note:
+        - The optimal shrinking parameter depends on the selection of the shrinking target.
+            Currently, `oas` is not supported for `const_corr` and `single_factor`.
+        - Remember to set `nan_option` to `fill` or `mask` if your data has missing values.
+
+    References:
+        [1] Ledoit, O., & Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices.
+            Journal of Multivariate Analysis, 88(2), 365–411. https://doi.org/10.1016/S0047-259X(03)00096-4
+        [2] Ledoit, O., & Wolf, M. (2004). Honey, I shrunk the sample covariance matrix.
+            Journal of Portfolio Management, 30(4), 1–22. https://doi.org/10.3905/jpm.2004.110
+        [3] Ledoit, O., & Wolf, M. (2003). Improved estimation of the covariance matrix of stock returns
+            with an application to portfolio selection.
+            Journal of Empirical Finance, 10(5), 603–621. https://doi.org/10.1016/S0927-5398(03)00007-0
+        [4] Chen, Y., Wiesel, A., Eldar, Y. C., & Hero, A. O. (2010). Shrinkage algorithms for MMSE covariance estimation.
+            IEEE Transactions on Signal Processing, 58(10), 5016–5029. https://doi.org/10.1109/TSP.2010.2053029
+        [5] https://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-0000-00007f64e5b9/cov1para.m.zip
+        [6] https://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-ffff-ffffde5e2d4e/covCor.m.zip
+        [7] https://www.econ.uzh.ch/dam/jcr:ffffffff-935a-b0d6-0000-0000648dfc98/covMarket.m.zip
+    """
+
+    SHR_LW = 'lw'
+    SHR_OAS = 'oas'
+
+    TGT_CONST_VAR = 'const_var'
+    TGT_CONST_CORR = 'const_corr'
+    TGT_SINGLE_FACTOR = 'single_factor'
+
+    def __init__(self, alpha: Union[str, float] = 0.0, target: Union[str, np.ndarray] = 'const_var', **kwargs):
+        """
+        Args:
+            alpha (str or float): shrinking parameter or estimator (`lw`/`oas`)
+            target (str or np.ndarray): shrinking target (`const_var`/`const_corr`/`single_factor`)
+            kwargs: see `RiskModel` for more information
+        """
+        super().__init__(**kwargs)
+
+        # alpha
+        if isinstance(alpha, str):
+            assert alpha in [self.SHR_LW, self.SHR_OAS], \
+                f'shrinking method `{alpha}` is not supported'
+        elif isinstance(alpha, (float, np.floating)):
+            assert 0 <= alpha <= 1, 'alpha should be between [0, 1]'
+        else:
+            raise TypeError('invalid argument type for `alpha`')
+        self.alpha = alpha
+
+        # target
+        if isinstance(target, str):
+            assert target in [self.TGT_CONST_VAR, self.TGT_CONST_CORR, self.TGT_SINGLE_FACTOR], \
+                f'shrinking target `{target} is not supported'
+        elif isinstance(target, np.ndarray):
+            pass
+        else:
+            raise TypeError('invalid argument type for `target`')
+        if alpha == self.SHR_OAS and target != self.TGT_CONST_VAR:
+            raise NotImplementedError('currently `oas` can only support `const_var` as target')
+        self.target = target
+
+    def _predict(self, X: np.ndarray) -> np.ndarray:
+        # sample covariance
+        S = super()._predict(X)
+
+        # shrinking target
+        F = self._get_shrink_target(X, S)
+
+        # get shrinking parameter
+        alpha = self._get_shrink_param(X, S, F)
+
+        # shrink covariance
+        if alpha > 0:
+            S *= (1 - alpha)
+            F *= alpha
+            S += F
+
+        return S
+
+    def _get_shrink_target(self, X: np.ndarray, S: np.ndarray) -> np.ndarray:
+        """get shrinking target `F`"""
+        if self.target == self.TGT_CONST_VAR:
+            return self._get_shrink_target_const_var(X, S)
+        if self.target == self.TGT_CONST_CORR:
+            return self._get_shrink_target_const_corr(X, S)
+        if self.target == self.TGT_SINGLE_FACTOR:
+            return self._get_shrink_target_single_factor(X, S)
+
+    def _get_shrink_target_const_var(self, X: np.ndarray, S: np.ndarray) -> np.ndarray:
+        """get shrinking target with constant variance
+
+        This target assumes zero pair-wise correlation and constant variance.
+        The constant variance is estimated by averaging all sample's variances.
+        """
+        n = len(S)
+        F = np.eye(n)
+        np.fill_diagonal(F, np.mean(np.diag(S)))
+        return F
+
+    def _get_shrink_target_const_corr(self, X: np.ndarray, S: np.ndarray) -> np.ndarray:
+        """get shrinking target with constant correlation
+
+        This target assumes constant pair-wise correlation but keep the sample variance.
