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呜啦啦 · 2025年04月30日

为什么书上的平价公式是除法,解答是用的减法

NO.PZ2024092001000048

问题如下:

The following table shows the expected inflation rates for three countries:

According to ex ante purchasing power parity (PPP):

选项:

A.the JPY/AUD (the amount ofJPY per 1 AUD) exchange rate is expected to decrease by 2%.

B.the USD/AUD (the amount ofUSD per 1 AUD) exchange rate is expected to decrease by 1%.

C.the JPY/USD (the amount ofJPY per 1 USD) exchange rate is expected to increase by 3%.

解释:

  1. A Correct because the ex ante version of PPP asserts that the expected changes in the spot exchange rate are entirely driven by expected differences in national inflation rates. Ex ante PPP tells us that countries that are expected to run persistently high inflation rates should expect to see their currencies depreciate over time. Ex ante PPP can be expressed as %Δ S e f/d = πef − π ed .

    %Δ S e f/d = πef − π ed = Japan inflation – Australia inflation = (1% – 3%) = – 2%

    Since Australia has a higher inflation rate than Japan, the AUD is expected to depreciate by (3% – 1%) 2% against the JPY.

  2. B Incorrect because according to the ex ante PPP theory, since the United States has a higher inflation rate than Australia, the USD/AUD is expected to increase (not decrease) by %Δ S e f/d = πef – π ed = US inflation – Australia inflation = (4% - 3%) = 1%.

  3. C Incorrect because according to the ex ante PPP theory, since the United States has a higher inflation rate than Japan, the USD is expected to depreciate (not appreciate) by %Δ S e f/d = πef – π ed = Japan inflation – US inflation = (1% - 4%) 3%, not appreciate by 3%.

A 选项正确

基于事前购买力平价(ex ante PPP)理论,预期即期汇率变动由两国预期通胀率差异决定,公式为:Sf/de=πfeπde


  • 货币对分析:假设以澳大利亚为 “本国”(d=AUD)、日本为 “外国”(f=JPY),则 Sf/d 表示 1 澳元兑日元数量(JPY/AUD)。
  • 通胀差异:日本通胀(1%)低于澳大利亚(3%),故 πfeπde=1%3%=2%
  • 汇率变动:负号表明 1 澳元能兑换的日元减少,即 澳元(AUD)相对日元(JPY)贬值 2%,符合 PPP 逻辑(高通胀货币预期贬值)。
B 选项错误

错误点在于汇率变动方向判断:


  • 美国(f=USD)通胀(4%)高于澳大利亚(d=AUD),根据公式 SUSD/AUDe=4%3%=+1%,即 1 澳元兑美元数量增加(USD/AUD 汇率上升),意味着 澳元升值、美元贬值
  • 但选项 B 称 “USD/AUD 预期减少”,与计算结果矛盾,故错误。
C 选项错误

错误点在于汇率变动方向与货币升值 / 贬值的混淆:


  • 美国(f=USD)通胀(4%)高于日本(d=JPY),公式应为 SUSD/JPYe=4%1%=+3%,即 1 日元兑美元数量增加(USD/JPY 汇率上升),实际是 美元相对日元贬值(因美国通胀更高)。
  • 但选项 C 称 “美元预期升值 3%”,与 PPP 结论(高通胀货币贬值)完全相反,故错误。

为什么书上的平价公式是除法,解答是用的减法,这样会影响计算结果吗

1 个答案

笛子_品职助教 · 2025年05月01日

嗨,爱思考的PZer你好:


为什么书上的平价公式是除法,解答是用的减法,这样会影响计算结果吗

除法是精确公式。

减法是近似公式。

对计算结果的影响不大。

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