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必过1030_ · 2019年12月08日

问一道题:NO.PZ2019103001000045

问题如下:

Hirji then considers a strategy to sell some long-term bonds from the French institutional client’s portfolio and purchase short maturity at-the-money options on long-term bond futures. The portfolio’s duration would remain unchanged. Prégent asks:

“How would portfolio performance be affected by this strategy if the yield curve were to remain stable?”

The answer to Prégent’s question is that the portfolio would most likely experience:

选项:

A.

a loss.

B.

no change.

C.

a gain.

解释:

A is correct.

Short maturity at- or near-the-money options on long-term bond futures contain a great deal of convexity. Thus, options increase the convexity of the French client’s portfolio. Options are added in anticipation of a significant change in rates. If the yield curve remains stable, the portfolio will experience a loss from both the initial purchase price of the options and the foregone interest income on the liquidated bonds.

能不能从duration的角度出发呢?因为portfolio的duration下降了。

1 个答案

发亮_品职助教 · 2019年12月09日

嗨,爱思考的PZer你好:


“能不能从duration的角度出发呢?因为portfolio的duration下降了。”


这道题不行的。因为本题组合的Duration没变。


注意题干:The portfolio’s duration would remain unchanged.

也就是卖掉原来的Long-term bonds,买入短期的Option,经过这一套买卖之后,组合的Duration仍然没变。

而因为Option的Convexity更大,所以对于Portfolio来说,就说保证了Duration不变的情况下,调大了组合的Convexity数据。

所以本题是增加组合Convexity的策略,但因为预期利率变动是Stable yield curve:收益率没有变动、Convexity会被浪费掉,而增加Convexity是要付出额外成本的,例如本题的期权费,所以在本题Stable yield curve的情况下,增加Convexity没法获得收益、反而付出了额外成本,会拖累整体收益。


另外注意Option也是有Duration的,我们现在的原版书不要求计算它的Duration了,但是只要配比合适,卖出长期债券、买入Option也可以保证组合的Duration不变。


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