The price of the three year US Government coupon bond with $5\%$ coupon rate is $1,115\mathrm{.}50.$ This bond pays coupons annually. The price of the one year Treasury zero coupon bond is $$988.$ The price of the two year Treasury zero coupon bond is $$995.$ The price of the three year Treasury coupon bond is $$990.$ All par values are $$1000.$ Is this coupon bond priced correctly? If not how can you exploit this mispricing?

Choice A: The coupon bond is underpriced. I will short $1000$ coupon bonds and use this money to buy $50$ one year coupon zero bonds, $50$ two year zero coupon bonds and $1050$ three year zero coupon bonds.

Choice B: The coupon bonds is overpriced. I will short $50$ one year zero coupon bonds, $50$ two year coupon bonds are $1050$ three years zero coupon bonds and use this money to buy $1000$ coupon bonds.

Choice C: The bond is correctly priced. There is no arbitrary opportunity to exploit.

Choice D: The coupon bond is underpriced. I will short $50$ one year zero coupon bonds, $50$ two year zero coupon bond and $1050$ three year zero coupon bond and use this money to buy $1000$ coupon bonds.

Choice E: The coupon bond is overpriced. I will short $1000$ coupon bond and use this money to buy $50$ one year coupon bonds, $50$ two year zero coupon bonds and $1050$ three year zero coupon bonds.