Question

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

1)How many expected returns do you need to implement the optimization?

3)How many covariances do you need to implement the optimization?

Answer 1

For the implementation of optimzation for a portfolio,

1) The number of expected returns required to implement the optimization is equal to the number of risky assets.

Since the portfolio contains 42 risk assets, Number of expected returns = 42

Therefore, Number of expected returns = 42

3)The number of covariances we need to implement the optimization is,

For the optimization of a portfolio, we need to have covariance for each pair of risky assets. This helps make the covariance matrix important for optimization.

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

Substituting N 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

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