+        The constant correlation is estimated by averaging all pairwise correlations.
+        """
+        n = len(S)
+        var = np.diag(S)
+        sqrt_var = np.sqrt(var)
+        covar = np.outer(sqrt_var, sqrt_var)
+        r_bar = (np.sum(S / covar) - n) / (n * (n - 1))
+        F = r_bar * covar
+        np.fill_diagonal(F, var)
+        return F
+
+    def _get_shrink_target_single_factor(self, X: np.ndarray, S: np.ndarray) -> np.ndarray:
+        """get shrinking target with single factor model"""
+        X_mkt = np.nanmean(X, axis=1)
+        cov_mkt = np.asarray(X.T.dot(X_mkt) / len(X))
+        var_mkt = np.asarray(X_mkt.dot(X_mkt) / len(X))
+        F = np.outer(cov_mkt, cov_mkt) / var_mkt
+        np.fill_diagonal(F, np.diag(S))
+        return F
+
+    def _get_shrink_param(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
+        """get shrinking parameter `alpha`
+
+        Note:
+            The Ledoit-Wolf shrinking parameter estimator consists of three different
+        """
+        if self.alpha == self.SHR_OAS:
+            return self._get_shrink_param_oas(X, S, F)
+        elif self.alpha == self.SHR_LW:
+            if self.target == self.TGT_CONST_VAR:
+                return self._get_shrink_param_lw_const_var(X, S, F)
+            if self.target == self.TGT_CONST_CORR:
+                return self._get_shrink_param_lw_const_corr(X, S, F)
+            if self.target == self.TGT_SINGLE_FACTOR:
+                return self._get_shrink_param_lw_single_factor(X, S, F)
+        return self.alpha
+
+    def _get_shrink_param_oas(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
+        """Oracle Approximating Shrinkage Estimator
+
+        This method uses the following formula to estimate the `alpha`
+        parameter for the shrink covariance estimator:
+            A = (1 - 2 / p) * trace(S^2) + trace^2(S)
+            B = (n + 1 - 2 / p) * (trace(S^2) - trace^2(S) / p)
+            alpha = A / B
+        where `n`, `p` are the dim of observations and variables respectively.
+        """
+        trS2 = np.sum(S**2)
+        tr2S = np.trace(S)**2
+
+        n, p = X.shape
+
+        A = (1 - 2 / p) * (trS2 + tr2S)
+        B = (n + 1 - 2 / p) * (trS2 + tr2S / p)
+        alpha = A / B
+
+        return alpha
+
+    def _get_shrink_param_lw_const_var(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
+        """Ledoit-Wolf Shrinkage Estimator (Constant Variance)
+
+        This method shrinks the covariance matrix towards the constand variance target.
+        """
+        t, n = X.shape
+
+        y = X**2
+        phi = np.sum(y.T.dot(y) / t - S**2)
+
+        gamma = np.linalg.norm(S - F, 'fro')**2
+
+        kappa = phi / gamma
+        alpha = max(0, min(1, kappa / t))
+
+        return alpha
+
+    def _get_shrink_param_lw_const_corr(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
+        """Ledoit-Wolf Shrinkage Estimator (Constant Correlation)
+
+        This method shrinks the covariance matrix towards the constand correlation target.
+        """
+        t, n = X.shape
+
+        var = np.diag(S)
+        sqrt_var = np.sqrt(var)
+        r_bar = (np.sum(S / np.outer(sqrt_var, sqrt_var)) - n) / (n * (n - 1))
+
+        y = X**2
+        phi_mat = y.T.dot(y) / t - S**2
+        phi = np.sum(phi_mat)
+
+        theta_mat = (X**3).T.dot(X) / t - var[:, None] * S
+        np.fill_diagonal(theta_mat, 0)
+        rho = np.sum(np.diag(phi_mat)) + r_bar * np.sum(np.outer(1 / sqrt_var, sqrt_var) * theta_mat)
+
+        gamma = np.linalg.norm(S - F, 'fro')**2
+
+        kappa = (phi - rho) / gamma
+        alpha = max(0, min(1, kappa / t))
+
+        return alpha
+
+    def _get_shrink_param_lw_single_factor(self, X: np.ndarray, S: np.ndarray, F: np.ndarray) -> float:
+        """Ledoit-Wolf Shrinkage Estimator (Single Factor Model)
+
+        This method shrinks the covariance matrix towards the single factor model target.
