Portfolio Variance from Covariance and Correlation

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Business Context

BlueRiver Capital is evaluating whether combining two assets will reduce risk in a client portfolio. The PM wants a clear explanation of covariance vs. correlation and a calculation of portfolio variance for a 2-asset mix.

Problem Statement

You are given annualized return statistics for two assets, A and B. Explain the difference between covariance and correlation, then quantify how each enters the portfolio variance calculation.

Given Data

Metric	Asset A	Asset B
Expected return	8.0%	12.0%
Volatility	20.0%	30.0%
Portfolio weight	60.0%	40.0%

Additional information:

Pairwise Statistic	Value
Covariance between A and B	0.024
Correlation between A and B	0.40

Assume the covariance and correlation are based on the same annualized return series and are internally consistent.

Requirements

Define covariance and correlation, and explain the difference in interpretation and scale.
Verify that the given covariance and correlation are consistent with the asset volatilities.
Compute the portfolio expected return.
Compute the portfolio variance using covariance.
Recompute the same portfolio variance using correlation.
Compute the portfolio standard deviation.
Briefly explain how portfolio risk would change if correlation increased to 0.80 or fell to -0.20.

Assumptions

Asset returns are measured over the same period and annualized.
Portfolio weights sum to 1.
Ignore transaction costs, rebalancing effects, and non-normal tail behavior.