1

Parity Conditions in International Finance and Currency Forecasting

Chapter 4

2

國際金融平價條件與外匯預測

4.1 套利與單一價格法則 4.2 購買力平價說 4.3 費雪效果 4.4 國際費雪效果 4.5 利率平價理論 4.6 遠期匯率與未來即期匯率的關係

3

ARBITRAGE( 套利 )AND THE LAW

OF ONE PRICE( 單一價格法則 )Five Parity Conditions Result From

Arbitrage Activities

1. Purchasing Power Parity (PPP)2. The Fisher Effect (FE)3. The International Fisher Effect

(IFE)4. Interest Rate Parity (IRP)5. Unbiased Forward Rate (UFR)

4

PART I. ARBITRAGE( 套利 )AND THE

LAW OF ONE PRICE( 單一價格法則 )

I. THE LAW OF ONE PRICE

A. Law states:Identical goods sell for the same price worldwide.

B. Theoretical basis:If the price after exchange-rate adjustment were not equal, arbitrage in the goods worldwide ensures eventually it will.

5

套利與單一價格法則 套利 (arbitrage)

在不同的市場，同時買、賣相同的資產或商品以賺取其價差。

單一價格法則： 單一價格法則是說全球可交易的相同的商品及

資產，經匯率調整後的價格，必須是相等的，頂多只差交易成本。

6

ARBITRAGE( 套利 )AND THE LAW

OF ONE PRICE( 單一價格法則 )C. Five Parity Conditions Linked by

The adjustment of rates and prices to inflation

7圖表 4.1 即期匯率、遠期匯率、通貨膨脹率及利率間的五種理論上的重要關係

8

ARBITRAGE AND THE LAW OF ONE PRICE

D. Inflation and home currency depreciation are:

1. Jointly determined by the growth of domestic

money supply (Ms) and

2. Relative to the growth ofdomestic money demand.

9

五大平價條件 共同起源：

各種比率及價格對通貨膨脹的調整。根據現代貨幣理論，通貨膨脹乃是貨幣供給擴張超過實質產出成長的必然結果。

貨幣中立性： 貨幣供給成長、通貨膨脹率、利率和匯率，這些都

可透過套利而連結在一起。 通貨膨脹

通貨膨脹與貨幣貶值會一同受到國內貨幣供給成長相對於需求成長的影響。

10

PART II.PURCHASING POWER PARITY

I. THE THEORY OF PURCHASING

POWER PARITY( 購買力平價說 )

states that spot exchange rates between currencies will change to the differential in inflation rates between

countries.

11

PURCHASING POWER PARITY

II.RELATIVE PURCHASING POWER PARITY( 相對版的購買力平價

說 )

A. states that the exchange rate of one currency against another

will adjust to reflect changes in the price levels of the two countries.

12

絕對版的購買力平價說 主張：

一單位本國貨幣 (HC) 在全世界應有相同的購買力。 範例：大麥克指數 (Big Mac Index) 假設：

自由貿易將使任一商品在所有國家的價格均相等，否則將存在套利機會）。

缺點： 忽視運輸成本、關稅、配額與其他限制對自由貿易

的影響，也忽略了產品的差異化。

13

相對版的購買力平價說 主張：

本國貨幣與外幣的交換比率會調整到足以反映兩國價格水準的改變。

其中購買力平價匯率（ PPP 匯率； PPP rate ）。 e0 是期初一單位外幣的美元價值 如果 ih 與 if 分別是本國與外國的通貨膨脹率

1

0

1

1h

f

ie

e i

(4.2) 式 1 01

1h

f

ie e

i

(4.3) 式

14

PURCHASING POWER PARITY

1. In mathematical terms:

et = (1 + ih)t

e0 (1 + if)t

where et = future spot rate e0 = spot rate ih = home inflation if = foreign inflation t = time period

15

PURCHASING POWER PARITY

2. If purchasing power parity is expected to hold, then the bestprediction for the one-periodspot rate should be

et = e0(1 + ih)t

(1 + if)t

16

PURCHASING POWER PARITY

3. A more simplified but less precise

relationship is

et - e0 = ih - if e0

that is, the percentage change should be approximately

equal tothe inflation rate differential.

17

PURCHASING POWER PARITY

4. PPP says

the currency with the higher inflation rate is expected to depreciate

relative to the currency with the lower rate of inflation.

18

購買力平價說 1/2

近似計算：

意義： 匯率於某一期間的改變，應等於同一期間的通

膨差。 高通貨膨脹率的貨幣應相對於低通貨膨脹率的

貨幣貶值。

(4.4) 式 1 0

0h f

e ee i

e

19圖表 4.3 購買力平價說

20

購買力的平價說 1/3

意涵： 匯率的變動應只是在抵銷外國價格水準相對本國價

格水準的變動。不會對本國廠商與其外國競爭者的相對競爭地位帶來任何影響才是。

名目匯率（ nominal exchange rate ，亦即實際匯率， actual exchange rate ）的改變，在決定幣值變動對一公司與一國家的真正影響時，可能並不重要。

只有實質匯率的改變才足以影響國內企業與其海外競爭者的相對競爭地位。

21

購買力的平價說 2/3

實質匯率：

實證結果： 在長期能成立，但在短期內則否。

(4.6) 式1

1f

t th

ie e

i

22

Sample Problem

Projected inflation rates for the U.S. and Germany for the next twelve months are 10% and 4%, respectively. If the current exchange rate is $.50/dm, what should the future spot rate be at the end of next twelve months?

