Exercise

# Monte Carlo Simulation

You can use Monte Carlo simulation of the 2005-2010 investment bank portfolio **assets** to find the 95% VaR.

The mean asset losses are in the Numpy array `mu`

. The efficient covariance matrix is `e_cov`

(note that here we're using the *daily*, not *annualized* variance as in previous exercises). You'll use these to create sample paths for asset losses over one day, to simulate the daily portfolio loss.

Using the covariance matrix `e_cov`

allows asset paths to be *correlated*, which is a realistic assumption.

The simulation `total_steps`

is set to 1440, as in the video. The number of runs `N`

is set to 10000.

For each run you'll compute the cumulative `losses`

, and then apply the `np.quantile()`

function to find the 95% VaR.

Portfolio `weights`

and `scipy.stats`

's `norm`

distribution are available.

Instructions 1/4

**undefined XP**

- Initialize the one-day cumulative
`daily_loss`

matrix--this will eventually be used to sum up simulated minute-by-minute losses for all 4 assets.