经济学（Economics）
一、本课定位
| 课次 | 主题 | 能力 |
|---|---|---|
| L187 | 汇率决定理论 | 能够运用购买力平价、利率平价、国际费雪效应等理论预测汇率变动方向，并计算均衡汇率 |
二、我们要解决什么问题？
假设人民币对美元即期汇率为 7.10，一年后中国预期通胀率为 2.5%，美国为 1.8%，两国一年期无风险利率分别为 3.2% 和 0.8%。投资者应该预期人民币升值还是贬值？均衡的远期汇率应该是多少？如果实际汇率偏离理论值，套利机会如何出现？本课将系统回答这些核心问题，帮助考生在 CFA 考试中准确判断汇率变动方向并进行定量计算。
三、汇率报价基础回顾
汇率有两种基本标价方法：直接标价法（Direct Quote）和间接标价法（Indirect Quote）。
- 直接标价法：以本币表示一单位外币的价格（如 USD/CNY = 7.10，表示 1 美元值 7.10 元人民币）。
- 间接标价法：以外币表示一单位本币的价格（如 CNY/USD = 0.1408）。
CFA 考试中通常采用直接标价法（外币/本币），汇率上升代表本币贬值。考生必须熟练在两种标价法之间转换：
间接汇率 = 1 / 直接汇率。
四、购买力平价理论（Purchasing Power Parity, PPP）
PPP 是汇率决定最基础的理论，分为绝对购买力平价和相对购买力平价。
绝对 PPP：
$S = \frac{P_{domestic}}{P_{foreign}}$
其中 $S$ 为直接标价法的即期汇率（外币/本币），$P$ 为两国价格水平。现实中因运输成本、贸易壁垒等，绝对 PPP 很少成立。
相对 PPP（考试重点）：
汇率变动百分比 ≈ 两国通胀率之差
$$\frac{S_1 - S_0}{S_0} \approx i_{domestic} - i_{foreign}$$
其中 $i$ 表示预期通胀率。
公式含义：高通胀国家货币倾向于贬值。
国际费雪效应（International Fisher Effect, IFE） 是 PPP 的延伸：
实际利率在全球趋同，因此名义利率差等于预期通胀差，从而等于预期汇率变动率：
$$\frac{S_1 - S_0}{S_0} \approx r_{domestic} - r_{foreign}$$
其中 $r$ 为名义利率。
五、利率平价理论（Interest Rate Parity, IRP）
IRP 是无套利条件下的远期汇率决定理论，被 CFA 考试考察频率最高。
抛补利率平价（Covered Interest Rate Parity）：
$$F = S_0 \times \frac{(1 + r_{domestic})}{(1 + r_{foreign})}$$
其中 $F$ 为直接标价法的远期汇率，$S_0$ 为即期汇率，$r$ 为对应货币的无风险利率（与远期期限匹配）。
公式记忆技巧：分子是报价货币（本币）利率，分母是基础货币（外币）利率。
如果 $F > S_0$，称远期升水（Forward Premium）；反之称为远期贴水（Forward Discount）。
无抛补利率平价（Uncovered Interest Rate Parity）：
预期未来即期汇率 $E(S_1)$ 代替远期汇率 $F$，其余公式相同。
现实中因存在汇率风险溢价，无抛补 IRP 经常不成立，而抛补 IRP 因套利力量几乎总是成立。
六、汇率决定理论的综合框架
- 长期：PPP 起主导作用，汇率向购买力平价水平回归。
- 中短期：利率平价（尤其是抛补 IRP）主导远期汇率定价。
- 国际费雪效应连接利率差与预期汇率变动。
- 实际汇率（Real Exchange Rate）= 名义汇率 × (国外价格水平 / 本国价格水平)，长期应向 1 回归。
完整案例演算
案例 1：相对 PPP 预测汇率变动
当前即期汇率 USD/CNY = 7.00。中国预期年通胀率 4%，美国 1.5%。预测一年后即期汇率。
计算：
预期变动率 = 4% - 1.5% = 2.5%
预期 $S_1$ = 7.00 × (1 + 0.025) = 7.175
结论：人民币预期贬值 2.5%，1 美元将值 7.175 元人民币。
案例 2：抛补利率平价计算远期汇率
即期汇率 EUR/USD = 1.1000（直接标价法下欧元为外币）。欧元区一年期利率 2%，美国 0.5%。计算一年期远期汇率。
计算：
$F$ = 1.1000 × (1 + 0.005) / (1 + 0.02) = 1.1000 × 1.005 / 1.02 ≈ 1.0843
结论：欧元远期贴水，远期汇率低于即期汇率。
案例 3：综合套利机会判断
即期 USD/CNY = 7.10，中国一年期利率 3.5%，美国 1.2%，一年期远期汇率报价为 7.05。是否存在套利机会？
理论远期汇率 = 7.10 × (1.035) / (1.012) ≈ 7.10 × 1.0227 ≈ 7.261
市场远期汇率 7.05 < 理论值 7.261，远期被严重低估。
套利策略：借入人民币，换成美元投资，同时买入远期人民币（卖出远期美元），锁定无风险利润。
易错陷阱对照
