开发者:上海品职教育科技有限公司隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

学习体验
App下载
手机上的品职教育

随时随地学习课程，支持音视频下载！
- 扫码下载品职教育APP
进入课程
登录 | 注册

Joveta · 2020年11月25日

问一道题：NO.PZ2016031001000081 [ CFA I ]

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：

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 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.

老师你好，麻烦能不能讲解一下这道题的计算，谢谢

添加评论

0
0

1 个答案

WallE_品职答疑助手 · 2020年11月26日

同学您好，

我只能告诉您思路哈，因为计算确实不好用文字去描述。咱们知道浮动利率债券的reference rate和quoted margin，也就知道了分子的coupon rate。因为浮动利率债券的coupon rate=reference rate+quoted margin。题目也已知浮动利率债券当前的债券价格，所以可以反求出折现率。同时折现率=reference rate+discount margin，所以进一步可以求出discount margin。

添加评论

0
0

1
回答
0
关注
813
浏览

我要回答关注问题

相关问题

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？

2024-09-30 10:44 1 · 回答

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。请问用计算器如何计算这道题？

2024-06-29 20:36 3 · 回答

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。題目不是半年的MRR + 80 bp了吗？不是（1%+ 80bp) 呢？

2024-06-16 11:57 1 · 回答

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。这题给30/360这句话是什么意思

2024-06-11 16:51 1 · 回答

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。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？

2024-06-10 09:50 1 · 回答