能不能请老师解一下这道题r的计算步骤....数学太差了....谢谢🙏-有问必答-品职教育专注CFA ESG FRM CPA 考研等财经培训课程

能不能请老师解一下这道题r的计算步骤....数学太差了....谢谢🙏

NO.PZ2016031001000081

问题如下：

A two-year floating-rate note pays 6-month Libor plus 80 basis points. The floater is priced at 97 per 100 of par value. Current 6-month Libor 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：

180 bps.

236 bps.

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 Libor, the formula for calculating discount margin is:

$PV=\frac{\frac{(Index+QM)\times FV}m}{{(1+\frac{Index+DM}m)}^1}+\frac{\frac{(Index+QM)\times FV}m}{{(1+\frac{Index+DM}m)}^2}+\cdots+\frac{\frac{(Index+QM)\times FV}m+FV}{{(1+\frac{Index+DM}m)}^4}$

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:

$97=\frac{\frac{(0.01+0.0080)\times100}2}{{(1+\frac{0.01+DM}2)}^1}+\frac{\frac{(0.01+0.0080)\times100}2}{{(1+\frac{0.01+DM}2)}^2}+\cdots+\frac{\frac{(0.01+0.0080)\times100}2+100}{{(1+\frac{0.01+DM}2)}^4}$

$97=\frac{0.9}{{(1+\frac{0.01+DM)}2)}^1}+\frac{0.9}{{(1+\frac{0.01+DM}2)}^2}+\frac{0.9}{{(1+\frac{0.01+DM}2)}^3}+\frac{0.9+100}{{(1+\frac{0.01+DM}2)}^4}$

To calculate DM, begin by solving for the discount rate per period:

$97=\frac{0.9}{{(1+r)}^1}+\frac{0.9}{{(1+r)}^2}+\frac{0.9}{{(1+r)}^3}+\frac{0.9+100}{{(1+r)}^4}$

r = 0.0168

Now, solve for DM:

$\frac{0.01+DM}2=0.0168$

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 Libor + 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。

能不能请老师解一下这道题r的计算步骤....数学太差了....谢谢🙏

能不能请老师解一下这道题r的计算步骤....数学太差了....谢谢🙏

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