+        """
+        t, n = X.shape
+
+        X_mkt = np.nanmean(X, axis=1)
+        cov_mkt = np.asarray(X.T.dot(X_mkt) / len(X))
+        var_mkt = np.asarray(X_mkt.dot(X_mkt) / len(X))
+
+        y = X**2
+        phi = np.sum(y.T.dot(y)) / t - np.sum(S**2)
+
+        rdiag = np.sum(y**2) / t - np.sum(np.diag(S)**2)
+        z = X * X_mkt[:, None]
+        v1 = y.T.dot(z) / t - cov_mkt[:, None] * S
+        roff1 = np.sum(v1 * cov_mkt[:, None].T) / var_mkt - np.sum(np.diag(v1) * cov_mkt) / var_mkt
+        v3 = z.T.dot(z) / t - var_mkt * S
+        roff3 = np.sum(v3 * np.outer(cov_mkt, cov_mkt)) / var_mkt**2 - np.sum(np.diag(v3) * cov_mkt**2) / var_mkt**2
+        roff = 2 * roff1 - roff3
+        rho = rdiag + roff
+
+        gamma = np.linalg.norm(S - F, 'fro')**2
+
+        kappa = (phi - rho) / gamma
+        alpha = max(0, min(1, kappa / t))
+
+        return alpha
+
+
+class POETCovEstimator(RiskModel):
+    """Principal Orthogonal Complement Thresholding Estimator (POET)
+
+    Reference:
+        [1] Fan, J., Liao, Y., & Mincheva, M. (2013). Large covariance estimation by thresholding principal orthogonal complements.
+            Journal of the Royal Statistical Society. Series B: Statistical Methodology, 75(4), 603–680. https://doi.org/10.1111/rssb.12016
+        [2] http://econweb.rutgers.edu/yl1114/papers/poet/POET.m
+    """
+
+    THRESH_SOFT = 'soft'
+    THRESH_HARD = 'hard'
+    THRESH_SCAD = 'scad'
+
+    def __init__(self, num_factors: int = 0, thresh: float = 1.0, thresh_method: str = 'soft', **kwargs):
+        """
+        Args:
+            num_factors (int): number of factors (if set to zero, no factor model will be used)
+            thresh (float): the positive constant for thresholding
+            thresh_method (str): thresholding method, which can be
+                - 'soft': soft thresholding
+                - 'hard': hard thresholding
+                - 'scad': scad thresholding
+            kwargs: see `RiskModel` for more information
+        """
+        super().__init__(**kwargs)
+
+        assert num_factors >= 0, '`num_factors` requires a positive integer'
+        self.num_factors = num_factors
+
+        assert thresh >= 0, '`thresh` requires a positive float number'
+        self.thresh = thresh
+
+        assert thresh_method in [self.THRESH_HARD, self.THRESH_SOFT, self.THRESH_SCAD], \
+            '`thresh_method` should be `soft`/`hard`/`scad`'
+        self.thresh_method = thresh_method
+
+    def _predict(self, X: np.ndarray) -> np.ndarray:
+
+        Y = X.T # NOTE: to match POET's implementation
+        p, n = Y.shape
+
+        if self.num_factors > 0:
+            Dd, V = np.linalg.eig(Y.T.dot(Y))
+            V = V[:, np.argsort(Dd)]
+            F = V[:, -self.num_factors:][:, ::-1] * np.sqrt(n)
+            LamPCA = Y.dot(F) / n
+            uhat = np.asarray(Y - LamPCA.dot(F.T))
+            Lowrank = np.asarray(LamPCA.dot(LamPCA.T))
+            rate = 1 / np.sqrt(p) + np.sqrt(np.log(p) / n)
+        else:
+            uhat = np.asarray(Y)
+            rate = np.sqrt(np.log(p) / n)
+            Lowrank = 0
+
+        lamb = rate * self.thresh
+        SuPCA = uhat.dot(uhat.T) / n
+        SuDiag = np.diag(np.diag(SuPCA))
+        R = np.linalg.inv(SuDiag**0.5).dot(SuPCA).dot(np.linalg.inv(SuDiag**0.5))
+
+        if self.thresh_method == self.THRESH_HARD:
+            M = R * (np.abs(R) > lamb)
+        elif self.thresh_method == self.THRESH_SOFT:
+            res = (np.abs(R) - lamb)
+            res = (res + np.abs(res)) / 2
+            M = np.sign(R) * res
+        else:
+            M1 = (np.abs(R) < 2 * lamb) * np.sign(R) * (np.abs(R) - lamb) * (np.abs(R) > lamb)
+            M2 = (np.abs(R) < 3.7 * lamb) * (np.abs(R) >= 2 * lamb) * (2.7 * R - 3.7 * np.sign(R) * lamb) / 1.7
+            M3 = (np.abs(R) >= 3.7 * lamb) * R
+            M = M1 + M2 + M3
+
+        Rthresh = M - np.diag(np.diag(M)) + np.eye(p)
+        SigmaU = (SuDiag**0.5).dot(Rthresh).dot(SuDiag**0.5)
+        SigmaY = SigmaU + Lowrank
+
+        return SigmaY