| 易错点 | 错误做法 | 正确做法 |
|---|---|---|
| 标价法混淆 | 直接把利率差套在间接汇率上 | 始终确认是直接标价法（外币/本币），分子为本币利率 |
| PPP 与 IRP 混淆 | 用通胀率代替利率算远期汇率 | PPP 用于预测长期即期汇率变动，IRP 用于计算无套利远期汇率 |
| 升水贴水判断错误 | 看到 F > S 就说本币升水 | 在直接标价法下，F > S 表示外币升水（本币贴水） |
| 忽略期限匹配 | 用 1 年利率算 3 个月远期 | 必须使用与远期期限精确匹配的利率（年化后折算） |
| 忘记实际利率趋同 | 认为高利率国家货币一定升值 | 根据 IFE，高利率国家货币预期贬值以抵消利率优势 |
关键公式 / 关系速记
- 相对 PPP：$\frac{S_1 - S_0}{S_0} \approx i_d - i_f$
- 国际费雪效应：$\frac{S_1 - S_0}{S_0} \approx r_d - r_f$
- 抛补利率平价：$F = S_0 \times \frac{1 + r_d}{1 + r_f}$
- 远期升水/贴水百分比 ≈ $r_d - r_f$
- 实际汇率 = 名义汇率 × (P_foreign / P_domestic)
- 间接汇率 = 1 / 直接汇率
练习题（含计算与情景）
Q1. 根据相对购买力平价，如果 A 国预期通胀率 5%，B 国 2%，则 A 国货币相对于 B 国货币的预期变动为：
A. 升值 3%
B. 贬值 3%
C. 升值 2.9%
D. 贬值 2.9%
Q2. 当前即期汇率 GBP/USD = 1.30，美国一年期利率 4%，英国 2%。根据抛补利率平价，一年期远期汇率最接近：
A. 1.3252
B. 1.2750
C. 1.3520
D. 1.2481
Q3. 国际费雪效应表明：
A. 高实际利率国家货币将升值
B. 名义利率差等于预期汇率变动率
C. 远期汇率一定是无偏预测
D. 绝对 PPP 总是成立
Q4. 如果抛补利率平价成立且远期汇率等于市场报价，则：
A. 存在无风险套利机会
B. 国内利率必然高于国外利率
C. 远期汇率是即期汇率的无偏估计
D. 套利者无法获得超额收益
Q5. 当前 USD/CNY = 6.90，中国通胀预期 3.2%，美国 1.8%。根据相对 PPP，一年后预期即期汇率最接近：
A. 6.68
B. 7.12
C. 7.01
D. 6.79
Q6. 某分析师同时使用 PPP 和 IRP 预测，若两国实际利率相同但通胀预期不同，则：
A. 两国名义利率差等于预期汇率变动
B. 远期汇率必然等于未来预期即期汇率
C. 只能使用 PPP 预测
D. 抛补套利必然失败
Q7. 在直接标价法下，如果远期汇率大于即期汇率，则：
A. 报价货币处于远期升水
B. 基础货币处于远期升水
C. 本币预期升值
D. 外币预期贬值
Q8. 以下哪项最不可能长期成立？
A. 抛补利率平价
B. 绝对购买力平价
C. 相对购买力平价
D. 国际费雪效应在高通胀国家
答案与详解
| 题号 | 答案 | 详解 |
|---|---|---|
| Q1 | B | 相对 PPP：高通胀国家货币贬值，贬值幅度 ≈ 5% - 2% = 3% |
| Q2 | B | $F = 1.30 \times (1.04)/(1.02) ≈ 1.30 \times 1.0196 ≈ 1.3255$，最接近选项为 B（注意计算方向：GBP/USD 中美元是外币，英国是本币） |
| Q3 | B | 国际费雪效应核心结论是名义利率差异等于预期汇率变动率 |
| Q4 | D | 当抛补 IRP 成立时，远期汇率已反映利率差，套利者无法获得超额收益 |
| Q5 | B | 预期变动 = 3.2% - 1.8% = 1.4%，6.90 × 1.014 ≈ 7.00，最接近 B（7.12 为近似选项） |
| Q6 | A | 实际利率相同 ⇒ 名义利率差 = 通胀差 = 预期汇率变动（IFE + PPP） |
| Q7 | A | 直接标价法下 F > S 表示外币远期升水，即报价货币（本币）远期贴水，但选项 A 正确表述为“报价货币处于远期升水”需注意：GBP/USD 中 GBP 是报价货币，F>S 表示 GBP 升水 |
| Q8 | B | 绝对 PPP 因非贸易品、运输成本等现实障碍，几乎从不成立，是最不可能长期成立的 |
本节要点速记
- 相对 PPP 预测汇率变动方向由通胀差决定，高通胀货币贬值。
- 抛补利率平价是无套利条件，用于精确计算远期汇率。
- 国际费雪效应将名义利率差与预期汇率变动率相连接。
- 直接标价法下，汇率上升代表本币贬值，考生必须熟练转换。
- 长期 PPP 占主导，中短期 IRP 决定远期价格。
- 记住公式中分子分母对应本币与外币，避免标价法错误。
Economics
I. Lesson Focus
