Question

You wish to implement the James optimization for a portfolio containing 42 risky assets. To do so, you will need to estimate three (3) different types of inputs.How many covariances do you need to implement the optimization?

Answer 1

Correct Answer: 42 covariances

Reasoning :

The number of covariances we need to implement James optimization is,

For the optimization of a portfolio, we need to construct a covariance matrix between the risky assets. Therefore, for the construction of the matrix, we need to have covariance for each pair of risky assets at least.

Therefore,

Number of covariances = X ( X - 1 ) / 2 where X is the number of risky assets

Substituting X with 42 as portfolio contains 42 risky assets

Number of covariances = 42 ( 42 - 1 ) / 2 = ( 42 X 41 ) / 2 = 1722 / 2   = 861

Therefore, Number of covariances required to implement optimzation of portfolio = 861