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hohoYoung · 2020年05月31日

问一道题:NO.PZ201712110200000201

* 问题详情,请 查看题干

问题如下:

Based on Exhibit 1, Alvarez finds that an arbitrage opportunity is:

选项:

A.

not available.

B.

available based on the dominance principle.

C.

available based on the value additivity principle.

解释:

B is correct.

Based on the dominance principle, an arbitrage opportunity exists. The dominance principle asserts that a financial asset with a risk-free payoff in the future must have a positive price today. Because Asset A and Asset B are both risk-free assets, they should have the same discount rate. Relative to its payoff, Asset A is priced at $500/525, or 0.95238, and Asset B is priced at $1,000/1,100, or 0.90909. Given its higher implied discount rate(10%) and lower corresponding price, Asset B is cheap relative to Asset A, which has a lower implied discount rate (5%) and higher corresponding price.

The arbitrage opportunity based on dominance is to sell two units of Asset A for $1,000 and buy one unit of Asset B. There is no cash outlay today, and in one year, the portfolio delivers a net cash inflow of $50 [= $1,100 – (2 ×$525)].

请问这道题的考点是哪个?dominance principle 跟 value additivity principle 分别是什么?在讲义上有吗?看到题目和选项的我 一头雾水。。。

1 个答案

吴昊_品职助教 · 2020年06月01日

某支债券的未来现金流,可以由其他债券组合的现金流构成。如果找到了,那我们看看这支债券的现值,和其他债券组合的现值是否相同,如果不等就有套利空间。这样的情况就是Value additivity。判断value additivity的关键就在未来现金流的拆分和组合。如果未来现金流之间有拆分组合关系,就是value additivity。

某支债券的现值(即现在购买成本),能否恰好拆解成其他几只债券的现值加总。如果可以,则说明当前投资这支债券,和投资其他的债券组合的投入成本是一样的。我们就看相同的投入成本,未来是否有一样的收益,如果不一样就有套利空间。这样的情况就是dominance principle。判断dominance principle的关键在现值能否拆分和组合。如果现值之间有拆分组合关系,就是dominance。

总结来说,additivity看的是未来现金流的拆分组合,而dominance看的是现值的拆分组合。这道题很明显,现值存在倍数关系,因此是dominance。