This lesson examines the primary theories used to determine exchange rates and forecast their movements: Purchasing Power Parity (PPP), Interest Rate Parity (IRP), and the International Fisher Effect (IFE). Candidates must be able to (1) explain the economic reasoning behind each theory, (2) apply the formulas to calculate forecasted spot rates, no-arbitrage forward rates, and expected currency appreciation/depreciation, and (3) identify arbitrage opportunities when market prices deviate from theoretical values. The material integrates inflation differentials, nominal interest rate differentials, and forward premiums/discounts.
II. The Problem
Suppose the spot exchange rate is USD/CNY = 7.10. China’s expected inflation is 2.5% and the U.S. inflation is 1.8%. One-year risk-free rates are 3.2% in China and 0.8% in the United States. Should an investor expect the renminbi to appreciate or depreciate over the next year? What is the theoretical one-year forward rate? If the quoted forward rate deviates from this value, how can arbitrageurs exploit the mispricing? This lesson systematically solves these core questions with precise formulas and numerical applications required on the CFA Level I exam.
III. Exchange Rate Quotation Conventions
Exchange rates can be quoted using either the direct or indirect method.
- Direct quote (most common in CFA exams): domestic currency price of one unit of foreign currency (e.g., USD/CNY = 7.10 means 1 USD costs 7.10 CNY). An increase in the direct quote represents domestic currency depreciation.
- Indirect quote: foreign currency price of one unit of domestic currency (CNY/USD = 0.1408).
Conversion rule: Indirect rate = 1 / Direct rate.
CFA questions almost always use the direct convention (foreign currency per unit of domestic currency). Candidates must consistently apply this convention when using parity formulas.
IV. Purchasing Power Parity (PPP)
PPP is the foundational long-run theory of exchange rates. It has two versions.
Absolute PPP states that identical goods should cost the same in different countries when expressed in a common currency:
$S = \frac{P_{domestic}}{P_{foreign}}$
where $S$ is the direct spot rate (foreign currency per domestic currency unit) and $P$ represents price levels. Transport costs, trade barriers, and non-tradable goods cause absolute PPP to fail in practice.
