The carry-roll-down is the return (coupon plus price change) assuming the yield curve remains unchanged over the holding period.

Initial Parameters:

• Coupon: $5%$per annum, paid semi-annually = `$2.5`$ per period.
• Initial Yield to Maturity: $4.00% \text{ (base)} + 0.20% \text{ (spread)} = 4.20%$semi-annually = `$2.10`%$ per period.
• N = $4$ periods.

Initial Price ($P_0$): $P_0 = \sum_{t=1}^{4} \frac{2.5}{(1.021)^t} + \frac{100}{(1.021)^4} = 101.5182$

Price after 6 months (unchanged yield, $P_1$): Since we assume the yield stays the same for a carry-roll-down scenario: $P_1 = \sum_{t=1}^{3} \frac{2.5}{(1.021)^t} + \frac{100}{(1.021)^3} = 101.1495$

Roll-down (Price Change): $P_1 - P_0 = 101.1495 - 101.5182 = -0.3687$

Carry (Coupon): $C = 2.5$

Carry-Roll-Down: $\text{Carry} + \text{Roll-down} = 2.5 - 0.3687 = 2.1313$

Matches Option A (2.13).