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

返回

可乐不加冰块儿 · 2023年08月25日

能不能用画图法讲解一下这道题？

  1. CFA II
  2. Derivative

NO.PZ2023020101000010

问题如下：

Three months ago (90 days), Kim purchased a bond with a 3% annual coupon and a maturity date of seven years from the date of purchase. The bond has a face value of US$1,000 and pays interest every 180 days from the date of issue. Kim is concerned about a potential increase in interest rates over the next year and has approached Riley for advice on how to use forward contracts to manage this risk. Riley advises Kim to enter into a short position in a fixed-income forward contract expiring in 360 days. The annualized risk-free rate now is 1.5% per year and the price of the bond with accrued interest is US$1,103.45.

Based on a 360-day year, the price of the forward contract on the bond purchased by Kim is closest to：

选项：

A.

US$1,082.

B.

US$1,090.

C.

US$1,120.

解释：

Note that time 0 is the forward contract initiation date, that is, 90 days after the purchase of the bond. Time T is the contract expiration date, that is, 360 days.

The forward contract price follows:

F0(T) = FV0,T [S0 – PVCI0,T]

Present value (PV) of coupons = PVCI0,T = 15/(1.015)90/360 + 15/(1.015)270/360 = 14.944 + 14.833 = US$29.778

F0(T) = (1103.45 – 29.778)(1.015)360/360 = US$1,090.

解析看不懂，七年的债券和forward有关系吗？而且担心利率会上涨不应该签一个涨了赚钱的合约吗？那就应该是long position啊，为什么题目里面说是short position呢？

添加评论
2 个答案

pzqa27 · 2023年10月04日

嗨，从没放弃的小努力你好：


如上图所示，具体的过程请参考之前写的文字过程

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

pzqa27 · 2023年08月28日

嗨，努力学习的PZer你好：


而且担心利率会上涨不应该签一个涨了赚钱的合约吗？那就应该是long position啊，为什么题目里面说是short position呢？


您说的很对，担心利率上涨，所以应该签一份利率上升的时候获利的合约，我们知道利率上升，债券价格下降，所以我们short 债券的forward，刚好可以在利率上升的时候获利。


七年的债券和forward有关系吗

有关系但也没啥特别大的关系，forward 合约是用来对冲利率风险的衍生品，七年的债券是现货，属于被对冲的债券


解析看不懂

现在要求这个forward的价格

F=（S-PVI）（1+r）^t

根据公式可以知道，我们要把这个forward 合约中间的coupon折现后剔除掉


已知coupon是半年支付一次，所以是3%/2*1000=15

那么半年支付一次，下一次支付日是在90天后，再下一次是在270天后


所以是

然后根据公式就可以写出


----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

Sibyl · 2023年10月01日

还是用画图法再解释下吧，没看懂

  • 2

    回答

  • 1

    关注

  • 349

    浏览
相关问题

NO.PZ2023020101000010 问题如下 Three months ago (90 ys), Kim purchase bonwith a 3% annucoupon ana maturity te of seven years from the teof purchase. The bonha favalue of US$1,000 anpays interest every 180ys from the te of issue. Kim is concerneabout a potentiincrease ininterest rates over the next yeanhapproacheRiley for aion how touse forwarcontracts to manage this risk. Riley aises Kim to enter into ashort position in a fixeincome forwarcontraexpiring in 360 ys. Theannualizerisk-free rate now is 1.5% per yeanthe priof the bonwithaccrueinterest is US$1,103.45.Baseon a 360-y year, the priof theforwarcontraon the bonpurchaseKim is closest to A.US$1,082. B.US$1,090. C.US$1,120. Notethtime 0 is the forwarcontrainitiation te, this, 90 ys after thepurchase of the bon Time T is the contraexpiration te, this, 360ys.Theforwarcontraprifollows:F0(T)= FV0,T [S0 – PVCI0,T]Presentvalue (PV) of coupons = PVCI0,T = 15/(1.015)90/360 +15/(1.015)270/360 = 14.944 + 14.833 = US$29.778F0(T)= (1103.45 – 29.778)(1.015)360/360 = US$1,090.协会教材在这里写的有矛盾，参见下面两个公式，一个是需要调整AIT，但是另一个又不需要进行调整。根据它的题目来看就是如果是根据标的资产的价格去求FP，那就不要减去AIT，但是如果要求QFP，就还需要减去AIT之后做转换. 这个不是说现在开始买一个360天到期的期权吗？是90天之前买的债券，期权不应该是求现在的远期价格吗

2024-11-04 10:35 1 · 回答

NO.PZ2023020101000010 问题如下 Three months ago (90 ys), Kim purchase bonwith a 3% annucoupon ana maturity te of seven years from the teof purchase. The bonha favalue of US$1,000 anpays interest every 180ys from the te of issue. Kim is concerneabout a potentiincrease ininterest rates over the next yeanhapproacheRiley for aion how touse forwarcontracts to manage this risk. Riley aises Kim to enter into ashort position in a fixeincome forwarcontraexpiring in 360 ys. Theannualizerisk-free rate now is 1.5% per yeanthe priof the bonwithaccrueinterest is US$1,103.45.Baseon a 360-y year, the priof theforwarcontraon the bonpurchaseKim is closest to A.US$1,082. B.US$1,090. C.US$1,120. Notethtime 0 is the forwarcontrainitiation te, this, 90 ys after thepurchase of the bon Time T is the contraexpiration te, this, 360ys.Theforwarcontraprifollows:F0(T)= FV0,T [S0 – PVCI0,T]Presentvalue (PV) of coupons = PVCI0,T = 15/(1.015)90/360 +15/(1.015)270/360 = 14.944 + 14.833 = US$29.778F0(T)= (1103.45 – 29.778)(1.015)360/360 = US$1,090.协会教材在这里写的有矛盾，参见下面两个公式，一个是需要调整AIT，但是另一个又不需要进行调整。根据它的题目来看就是如果是根据标的资产的价格去求FP，那就不要减去AIT，但是如果要求QFP，就还需要减去AIT之后做转换. 请问这道题的AIt是30么