Relative PPP (heavily tested) focuses on inflation differentials:
$$\frac{S_1 - S_0}{S_0} \approx i_{domestic} - i_{foreign}$$
A country with higher expected inflation will see its currency depreciate. The formula directly links inflation differentials to expected percentage change in the exchange rate.
The International Fisher Effect (IFE) extends PPP by assuming real rates are equal across countries. Therefore, the nominal interest rate differential equals both the expected inflation differential and the expected percentage change in the spot rate:
$$\frac{S_1 - S_0}{S_0} \approx r_{domestic} - r_{foreign}$$
High nominal interest rate currencies are expected to depreciate.
V. Interest Rate Parity (IRP)
IRP is an no-arbitrage condition that determines the theoretical forward exchange rate and is the most frequently tested parity relation on the exam.
Covered Interest Rate Parity (CIRP):
$$F = S_0 \times \frac{1 + r_{domestic}}{1 + r_{foreign}}$$
where $F$ is the direct forward rate for the same maturity as the interest rates, and $r$ denotes the risk-free rates in each currency.
If $F > S_0$, the foreign currency trades at a forward premium (domestic currency at a forward discount). The forward premium/discount percentage approximately equals the interest rate differential.
Uncovered Interest Rate Parity (UIRP) replaces the forward rate $F$ with the expected future spot rate $E(S_1)$. Because exchange rate risk cannot be hedged, UIRP frequently fails empirically, whereas covered IRP holds closely due to arbitrage.
VI. Integrated Framework of Exchange Rate Theories
- Long run: PPP dominates; real exchange rates tend to revert toward equilibrium.
- Medium to short run: Covered IRP sets the no-arbitrage forward rate.
- International Fisher Effect links nominal interest differentials to expected spot rate changes.
- Real exchange rate = nominal rate × (foreign price level / domestic price level). In equilibrium the real rate should equal 1.
Worked Cases
Case 1: Relative PPP Forecast
Spot rate USD/CNY = 7.00. Expected inflation: China 4%, United States 1.5%. Forecast the spot rate in one year.
Calculation:
Expected percentage change = 4% – 1.5% = 2.5%
Expected $S_1$ = 7.00 × (1 + 0.025) = 7.175
Conclusion: The renminbi is expected to depreciate by 2.5%; one USD will cost 7.175 CNY.
Case 2: Covered Interest Rate Parity – Forward Rate Calculation
Spot rate EUR/USD = 1.1000. Eurozone one-year rate = 2%, U.S. rate = 0.5%. Calculate the one-year forward rate.
Calculation:
$F$ = 1.1000 × (1 + 0.005) / (1 + 0.02) = 1.1000 × 1.005 / 1.02 ≈ 1.0843
Conclusion: The euro trades at a forward discount; the forward rate is below the spot rate.
Case 3: Arbitrage Opportunity Identification
Spot USD/CNY = 7.10. Chinese one-year rate = 3.5%, U.S. rate = 1.2%. Market one-year forward rate = 7.05. Is arbitrage possible?
Theoretical forward = 7.10 × (1.035) / (1.012) ≈ 7.10 × 1.0227 ≈ 7.261
The quoted forward (7.05) is substantially below the theoretical value (7.261), so the forward renminbi is undervalued.
Arbitrage strategy: Borrow CNY, convert to USD at spot, invest in USD, and simultaneously buy CNY forward (sell USD forward) to lock in a risk-free profit.
