BlackLitterman¶

class
qf_lib.portfolio_construction.black_litterman.black_litterman.
BlackLitterman
(hist_cov: qf_lib.containers.dataframe.qf_dataframe.QFDataFrame, weights: qf_lib.containers.series.qf_series.QFSeries, sample_size: int, sharpe: float = 0.5)[source]¶ Bases:
object
Creates an object allowing calculation of the distribution of the returns using Black Litterman model
 Parameters
hist_cov (QFDataFrame) – covariance matrix of historical excess returns of assets; should be annualized
weights (QFSeries) – weights of assets in the market cap index
sample_size (int) – number of simple returns used to estimate the historical covariance
sharpe (float) – average sharpe ratio of the market (by default value of 0.5 is used)
Attributes
Matrix of variance of the views Matrix is square and diagonal.
Matrix of views P.
Vector of expected performance Q.
Methods
add_absolute_view
(asset_index, …)Adds a new view that will be taken into account in calculating the posterior
add_relative_view
(outperforming_asset_index, …)Adds a new view that will be taken into account in calculating the posterior
Calculates lambda corresponding to risk aversion in the formula:
Calculate shape of posterior distribution including the views.
Function calculates the prior for the BL model:

property
Omega
¶ Matrix of variance of the views Matrix is square and diagonal. Each value Omega[i,i] corresponds to the variance of a specific view nr of rows = number of different views nr of columns = number of different views For example:  (0.0001, 0.0000) means we expect volatility of the first view to be sqrt(0.0001) = 0.01 = 1%  (0.0000, 0.0025) means we expect volatility of the first view to be sqrt(0.0025) = 0.05 = 5% NOTE: self._omega is stored as horizontal vector. Values are copied on diagonal

property
P
¶ Matrix of views P. nr of rows = number of different views nr of columns = number of assets Example for 4 assets and 2 views:
(0, 1, 0, 0) means go long second asset
(0, 1, 0, 1) means go long second asset while shorting first asset

property
Q
¶ Vector of expected performance Q. Also sometimes refered as vector v nr of rows = number of different views nr of columns = 1 For example:  [0.10]  [0.03] means that we have two views and we expect to realise 10% above risk free rate on first view and 3% on second

add_absolute_view
(asset_index: int, outperformance: float, view_vol: float)[source]¶ Adds a new view that will be taken into account in calculating the posterior
 Parameters
short_asset_index (int) – index of the asset that we expect to outperform the market (indexing starts at 0)
outperformance (float) – how much are we expecting one asset to outperform the market
view_vol (float) – volatility of the view. This is the measure of a standard deviation of the outperformance value. For example: 0.02 means that the real outperformance will be provided outperformance + 2% within one standard deviation confidence interval.

add_relative_view
(outperforming_asset_index: int, underperforming_asset_index: int, outperformance: float, view_vol: float)[source]¶ Adds a new view that will be taken into account in calculating the posterior The investor believs that outperforming_asset will outperform the underperforming_asset by outperformance with the volatility of the view of view_vol
 Parameters
outperforming_asset_index (int) – index of the asset that you believe will outperform (indexing starts at 0)
underperforming_asset_index (int) – index of the asset that you believe will underperform (indexing starts at 0)
outperformance (float) – how much are we expecting one asset to outperform the other
view_vol (float) – volatility of the outperformance. This is the measure of a standard deviation of the outperformance value. For example: 0.02 means that the real outperformance will be provided outperformance + 2% within one standard deviation confidence interval.

calculate_lambda
()[source]¶ Calculates lambda corresponding to risk aversion in the formula: max(w): w’R  lambda/2 * w’ * Cov * w:
lambda is calculated in the followign way: lambda = sharpe_ratio_of_market / vol_of_market.

calculate_posterior
() → Tuple[qf_lib.containers.series.qf_series.QFSeries, qf_lib.containers.dataframe.qf_dataframe.QFDataFrame][source]¶ Calculate shape of posterior distribution including the views. It is calculated using a numerically stable formula posterior_mean = prior_mean + tau * hist_cov * P’ * ( tau * P * hist_cov * P’ + Omega)^(1) * (Q  P * prior_mean) posterior_cov = (1 + tau) * hist_cov  tau^2 * hist_cov * P’ * (tau * P * hist_cov * P’ + Omega)^(1) * P * hist_cov
 Returns
 Return type
Tuple[QFSeries, QFDataFrame]

calculate_prior
() → Tuple[qf_lib.containers.series.qf_series.QFSeries, qf_lib.containers.dataframe.qf_dataframe.QFDataFrame][source]¶ Function calculates the prior for the BL model:  prior_mean = lambda * hist_cov * market_cap_weights  prior_cov = tau * hist_cov
 Returns
Tuple(prior_mean, prior_cov)
 Return type
Tuple[QFSeries, QFDataFrame]