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开泰-王飞 · 2021年08月09日

利率曲线向上平移,不是短期利率变化小于长期利率变化吗?应该是长期债券价格下降的大于短期价格,为何低卖高买?

NO.PZ2018091701000077

问题如下:

Smith has a bond portfolio which consists two zero-coupon bonds. Bond 1 has a duration of 3.5 year, and the market value is $47.5 million. Bond 2 has a duration of 12 year, the market value is $52.5 million. The range of portfolio asset weights must be within 45%-55%. It is expected that the yield curve will parallel shift 20bp upward. To reduce the interest rate risk, Smith should:

选项:

A.

Buy $7.5 million Bond 2 and invest $7.5 million in Bond 1

B.

Sell $7.5 million Bond 2 and invest $7.5 million in Bond 1

C.

Sell $2.5 million Bond 1 and invest $2.5 million in Bond 2

解释:

B is correct.

考点:fixed-income exposure measures。

解析 : Duration是衡量利率风险的指标 。 为了降低利率风险 , 也就是减小Duration , Smith应该卖掉Duration大的债券 , 购买Duration小的债券 。 具体的金额不超过资产比重在45%-55%之间的这个范围限制 。 所以Bond 2的卖出上限是52.5-45=7.5 million , 同时购买相同金额的Bond 1 。

是不是方向弄错了?

2 个答案

星星_品职助教 · 2022年07月11日

@huangme7

价格下降的多的是duration更大的债券,bond 2的duration更大。

星星_品职助教 · 2021年08月09日

同学你好,

利率上涨这件事情还没有发生(... will parallel shift 20bp upward),如果发生后才是“长期债券价格下降的大于短期价格”。

所以现在为了避免未来利率上升的损失,需要尽量多的卖出duration大的债券(未来价格会下降的多),买入duration小的债券。也就是卖Bond 2(D=12),买Bond 1(D=3.5)


huangme7 · 2022年07月11日

为什么 长期相较短期价格下降得更多?

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