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tx84908 · 2021年11月04日

不是很明白为啥要选minimum expected return来计算折现率

NO.PZ2018011501000006

问题如下:

In the private wealth area, the firm has designed five sub-portfolios with differing asset allocations that are used to fund different client goals over a five-year horizon. Exhibit 3 shows the expected returns and volatilities of the sub-portfolios and the probabilities that the sub-portfolios will exceed an expected minimum return. Client Luis Rodríguez wants to satisfy two goals. Goal 1 requires a conservative portfolio providing the highest possible minimum return that will be met at least 95% of the time. Goal 2 requires a riskier portfolio that provides the highest minimum return that will be exceeded at least 85% of the time.

Exhibit3 Characteristics of Sub-portfolios

Based on Exhibit 3, which subportfolios best meet the two goals expressed by client Rodríguez?

选项:

A.

Subportfolio A for Goal 1 and Subportfolio C for Goal 2

B.

Subportfolio B for Goal 1 and Subportfolio C for Goal 2

C.

Subportfolio E for Goal 1 and Subportfolio A for Goal 2

解释:

A is correct.

Goal 1 requires a success rate of at least 95%, and Subportfolio A has the highest minimum expected return (2.05%) meeting this requirement. Goal 2 requires the highest minimum expected return that will be achieved 85% of the time. Subportfolio C meets this requirement (and has a minimum expected return of 3.26%).

考点:goal-based approach

解析:Goal 1要求的成功概率为至少95%,Goal 2要求的成功概率为至少85%。95%的概率下,2.05%比1.75%,1.06%,0.25%,-0.6%都要大,所以Goal 1的highest minimum expected return为2.05%。同理,在85%的概率下, 3.26%是一行中最大的收益率,所以Goal 2的highest minimum expected return为 3.26%。它们对应的sub-portfolio是A和C。因此A选项正确。

在计算需要 多少钱allocate在某个portfolio时用的折现率是minimum expected return,但是为什么在计算整个account的expected return还是用回各个portfolio的expected rate of return进行加权平均呢?感觉还挺矛盾的。

1 个答案

pzqa015 · 2021年11月04日

嗨,爱思考的PZer你好:


这里不矛盾哈。这是两个不同背景下的问题,两个expected表示的含义不同,可以这样理解着记忆:

我们分析目标时,一般都会加上概率这个条件,比如我们会说,未来十年我的资产达到100万元的概率是80%,达到500万元的概率是40%,所以,加上概率后更严谨。回到这里计算goal based approach,跟前面反过来,已知未来的要达到的资产目标,反求现在需要准备多少钱,如果可以接受较高的投资汇报(折现率),现在就可以少准备些钱,所以,我们要选择一个投资收益最高的组合,但是,每个组合的投资收益是有分布的,是个变量,在不同概率水平下,投资收益有不同的值,比如,某个组合未来90%可能实现至少4.5%收益,100%实现至少4%的年化收益,这样goal和投资收益就通过概率联系在一起了,如果我们想有90%的概率实现某个目标,那么就应该找出所有可投资组合90%概率下至少能实现的收益,这就是minimum expected returm,这里的expected是预期而不是平均的意思。找到可选组合后,为了期初省钱,从所有组合里面选择投资收益最大的,也就是从minimum expected return来折现。

第二个问题计算portfolio expected return,这个expected是均值的意思,既然要计算portfolio的收益均值,那么就要用所有子portfolio的收益均值,所以用expected return。

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