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CFApipa · 2022年11月17日

错很多次了...能否麻烦老师解一下这道题的计算步骤具体哪个知识点和公式,谢谢

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。

错很多很多次了......能否麻烦老师解一下这道题的计算步骤具体哪个知识点和公式, 谢谢!

1 个答案

吴昊_品职助教 · 2022年11月17日

嗨,从没放弃的小努力你好:


1、这道题可以参考基础班讲义P164页的例题。视频位置在R41,Yield Measures for Floating-Rate Notes。如下图所示。


2、本题考察的是浮动利率债券折现,分子现金流,对应信息点:pays 6-month MRR plus 80 basis points。一期的现金流为(0.01+0.008)×100/2=0.9

这个0.9就是每一期的PMT,然后计算器第三行:PV=-97,FV=100,PMT=0.9,PMT=0.9,求得I/Y=1.681%

算出1.681%之后,再反推出discount margin为236bp。

----------------------------------------------
努力的时光都是限量版,加油!

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NO.PZ2016031001000081问题如下 A two-yefloating-rate note pays 6-month MRR plus 80 basis points. The floater is price97 per 100 of pvalue. The current 6-month MRR is 1.00%. Assume a 30/360 y count convention anevenly spaceperio. The scount margin for the floater in basis points (bps) is closest to: A.180 bps.B.236 bps.C.420 bps. B is correct.The scount or requiremargin is 236 basis points. Given the floater ha maturity of two years anis linketo 6-month MRR, the formula for calculating scount margin is: where:PV = present value, or the priof the floating-rate note = 97Inx = referenrate, stateannupercentage rate = 0.01QM = quotemargin, stateannupercentage rate = 0.0080FV = future value paimaturity, or the pvalue of the bon= 100m = periocity of the floating-rate note, the number of payment perio per ye= 2 = scount margin, the requiremargin stateannupercentage rateSubstituting given values in:To calculate , begin solving for the scount rate per perior = 0.0168Now, solve for :(0.01+)/2=0.0168 = 0.0236The scount margin for the floater is equto 236 basis points.考点浮动利率债券解析浮动利率债券的Coupon Rate = Referenrate + QuoteMargin,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Sprea就是QuoteMargin。这道题中QuoteMargin是80bps。Referenrate和QuoteMargin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Referenrate + scount margin。基准利率和scount 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scount 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scount Margin。本题知道浮动利率债券的Referenrate和Quotemargin,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scount margin为236bp。 为看来题目解析和其他人的提问,但是对这句话不是很理解the current 6-month MRR is 1%, 这句话为什么可以直接理解一年的MRR呢?

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