DEBUG: add time in each cell

Author: kp992

lectures/black_litterman.md

@@ -171,6 +171,8 @@ A common reaction to these outcomes is that they are so implausible that a portf
 manager cannot recommend them to a customer.
 
 ```{code-cell} ipython3
+%%time
+
 np.random.seed(12)
 
 N = 10                                           # Number of assets
@@ -302,6 +304,8 @@ a pair $(\delta_m, \mu_m)$ that tells the customer to hold the
 market portfolio.
 
 ```{code-cell} ipython3
+%%time
+
 # Observed mean excess market return
 r_m = w_m @ μ_est
 
@@ -387,6 +391,8 @@ and $\tau$ is chosen heavily to weight this view, then the
 customer's portfolio will involve big short-long positions.
 
 ```{code-cell} ipython3
+%%time
+
 def black_litterman(λ, μ1, μ2, Σ1, Σ2):
     """
     This function calculates the Black-Litterman mixture
@@ -610,6 +616,8 @@ $\bar d_2$ (or $\lambda$ ), we can trace out the whole curve
 as the figure below illustrates.
 
 ```{code-cell} ipython3
+%%time
+
 np.random.seed(1987102)
 
 N = 2                                           # Number of assets
@@ -691,6 +699,8 @@ following figure, on which the curve connecting $\hat \mu$
 and $\mu_{BL}$ are bending
 
 ```{code-cell} ipython3
+%%time
+
 λ_grid = np.linspace(.001, 20000, 1000)
 curve = np.asarray([black_litterman(λ, μ_m, μ_est, Σ_est,
                                     τ * np.eye(N)).flatten() for λ in λ_grid])
@@ -1239,9 +1249,12 @@ observations is related to the sampling frequency
 
 - For any given $h$, the autocorrelation converges to zero as we increase the distance -- $n$-- between the observations. This represents the "weak dependence" of the $X$ process.
 
+
 - Moreover, for a fixed lag length, $n$, the dependence vanishes as the sampling frequency goes to infinity. In fact, letting $h$ go to $\infty$ gives back the case of IID data.
 
 ```{code-cell} ipython3
+%%time
+
 μ = .0
 κ = .1
 σ = .5
@@ -1341,6 +1354,8 @@ the sampling frequency $h$ relative to the IID case that we
 compute in closed form.
 
 ```{code-cell} ipython3
+%%time
+
 @jit
 def sample_generator(h, N, M):
     ϕ = (1 - np.exp(-κ * h)) * μ
@@ -1362,6 +1377,8 @@ def sample_generator(h, N, M):
 ```
 
 ```{code-cell} ipython3
+%%time
+
 # Generate large sample for different frequencies
 N_app, M_app = 1000, 30000        # Sample size, number of simulations
 h_grid = np.linspace(.1, 80, 30)