Repository for the dashboard app deployed here
This is an implementation of the Modern Portfolio Theory MPT. Here, I have applied the MPT on the stocks listed at the National Stock Exchange in India (NSE). I have engineered two portfolios, a high risk-high reward strategy portfolio labelled below as Maximum Sharpe Ratio Portfolio (Blue) and another that gives good returns with very low risk labelled below as Minimum Volatility Portfolio (Red) and another portfolio that works on.
Both the portfolios vastly overperform the benchmark as seen here (Benchmark Nifty 50 in green). An interesting observation from this portfolio is the minimal drawdown during the onset of Covid induced market correction for the minimum volatility portfolio (Highlighted in Red).
In addition to the point to point returns, the dashboard also lists the performance of the engineered portfolios with the benchmark (Nifty50) and with another low volatility portfolio.
The main idea is to designate weights to individual stocks such that the resulting portfolio maximizes the returns while maximizing the Sharpe Ratio (Risk Adjusted Returns). So given the mean returns and covariance betweeen the individual stocks, I define the negative sharpe ratio as:
def negative_sharpe_ratio(weights, mean_returns, cov_matrix, risk_free_rate=0.0):
"""
Calculate the negative Sharpe Ratio.
Parameters
----------
weights : numpy.ndarray or list of floats
Weightage of each stock in the final portfolio.
mean_returns : pandas.core.series.Series
Arithematic mean of the daily stock returns between the given datetime
range.
cov_matrix : pandas.core.frame.DataFrame
Covariance matrix containing the covariance between the stocks in the
stock_list.
risk_free_rate : float, optional
Rate at which one can borrow with zero volatility. The default is 0.0.
Returns
-------
float
Return the negative Sharpe ratio.
"""
p_returns, p_std = portfolio_performance(weights, mean_returns, cov_matrix)
return -(p_returns-risk_free_rate)/p_stdThis is then maximized using scipy.minimize
def maximize_sharpe_ratio(mean_returns, cov_matrix, risk_free_rate=0, constraint_set=(0, 1)):
"""
Get the weights for stocks that will get maximum Sharpe ratio.
Parameters
----------
mean_returns : pandas.core.series.Series
Arithematic mean of the daily stock returns between the given datetime
range.
cov_matrix : pandas.core.frame.DataFrame
Covariance matrix containing the covariance between the stocks in the
stock_list.
risk_free_rate : float, optional
Rate at which one can borrow with zero volatility. The default is 0.0.
constraintSet : tuple, optional
Constraint on the percentage allocation of each stock in the portfolio.
The default is (0, 1).
Returns
-------
results : numpy.ndarray
Returns the weights for given stocks such that the portfolio has
the maximum sharp ratio.
"""
num_assets = len(mean_returns)
args = (mean_returns, cov_matrix, risk_free_rate)
constraints = ({'type': 'eq', 'fun': lambda x: np.sum(x) - 1})
bound = constraint_set
bounds = tuple(bound for asset in range(num_assets))
results = sc.minimize(negative_sharpe_ratio, np.full(num_assets, 1/num_assets),
args=args, method='SLSQP', bounds=bounds,
constraints=constraints)
return resultsIn case you need help or have suggestions or you want to report an issue, please do so in a reproducible example at the corresponding GitHub page.