NO.PZ2016031001000081
问题如下：
A two-year floating-rate note pays 6-month MRR plus 80 basis points. The floater is priced at 97 per 100 of par value. The current 6-month MRR is 1.00%. Assume a 30/360 day count convention and evenly spaced periods. The discount margin for the floater in basis points (bps) is closest to:
选项：
A.180 bps.
B.236 bps.
C.420 bps.
解释：
B is correct.
The discount or required margin is 236 basis points. Given the floater has a maturity of two years and is linked to 6-month MRR, the formula for calculating discount margin is:
where:
PV = present value, or the price of the floating-rate note = 97
Index = reference rate, stated as an annual percentage rate = 0.01
QM = quoted margin, stated as an annual percentage rate = 0.0080
FV = future value paid at maturity, or the par value of the bond = 100
m = periodicity of the floating-rate note, the number of payment periods per year = 2
DM = discount margin, the required margin stated as an annual percentage rate
Substituting given values in:
To calculate DM, begin by solving for the discount rate per period:
r = 0.0168
Now, solve for DM:
(0.01+DM)/2=0.0168
DM = 0.0236
The discount margin for the floater is equal to 236 basis points.
考点：浮动利率债券
解析：浮动利率债券的Coupon Rate = Reference rate + Quoted Margin，比如一个每半年付息一次的浮动利率债券，其Coupon Rate是：6-month MRR + 50 bps，50 bps（息差Spread）就是Quoted Margin。这道题中Quoted Margin是80bps。Reference rate和Quoted Margin共同决定Coupon Rate。
给浮动利率债券未来现金流折现时，使用的折现率是Reference rate + Discount margin。基准利率和Discount margin共同构成对这个浮动利率债券的要求回报率。所以在基准利率的基础上，加上一个Discount Margin后，折现未来现金流可以得到当前浮动利率债券。或者知道当前浮动利率债券价格和基准利率，可以反求Discount Margin。
本题知道浮动利率债券的Reference rate和Quoted margin，也就知道分子的Coupon rate；也知道浮动利率债券当前的债券价格，所以可以反求出来折现率，从而进一步求Discount margin为236bp。
我对求margin 的这个过程有点疑惑，因为 0.01 已经是 6 month market rate, 我不太明白为什么0.01 还要被除以2 呢？
