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梦梦 · 2024年07月16日

关于spread题目的选项翻译

NO.PZ2023090401000078

问题如下:

Question A bond fund manager has requested quotes from a bond dealer on two bonds, Bond X and Bond Y, with the same maturity date and coupon rate. The dealer informs the manager that Bond X trades at a spread of 30 bps over the Treasury market, while Bond Y trades at a spread of 70 bps. Which of the following statements is a correct conclusion for the manager to make?

选项:

A.

Bond X earns a lower return than that of the comparable Treasury bond, since its spread serves to increase the discount rate of its cash flows.

B.

The price of Bond X is currently higher than the price of Bond Y.

C.

To equate the present value of Bond Y’s cash flows to its face value, 70 bps would need to be added to the yield to maturity of a Treasury bond with comparable maturity.

D.

The spread differential indicates that there is a 0.4% difference in price between Bond X and Bond Y.

解释:

Explanation:

B is correct. Spread is a measure of the excess return earned on a bond over the return provided by a reference security or securities (e.g. Treasury securities). Because the cash flows offered by the reference security are discounted by the appropriate forward rates, adding a spread to these rates serves to decrease the corresponding discount factors. The larger the spread, the greater the decrease in the discount factors, therefore the lower the bond price. Thus, the price of Bond Y (with its 70 bps spread) is lower than the price of Bond X (with its 30 bps spread).

A is incorrect. As mentioned above, spreads can be interpreted as the excess return earned over the return provided by the comparable reference security. Bond X’s positive spread indicates a higher return than the Treasury bond.

C is incorrect. Spreads are applied to the forward rate curve of the reference security, not its yield to maturity.

D is incorrect. This is not a valid application of spreads.

Section: Valuation and Risk Models

Learning Objective: Define and interpret the spread of a bond and explain how a spread is derived from a bond price and a term structure of rates.

Reference: Global Association of Risk Professionals. Valuation and Risk Models. New York, NY: Pearson, 2022. Chapter 11. Bond Yields and Return Calculations

老师好,能否翻译一下C选项的中文和答案对C选项的解释?

5 个答案
已采纳答案

李坏_品职助教 · 2024年07月21日

嗨,努力学习的PZer你好:


对,0-1时刻的forward rate的确等于0-1时刻的spot rate,这是个特例。


其他时间段的forward rate与spot rate不相等。

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梦梦 · 2024年07月21日

好嘞,明白了

李坏_品职助教 · 2024年07月21日

嗨,努力学习的PZer你好:


加油!!

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

李坏_品职助教 · 2024年07月18日

嗨,从没放弃的小努力你好:


这个讲解在原版书教材里也没有说为什么。如果同学对原理感兴趣的话我推荐去阅读法博齐写的Fixed Income英文教材。


债券现金流的折现,原理就是把每个时间点的现金流折现到0时刻。t=1时刻的现金流折现到t=0用的是0-1时刻的spot rate,而为了把t=2时刻的现金流折现到t=0,可以用0-2时刻的spot rate。但是当期限较长时,spot rate是无法直接查出数据的,只能用较短期限的forward rate去组合(也就是先从t=2折现到t=1, 再从t=1折现到t=0)。


(1+ 0-2时刻的spot rate)^2 = (1+ 0-1时刻的forward rate) * (1+ 1-2时刻的forward rate),这样就可以用短期的forward rate去组合成长期的spot rate。


所以折现率用的都是期限较短的forward rate组合起来:

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梦梦 · 2024年07月21日

我记得您之前讲过“(1+ 0-2时刻的spot rate)^2 = (1+ 0-1时刻的spot rate) * (1+ 1-2时刻的forward rate)”,那这个表达式(1+ 0-2时刻的spot rate)^2 = (1+ 0-1时刻的forward rate) * (1+ 1-2时刻的forward rate)和上面那个表达式求出的“(1+ 0-2时刻的spot rate)”一样吗?如果一样的话,“(1+ 0-1时刻的forward rate) 不就等于(1+ 0-1时刻的spot rate) ”?

李坏_品职助教 · 2024年07月17日

嗨,爱思考的PZer你好:


同学,我建议你再仔细学一下基础班视频,Bond Spread这部分:

这个是基础班讲义截图。

这里在计算bond price的时候,折现率用的是一系列的forward rate + s,比如f1指的是0-1时刻的远期利率,f2指的是1-2时刻的远期利率……而s指的就是spread。所以spread是加在一系列的forward rate上。


根据讲义里的例题:

为了让债券未来现金流的现值之和恰好等于面值100,需要再forward rates的基础上加上spread组成折现率。由此判断C选项是错误的。

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加油吧,让我们一起遇见更好的自己!

梦梦 · 2024年07月18日

老师好,我看了这张图的文字,并没有说为什么用forward rate折现?

李坏_品职助教 · 2024年07月16日

嗨,爱思考的PZer你好:


C选项的意思是:为了让债券Y未来现金流的现值之和其面值,折现率应该这样设定:给相同期限的国债的到期收益率加上70个bp。


这个说法是错误的。为了计算出债券Y的折现率,spread应该是加在国债的forward rate curve上面,而不是加在到期收益率上面。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

梦梦 · 2024年07月17日

1、为什么spread是加在国债的forward rate curve上面?2、为什么未来现金流折现等于面值,需要在“国债的forward rate curve上面+spread?

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2024-04-16 08:31 1 · 回答