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· 2021年03月29日

如何理解

NO.PZ2016031001000060

问题如下:

Suppose a bond’s price is expected to increase by 5% if its market discount rate decreases by 100 basis points. If the bond’s market discount rate increases by 100 basis points, the bond price is most likely to change by:

选项:

A.

5%.

B.

less than 5%.

C.

more than 5%.

解释:

B is correct.

The bond price is most likely to change by less than 5%. The relationship between bond prices and market discount rate is not linear. The percentage price change is greater in absolute value when the market discount rate goes down than when it goes up by the same amount (the convexity effect). If a 100 basis point decrease in the market discount rate will cause the price of the bond to increase by 5%, then a 100 basis point increase in the market discount rate will cause the price of the bond to decline by an amount less than 5%.

凸性应该是涨多跌少,这题利率涨5%,价格不应该涨的高于100bp吗
1 个答案

吴昊_品职助教 · 2021年03月30日

嗨,爱思考的PZer你好:


同学你好:

涨多跌少,指的是利率上升和下降相同幅度,导致的价格变化不同。利率下降带来的债券价格上升幅度,要大于,利率上升带来的债券价格下降幅度。

回到这道题中,现在利率分别上升和下降100bps,导致的债券价格变化不同。利率下降100bps时的涨价幅度5% > 利率上升100bps时的跌价幅度,所以跌价幅度小于5%,即less than 5%。从下图中也能看出,价格上涨幅度明显大于价格下降幅度。我们说的涨多跌少,对象是债券价格。


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