VCOV

Question 1

Single Index Model

Answer 1

A simplified asset return model where each asset’s return is related to the market index.

Key Idea:
Asset returns are driven by market movements + firm-specific noise.

Question 2

Options Method

Answer 2

Uses option-implied data instead of historical returns.

Assumes that option prices reflect market expectations of future risk and correlation.

Question 3

Shrinkage Method

Answer 3

Used to improve the stability of the estimated covariance matrix by adjusting extreme values toward a target (e.g., average correlation).

Key Idea: Combines the sample covariance matrix with a structured estimator to reduce estimation error.

Used for portfolio optimization with limited data or high dimensionality.

Question 4

Constant Correlation

Answer 4

A simplified approach that assumes all asset pairs have the same average correlation.

Key Idea: Replaces all pairwise correlations with the average sample correlation.

Used to create a more stable and less noisy correlation matrix, especially with many assets.

Question 5

Constant Correlation formula

Answer 5

SD(i,j) = Covariance(i,j)

Question 6

Shrinkage formula

Answer 6

Lamba x Sample VCov + (1-Lambda) x Other matrix

Question 7

Single index formula

Answer 7

SD(i,j) = B(i)*B(j) * variance of market returns