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momo · 2024年02月12日

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NO.PZ202305230100005408

问题如下:

An investor’s well-diversified portfolio has $200,000 in cash. The investor aims to invest in short-term, one-year Large-Cap Company bonds, prior to using the cash to invest in an upcoming IPO. There are currently two Large-Cap Company bonds on the market to purchase, both with one-year maturities. One of the bonds, Bond A, is a non-callable bond, while Bond B is a callable bond. As a fixed-income analyst, you are asked to conduct an analysis.


What impact would a “flight to safety” (i.e., government bond yields falling and credit spreads widening) have on the analytical duration estimate of Bond A?

选项:

A.

Decreased duration

B.

Increased duration

C.

No impact

解释:

C is correct. There would be no impact on the analytical duration estimate. However, an empirical duration estimate would be impacted. A flight to safety would result in an increase in the bond price due to the falling benchmark yield being offset by widening credit spread. This would lead to a lower empirical duration than analytical duration.

没太明白

1 个答案

pzqa27 · 2024年02月14日

嗨,从没放弃的小努力你好:


首先我们知道,一个公司债的收益率Ya是可以认为在benchmark的收益率Yb的基础上,加上一个credit spread.

即Ya=Yb+spread.

duration可以认为是收益率变化对价格变化的敏感度,即Δp/Δyb

现在的情况是 “flight to safety” 也就是benchmark的收益率是下降的,而由于现在市场不好,spread是上升的,

而公司债的收益率变化可以写成

ΔYa=ΔYb+Δspread

ΔYb是一个负的,因为Yb下降,而spread是上升,所以Δspread是正的,这俩加一起刚好抵消了一部分,因此造成公司债的价格变化比较小

所以公司债的empirical duration 相对analytical duration小,但是这个 “flight to safety”并不影响债券的analytical duration。所以选C

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虽然现在很辛苦,但努力过的感觉真的很好,加油!