0

1

1

t

ht t

f

ie e

i

1

1 1

1.10.50

1.04e

1 .50(1.0577)e

1 $.529e

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PART III.THE FISHER EFFECT 費雪效果 I. THE FISHER EFFECT

states that nominal interest rates (r) are a function of the real interest rate (a) and a premium (i) for inflation expectations.

r = a + i

24

費雪效果 1/2

名目利率 (r) 乃由下列兩部分所構成： (1) 實質的必要報酬率 (a) ，及 (2) 通貨膨脹溢酬 ( 等於預期通貨膨脹率 i ) 。 1+ 名目利率 =(1+ 實質利率 )(1+ 預期通貨膨脹

率 ) 1+r=(1+a)(1+i)

或 r=a+i+ai 近似表示法

r=a+i

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費雪效果 2/2

透過各國間的套利活動，實質報酬應趨於相等。 在無政府干預下的均衡狀態，將遵循「名目利

率差異 (interest rate differential) 近似於預期的通貨膨脹率的差異」 rh–rf=ih–if

具有高通貨膨脹率的貨幣應較具有低通貨膨脹率的貨幣承擔高的利率。

26

實質利率差異 1/2

許多觀察家相信在日漸國際化的資本市場內，重大的實質利率差異不太可能長期存在。 資本市場整合 (capital market integration) 意指

實質利率是由資金的全球供需所決定。 資本市場區隔 (capital market segmentation)恰恰相反，後者主張實質利率是由當地借貸條件所決定。

27

實質利率差異 2/2

實證結果： 實質利率差異是有可能存在的，而且沒被套利

而消失。 各國的實質利率有收斂的趨勢。 實質利率差異可源自於各國採行截然不同的稅

制或對資金自由流動強加規定限制。

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PART IV. THE INTERNATIONAL

FISHER EFFECT 國際費雪效果

A. Real Rates of Interest

1. Should tend toward equality

everywhere through arbitrage.

2. With no government interference

nominal rates vary by inflation

differential or

rh - rf = ih - if

29

THE INTERNATIONAL FISHER EFFECT

B. According to the IFE,

countries with higher inflation rates have higher interest

rates.

C. Due to capital market integration globally, interest rate differentials are eroding.

30

THE INTERNATIONAL FISHER EFFECT

I. IFE STATES:

A. the spot rate adjusts to the interest rate differential between two

countries.

B. IFE = PPP + FE

et = (1 + rh)t

e0 (1 + rf)t

31

THE INTERNATIONAL FISHER EFFECT

B. Fisher postulated:

1. The nominal interest rate differential should reflect

the inflation rate differential.

2. Expected rates of return are equal in the absence of

government intervention.

32

THE INTERNATIONAL FISHER EFFECT

C. Simplified IFE equation:

rh - rf = et - e0

e0

33

THE INTERNATIONAL FISHER EFFECT

D. Implications if IFE1. Currency with the lower

interest rate expected to appreciate relative to onewith a higher rate.

2. Financial market arbitrage:insures interest rate differential

is an unbiased predictor of change in future spot rate.

34

圖表 4.10 國際費雪效果

35

The International Fisher Effect

If the ¥/$ spot rate is ¥108/$ and the interest rates in Tokyo and New York are 6% and 12%, respectively, what is the future spot rate two years from now?

0

1

1

t

ht t

f

re e

r

2

2 2

1.06108

1.12e

2

1.1236108

1.2544e

2 ¥96.74 / $e

36

PART V.INTEREST RATE PARITY THEORY

利率平價理論

I. INTRODUCTION

A. The Theory states:

the forward rate (F) differs from the spot rate (S) at equilibrium by an amount

equal to the interest differential (rh - rf) between two countries.

37

INTEREST RATE PARITY THEORY

2. The forward premium or

discount equals the interest

rate differential.

F - S/S = (rh - rf)

where rh = the home rate

rf = the foreign rate

38

INTEREST RATE PARITY THEORY

3. In equilibrium, returns on

currencies will be the same

i. e. No profit will be realizedand interest parity existswhich can be written(1 + rh) = F

(1 + rf) S

39

INTEREST RATE PARITY THEORY

B. Covered Interest Arbitrage

1. Conditions required:interest rate differential does not

equal the forward premium or discount.

2. Funds will move to a countrywith a more attractive rate.

40

INTEREST RATE PARITY THEORY

3. Market pressures develop:

a. As one currency is moredemanded spot and soldforward.

b. Inflow of funds depressesinterest rates.

c. Parity is eventually reached.

41

INTEREST RATE PARITY

If the Swiss franc is $.68/SF on the spot market and the annualized interest rates in the U.S. and Switzerland, respectively, are 7.94% and 2%, what is the 180 day forward rate under parity conditions?

0

1

1h

t

f

rf e

r

180

.07941

2.68

.021

2

f

180 $.70 /f SF

42

INTEREST RATE PARITY THEORY

C. Summary:

Interest Rate Parity states:

1. Higher interest rates on a currency offset by forwarddiscounts.

2. Lower interest rates are offsetby forward premiums.

43

PART VI.THE RELATIONSHIP BETWEEN THE

FORWARD AND THE FUTURE SPOT RATE遠期匯率與未來即期匯率

I. THE UNBIASED FORWARD RATE (UFR)

A. States that if the forward rate is

unbiased, then it should reflect the

expected future spot rate.

B. Stated asft = E(et+1)