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

skcygbb · 2021年02月05日

modifiedduration与spreadduration

NO.PZ2019103001000069

问题如下:

Emma Gerber and Juliette Petit are senior and junior credit portfolio managers, respectively, for a European money management firm. They are discussing credit management strategies and preparing for an annual meeting with a major client.

One of their high-yield bond holdings is a 10-year bond issued by EKN Corporation (EKN). The bond has a price of 91.82, a modified duration of 8.47, and a spread duration of 8.47. For this bond, Petit speculates on the effects of an interest rate increase of 20 bps and, because of a change in its credit risk, an increase in the EKN bond’s credit spread of 20 bps. Petit comments that because the modified duration and credit spread duration of the EKN bond are equal, the bond’s price will not change (all else being equal) in response to the interest rate and credit spread changes.

Is Petit’s prediction correct that the EKN bond price will not change in response to the interest rate and credit spread changes, all else being equal?

选项:

A.

Yes

B.

No, the bond price should decrease

C.

No, the bond price should increase.

解释:

B is correct.

An increase in interest rates results in a decrease in the bond price. An increase in the credit spread also results in a decrease in the bond price. For the EKN bond, its modified duration shows the effect of the 20 bp increase in interest rates. The approximate percentage price change resulting from the increase in interest rates is –8.47 × 0.0020 = –1.694%. The spread duration shows the effect of the 20 bp increase in the credit spread. The approximate percentage price change resulting from the increase in the credit spread is –8.47 × 0.0020 = –1.694%. The combined effect is a total change of –3.388%, or a price decrease of roughly 3.4%.

老师SD=0是说明是国债那么当MD=SD时应该说明什么呢??

1 个答案

发亮_品职助教 · 2021年02月06日

嗨,努力学习的PZer你好:


“那么当MD=SD时应该说明什么呢??”


说明这是普通的固定利率债券(Option-free fixed coupon bond)。

债券自身的收益率等于 = 国债的收益率 + Spread

Spread duration衡量的是:按住国债收益率不变,只有债券的Spread变动一单位时,债券的价格变动多少单位。

现在假设债券的Spread变动1%,那么债券的价格变动为:

Spread duration × 1%


我们发现,如果按住国债收益率不变,只有债券的Spread变动1%,从另外一个角度看,其实是债券自身的收益率变动1%。那么如果从Modified duration的角度来衡量,债券的价格变动为:

Modified duration × 1%


当Spread变动1%时,以上从MD和SD两个角度都能计算出债券价格的变动幅度,且这两个变动幅度是一样大的:

Spread duration × 1% = Modified duration × 1%

我们就能推出SD等于MD。

注意,以上关系只适用于普通的固定利率债券。


对于国债,由于他就是基准利率,没有Spread,所以他的SD=0,而MD不等于0;

对于浮动利率债券,他的MD很小几乎等于0,而SD不为零,存在有效的SD。

对于含权债券,不存在一个有效的MD,而存在有效的SD

因此,当MD=SD时,该债券为普通的不含权、固定利率债券。


-------------------------------
加油吧,让我们一起遇见更好的自己!


发亮_品职助教 · 2021年02月08日

是的~ 这种含权债券首先是公司债,具有信用风险,所以存在spread对债券价格的影响; 同时,由于他有权利,价格的变动也会影响债券未来现金流,价格的变动可以是来自Spread的变动,也可以是来自基准利率的变动,分析时多了一个是否行权。但是Credit spread对该债券价格的影响是依然存在的。