cvxpy two: risk preference
When you invest in stocks you want to get a high return, but a low risk. There's also going to be a few constraints. That sounds like a job for cvxpy.
The code is not listed in the video, but if you want to repeat this yourself, you can use the following code to make the same charts.
def solve_problem(dataf, risk_pref=0.1): mean_stock = dataf.diff().mean().values cov_stock = dataf.diff().cov().values x = cp.Variable(len(mean_stock)) stock_return = mean_stock.T * x stock_risk = cp.quad_form(x, cov_stock) objective = cp.Maximize(stock_return - risk_pref * stock_risk) constraints = [cp.sum(x) == 1, x >= 0] prob = cp.Problem(objective=objective, constraints=constraints) return prob.solve(), x.value import numpy as np import matplotlib.pylab as plt steps = np.linspace(0.01, 2, 100) x_vals = np.zeros((steps.shape, 4)) profit = np.zeros(steps.shape) for i, r in enumerate(steps): p, xs = solve_problem(df_stocks.set_index('Date'), risk_pref=r) x_vals[i, :] = xs profit[i] = p
plt.figure(figsize=(12, 4)) plt.plot(steps, profit) plt.xlabel("risk avoidance") plt.ylabel("1 day ahead expected return");
plt.figure(figsize=(12, 4)) tickers = ["MSFT", "KLM", "ING", "MOS"] for idx, stock in enumerate(tickers): plt.plot(steps, x_vals[:, idx], label=stock) plt.xlabel("risk avoidance") plt.ylabel("proportion of investment") plt.legend();
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