The beta of a portfolio with respect to its benchmark is calculated using the following formula:

$\beta = \frac{p \times \text{volatility of portfolio}}{\text{volatility of benchmark}}$

Where:

• $p$ represents the correlation coefficient between the portfolio returns and the benchmark returns.
• The volatility of the portfolio and the benchmark are the standard deviations of their returns.

Given in the problem:

• The correlation coefficient $p$ is 0.8.
• The volatility of the portfolio is 5% (or 0.05 in decimal form).
• The volatility of the benchmark is 4% (or 0.04 in decimal form).

Plugging these values into the formula gives:

$\beta = \frac{0.8 \times 0.05}{0.04} = \frac{0.04}{0.04} = 1.00$

Thus, the beta of the portfolio with respect to its benchmark is 1.00, which indicates that the portfolio's returns move in lockstep with the benchmark's returns, with the same magnitude of fluctuation. This is why option D is the correct answer.