2024-10-26 00:29 1 · 回答

NO.PZ2023020101000010 问题如下 Three months ago (90 ys), Kim purchase bonwith a 3% annucoupon ana maturity te of seven years from the teof purchase. The bonha favalue of US$1,000 anpays interest every 180ys from the te of issue. Kim is concerneabout a potentiincrease ininterest rates over the next yeanhapproacheRiley for aion how touse forwarcontracts to manage this risk. Riley aises Kim to enter into ashort position in a fixeincome forwarcontraexpiring in 360 ys. Theannualizerisk-free rate now is 1.5% per yeanthe priof the bonwithaccrueinterest is US$1,103.45.Baseon a 360-y year, the priof theforwarcontraon the bonpurchaseKim is closest to A.US$1,082. B.US$1,090. C.US$1,120. Notethtime 0 is the forwarcontrainitiation te, this, 90 ys after thepurchase of the bon Time T is the contraexpiration te, this, 360ys.Theforwarcontraprifollows:F0(T)= FV0,T [S0 – PVCI0,T]Presentvalue (PV) of coupons = PVCI0,T = 15/(1.015)90/360 +15/(1.015)270/360 = 14.944 + 14.833 = US$29.778F0(T)= (1103.45 – 29.778)(1.015)360/360 = US$1,090.协会教材在这里写的有矛盾，参见下面两个公式，一个是需要调整AIT，但是另一个又不需要进行调整。根据它的题目来看就是如果是根据标的资产的价格去求FP，那就不要减去AIT，但是如果要求QFP，就还需要减去AIT之后做转换. 1、3% annucoupon和pays interest every 180 ys是否矛盾2、害怕利率上涨使得债券价格下跌，不是应该是去long interest forwar为什么是short forwar

2024-09-16 17:28 1 · 回答

NO.PZ2023020101000010 问题如下 Three months ago (90 ys), Kim purchase bonwith a 3% annucoupon ana maturity te of seven years from the teof purchase. The bonha favalue of US$1,000 anpays interest every 180ys from the te of issue. Kim is concerneabout a potentiincrease ininterest rates over the next yeanhapproacheRiley for aion how touse forwarcontracts to manage this risk. Riley aises Kim to enter into ashort position in a fixeincome forwarcontraexpiring in 360 ys. Theannualizerisk-free rate now is 1.5% per yeanthe priof the bonwithaccrueinterest is US$1,103.45.Baseon a 360-y year, the priof theforwarcontraon the bonpurchaseKim is closest to A.US$1,082. B.US$1,090. C.US$1,120. Notethtime 0 is the forwarcontrainitiation te, this, 90 ys after thepurchase of the bon Time T is the contraexpiration te, this, 360ys.Theforwarcontraprifollows:F0(T)= FV0,T [S0 – PVCI0,T]Presentvalue (PV) of coupons = PVCI0,T = 15/(1.015)90/360 +15/(1.015)270/360 = 14.944 + 14.833 = US$29.778F0(T)= (1103.45 – 29.778)(1.015)360/360 = US$1,090.协会教材在这里写的有矛盾，参见下面两个公式，一个是需要调整AIT，但是另一个又不需要进行调整。根据它的题目来看就是如果是根据标的资产的价格去求FP，那就不要减去AIT，但是如果要求QFP，就还需要减去AIT之后做转换. 虽然不影响计算结果，但是这里难道不应该用365天/年来算吗？

2024-08-13 10:48 2 · 回答

NO.PZ2023020101000010 问题如下 Three months ago (90 ys), Kim purchase bonwith a 3% annucoupon ana maturity te of seven years from the teof purchase. The bonha favalue of US$1,000 anpays interest every 180ys from the te of issue. Kim is concerneabout a potentiincrease ininterest rates over the next yeanhapproacheRiley for aion how touse forwarcontracts to manage this risk. Riley aises Kim to enter into ashort position in a fixeincome forwarcontraexpiring in 360 ys. Theannualizerisk-free rate now is 1.5% per yeanthe priof the bonwithaccrueinterest is US$1,103.45.Baseon a 360-y year, the priof theforwarcontraon the bonpurchaseKim is closest to A.US$1,082. B.US$1,090. C.US$1,120. Notethtime 0 is the forwarcontrainitiation te, this, 90 ys after thepurchase of the bon Time T is the contraexpiration te, this, 360ys.Theforwarcontraprifollows:F0(T)= FV0,T [S0 – PVCI0,T]Presentvalue (PV) of coupons = PVCI0,T = 15/(1.015)90/360 +15/(1.015)270/360 = 14.944 + 14.833 = US$29.778F0(T)= (1103.45 – 29.778)(1.015)360/360 = US$1,090.协会教材在这里写的有矛盾，参见下面两个公式，一个是需要调整AIT，但是另一个又不需要进行调整。根据它的题目来看就是如果是根据标的资产的价格去求FP，那就不要减去AIT，但是如果要求QFP，就还需要减去AIT之后做转换. 老师，没看懂答案，这个题maturity不是7年吗？能用画图法讲解一下吗

2024-07-17 11:32 3 · 回答