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毛昱婷 · 2023年08月05日

按计算器按出来答案不对，碰到其他题怎么办

  1. CFA I
  2. Quantitative

NO.PZ2023052407000011

问题如下：

The current exchange rate between the euro and US dollar is USD/EUR1.025. Risk-free interest rates for one year are 0.75 percent for the euro and 3.25 percent for the US dollar. The one-year USD/EUR forward rate that best prevents arbitrage opportunities is:

选项：

A.

USD/EUR1.051

B.

USD/EUR1.025

C.

USD/EUR0.975

解释：

A is correct. To avoid arbitrage opportunities in exchanging euros and US dollars, investors must be able to lock in a one-year forward exchange rate of USD/EUR1.051 today. The solution methodology is shown below.

In one year, a single unit of euro invested risk-free is worth EUR1.0075 (=e0.0075).

In one year, a single unit of euro converted to US dollars and then invested risk-free is worth USD1.0589 (=1.025*e0.0325).

To convert USD1.0589 into EUR1.0075 requires a forward exchange rate of USD/EUR1.051 (=1.0589/1.0075).

算这道题的时候如果在3.25%-0.75%这一步没有口算等于2.5%，而是直接全部按计算器1.025e^(3.25%-0.75%)的话得出的答案就不对，计算器算的3.25%-0.75%答案是0.032256。。。为什么会这样

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星星_品职助教 · 2023年08月05日

同学你好，

这个计算的结果说明错误的按了百分号键。

金融计算器的百分号有其独特的计算逻辑，虽然按第一个数字3.25后再按%是可以得到0.0325的。但是，如果连着计算，紧接着输入减0.75后再按百分号，此时百分号就不是给0.75加百分号，即计算的就不是0.0325-0.0075的值，而是求0.0325-0.0325×0.75%的值。所以才会得到0.0323.

这种对于百分号的处理并不符合直觉习惯，我们平常也不用，也没有据此设计的题目，故不需要掌握和研究。对于金融计算器而言，百分数直接化为小数后再输入即可。

以本题为例，既可以直接输入0.0325-0.0075后得到0.025，也可以计算3.25-0.75=2.5后，再化为0.025。不需要口算3.25-0.75，只需要将得到的2.5（%）转化为小数0.025就可以。

然后在0.025的基础上按2nd+LN，就可以算出e的0.025次方=1.0253


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