LETS PLOT THE COMPARISON

[ ]: Stochastic Gradient Descent algorithm [56]: X_np = X. values Y_np = Y. values n,k=X_np . shape m=Y_np . shape[1] params=np . zeros ( (k,m) , dtype=float) sse={} for i in range(1, iters+1): Y_hat=x_np @ params grads=(X_np . T@(Y_hat-Y_np)) params-=lr*grads sse[i]=np. sum( (Y_np-Y_hat)**2) params_df = pd. DataFrame(params, index=X. columns, columns=Y. columns) [57]: params_df . round(6) [57] : Low Equity Medium Equity High Equity const 0.002829 0.001831 0.001398 SA Equity 0.167218 0.351015 0.437615 SA Bonds 0.075452 0.032487 0.019809 SA Property 0.055711 0.046449 0.045622 SA Cash 0.011567 0.010205 0.011823 Offshore Equity 0.087795 0.123234 0.138990 Offshore Bonds 0.032450 0.036426 0.043553 [59]: comparison=pd . concat([beta_cf, params_df], axis=1, keys=["Closed Form","SGD"]) [60]: comparison [60 ] : Closed Form SGD Low Equity Medium Equity High Equity Low Equity Medium Equity High Equity const -0.000350 -0.001181 -0.002121 0.002829 0.001831 0.001398 SA Equity 0.167747 0.353080 0.440542 0.167218 0.351015 0.437615 SA Bonds 0.080727 0.029612 0.013444 0.075452 0.032487 0.019809 SA Property 0.054168 0.046160 0.045769 0.055711 0.046449 0.045622 SA Cash 0.547691 0.525145 0.616062 0.011567 0.010205 0.011823