The U$.$S$.$ Treasury and the UK Government have just issued new $10-$year notes paying a $5\%$ coupon rate. Since the notes have the

same payment dates and the same coupon rates, they have the same duration and convexity in their respective currencies. Ray

and Mel both manage USD$-$based funds. Ray buys the new Treasury. Mel buys the UK Gilt and hedges the currency with a $3-$month

forward contract. One month later, the yields on the $10-$year notes have each declined by $20$ basis points, the short end of the U$.$S$.$

curve has widened by $15$ basis points relative to the UK curve, and the spot exchange rate is unchanged. How have Ray and Mel's

positions performed?

Select one

A$.$ They have gained the same amount in USD.

B$.$ Ray's position has gained more than Mel's in USD.

C$.$ Mel's position has gained more than Ray's in USD.

D$.$ Their relative performance cannot be determined without more information.