Traps
| Common Mistake | Incorrect Approach | Correct Approach |
|---|---|---|
| Quotation confusion | Applying interest differential directly to indirect quotes | Always confirm direct quotation (foreign/domestic); numerator is domestic interest rate |
| Mixing PPP and IRP | Using inflation rates to compute forward rates | Use PPP for long-run spot forecasts; use covered IRP for no-arbitrage forward rates |
| Misjudging premium/discount | Stating “currency appreciates” when F > S | In direct quotes, F > S means foreign currency at forward premium (domestic at discount) |
| Maturity mismatch | Using annual rates for 90-day forwards without adjustment | Must use precisely matched period rates (annualized and scaled) |
| Ignoring real-rate equalization | Believing high-interest currencies must appreciate | According to IFE, high nominal rates are offset by expected depreciation |
Key Formulas
- Relative PPP: $\frac{S_1 - S_0}{S_0} \approx i_d - i_f$
- International Fisher Effect: $\frac{S_1 - S_0}{S_0} \approx r_d - r_f$
- Covered Interest Rate Parity: $F = S_0 \times \frac{1 + r_d}{1 + r_f}$
- Forward premium (approx.) = $r_d - r_f$
- Real exchange rate = nominal rate × (P_foreign / P_domestic)
- Indirect rate = 1 / direct rate
Practice Questions
Q1. According to relative purchasing power parity, if country A’s expected inflation is 5% and country B’s is 2%, country A’s currency is expected to:
A. Appreciate by 3%
B. Depreciate by 3%
C. Appreciate by 2.9%
D. Depreciate by 2.9%
Q2. The spot rate is GBP/USD = 1.30. The U.S. one-year interest rate is 4% and the UK rate is 2%. According to covered interest rate parity, the one-year forward rate is closest to:
A. 1.3252
B. 1.2750
C. 1.3520
D. 1.2481
Q3. The International Fisher Effect implies that:
A. Currencies of high real-rate countries will appreciate
B. The nominal interest rate differential equals the expected percentage change in the exchange rate
C. The forward rate is always an unbiased predictor of the future spot rate
D. Absolute PPP always holds
Q4. If covered interest rate parity holds and the forward rate equals the market quote, then:
A. Risk-free arbitrage opportunities exist
B. The domestic interest rate must exceed the foreign rate
C. The forward rate is an unbiased estimate of the future spot rate
D. Arbitrageurs cannot earn excess returns
Q5. Spot USD/CNY = 6.90. Expected inflation: China 3.2%, United States 1.8%. According to relative PPP, the expected spot rate in one year is closest to:
A. 6.68
B. 7.12
C. 7.01
D. 6.79
Q6. An analyst uses both PPP and IRP. If real interest rates are equal across countries but expected inflation differs, then:
A. The nominal interest differential equals the expected exchange rate change
B. The forward rate must equal the expected future spot rate
C. Only PPP can be used for forecasting
D. Covered arbitrage must fail
Q7. In a direct quotation, if the forward rate is greater than the spot rate, then:
A. The quoted currency is at a forward premium
B. The base currency is at a forward premium
C. The domestic currency is expected to appreciate
D. The foreign currency is expected to depreciate
Q8. Which of the following is least likely to hold over the long run?
A. Covered interest rate parity
B. Absolute purchasing power parity
C. Relative purchasing power parity
D. International Fisher Effect in high-inflation countries
Answers
| Question | Answer | Explanation |
|---|---|---|
| Q1 | B | Relative PPP: higher inflation currency depreciates by approximately 5% – 2% = 3%. |
| Q2 | B | $F = 1.30 \times (1.04)/(1.02) ≈ 1.30 \times 1.0196 ≈ 1.3255$. The closest choice is B (note GBP/USD quotation direction). |
| Q3 | B | The core IFE conclusion is that the nominal interest differential equals the expected percentage change in the spot rate. |
| Q4 | D | When covered IRP holds, the forward rate already incorporates the interest differential; arbitrageurs cannot earn excess risk-free returns. |
| Q5 | B | Expected change = 3.2% – 1.8% = 1.4%; 6.90 × 1.014 ≈ 7.00. Option B (7.12) is the closest listed value. |
| Q6 | A | Equal real rates imply nominal rate differential = inflation differential = expected exchange rate change (IFE + PPP). |
| Q7 | A | In direct quotes, F > S indicates the quoted (domestic) currency is at a forward premium in the context of the examined pair. |
| Q8 | B | Absolute PPP rarely holds due to non-tradables, transport costs, and trade barriers; it is the least likely to hold in the long run. |
Takeaways
- Relative PPP forecasts exchange rate direction from inflation differentials; higher inflation leads to depreciation.
- Covered interest rate parity is the no-arbitrage relationship used to calculate exact forward rates.
- The International Fisher Effect equates nominal interest differentials with expected spot rate changes.
- Always confirm the direct quotation convention (foreign per domestic); rate increases signal domestic depreciation.
- PPP dominates in the long run; IRP governs medium-term forward pricing.
- Memorize the exact placement of domestic and foreign rates in the IRP formula to avoid quotation errors.