At the risk of appearing to be stupid, I have to ask you what a “par yield curve” is. As in: Given an upward sloping par yield curve, the spot rate curve will be: a. Upward sloping and higher. b. Upward sloping and lower. c. Downward sloping and higher. d. Downward sloping and lower. Thank you !!! Choice “a” is correct. An upward sloping forward rate curve always lies above the upward sloping spot curve from which it was calculated. Likewise, the upward sloping spot curve always lies above the upward sloping par curve from which the spot curve was calculated. Choice “b” is incorrect. The spot rate curve will be higher than the upward sloping par yield curve. Choice “c” is incorrect. The spot rate curve will be upward sloping. Choice “d” is incorrect. The spot rate curve will be upward sloping and higher than the par yield curve.
Not a stupid question but by “par yield curve” they are referring to what is typically called just the ‘yeild curve.’ By ‘par’ they mean that the yield curve is comprised of securities that are not at a discount, (par means the coupon = yield). The spot yield curve is a zero% coupon curve. Because duration is longer on the zero coupon curve (ie spot curve), the zero coup curve will be higher than the coupon curve (ie. par curve) when the coupon curve is upward sloping, and the spot curve will be downward sloping and lower than the coupon curve when the coupon curve is downward sloping.