Exercise

# Compute dynamic portfolio variance

In this exercise, you will practice computing the variance of a simple two-asset portfolio with GARCH dynamic covariance.

The Modern Portfolio Theory states that there is an optimal way to construct a portfolio to take advantage of the diversification effect, so one can obtain a desired level of expected return with the minimum risk. This effect is especially evident when the covariance between asset returns is negative.

Suppose you have a portfolio with only two assets: EUR/USD and CAD/USD currency pairs. Their variance from the GARCH models have been saved in `variance_eur`

and `variance_cad`

, and their covariance has been calculated and saved in `covariance`

. Compute the overall portfolio variances by varying the weights of the two assets, and visualize their differences.

Instructions

**100 XP**

- Set the EUR/USD weight
`Wa1`

in portfolio a to 0.9, and`Wb1`

in portfolio b to 0.5. - Calculate the variance
`portvar_a`

for portfolio a with`variance_eur`

,`variance_cad`

and`covariance`

; do the same to compute`portvar_b`

for portfolio b.