Explanation

The covariance between portfolio returns and market returns can be calculated using the beta formula:

Beta (β) = Covariance(Portfolio, Market) / Variance(Market)

Where:

• Beta = 0.5 (given)
• Variance(Market) = (Standard Deviation of Market)^2 = (0.20)^2 = 0.04

Rearranging the formula:

Covariance(Portfolio, Market) = Beta × Variance(Market)

Covariance = 0.5 × 0.04 = 0.02

Wait, let me recalculate carefully:

Beta = Cov(P,M) / Var(M) 0.5 = Cov(P,M) / (0.20)^2 0.5 = Cov(P,M) / 0.04 Cov(P,M) = 0.5 × 0.04 = 0.02

But looking at the options: A. 0.005 B. 0.010 C. 0.020

My calculation gives 0.020, which corresponds to option C. However, let me double-check the calculation:

Standard deviation of market = 20% = 0.20 Variance of market = (0.20)^2 = 0.04 Beta = 0.5 Covariance = Beta × Variance = 0.5 × 0.04 = 0.02

This is exactly 0.020, which matches option C.

Alternatively, we can also calculate covariance using: Covariance = Correlation × σ_P × σ_M Where correlation can be found from: Beta = Correlation × (σ_P / σ_M) 0.5 = Correlation × (0.10 / 0.20) 0.5 = Correlation × 0.5 Correlation = 1

Then: Covariance = 1 × 0.10 × 0.20 = 0.02

Both methods give 0.020, so the correct answer is C. 0.020.