Final Answer:
The true cost is calculated by dividing the change in the value of the hedged position by the change in the exchange rate. The annualized cost is obtained by adjusting for the 3-month contract period. So, the correct option is b. 14.787% annualized.
Step-by-step explanation:
The correct option is b. 14.787% annualized. The true cost of the forward contract can be determined through several steps. First, calculate the forward points by subtracting the forward rate from the spot rate at the beginning: 0.833 - 0.856 = -0.023. Next, calculate the daily forward rate by dividing the forward points by the number of days: -0.023 / 90 = -0.0002556. Multiply this by 365 to annualize the daily rate: -0.0002556 * 365 = -0.093324%. This negative value indicates a gain rather than a cost.
Now, subtract this annualized forward rate from the actual return of the portfolio, which is a decline of 2.50%: -2.50% - (-0.093324%) = -2.406676%. To convert this to an annualized percentage, multiply by (365 / 90): -2.406676% * (365 / 90) = -9.76009%. Add this to the initial return to get the net annualized return: -9.76009% - 2.50% = -12.26009%.
Finally, since the cost is negative, we change its sign, resulting in a true cost of 12.26009%. In conclusion, the true cost of the forward contract is 12.26009% annualized, reflecting the combined impact of the change in the value of the gilt portfolio and the forward contract over the 3-month period.