Value of the investment – CIP example
投資價值– CIP舉例


• Value of this investment would be:
此項投資的價值將是：
  = £1.$/£S.(1+rUS).£/$F
But this time with no foreign exchange risk…
但是，這一次，沒有外匯風險...
This deal better complies with the principle of interest rate parity, as the investments in both countries are now of equal risk.
這筆交易更符合利率平價的原則，在這兩個國家的投資，現在同等的風險。
£/$F = forward exchange of £s for $s in the US market, which would equal (1/$/£F) where $/£F is the forward price of £s in $ prices in the UK market.
http://ukthesis.org/gjswglzy

CIP equation
CIP方程

• From above we know that the investments in £ or $ government securities will give equal returns:
從上面我們知道，以英鎊或美元政府證券的投資將給予同等的回報：
• £1.(1+rUK) = £1.$/£S.(1+rUS).£/$F
or
• (1+rUK) = $/£S.(1+rUS).£/$F
• (1+rUK)/(1+rUS) = $/£S.£/$F
• (1+rUK)/(1+rUS) = $/£S/$/£F

Questions IRP
IRP問題

• (1+rUK) = $/£S.(1+rUS).£/$F
1. If the $ per £ spot exchange rate is $2, the UK interest rate is 5% (0.05) and the US interest rate is 10% (0.10), what would the forward exchange rate be
如果美元英鎊現貨匯率為2美元，英國的利率為5％（0.05）和美國的利率為10％（0.10），遠期匯率
(a) £s per $
(b) $s per £

Answers
IRP 回答

• (1+rUK) = $/£S.(1+rUS).£/$F
• (1.05) = 2.(1.10). £/$F
• (1.05) / (2 x 1.10) = £/$F
• £/$F = 1.05 / 2.2 = 0.477 (to 3sf)
• (a) so the forward exchange rate is £0.477 per $.
• (b) the inverse rate would be 1/0.477 = $2.095 per £

Inflation
通貨膨脹

• Relative Purchasing Power Parity
相對購買力平價
• If levels of prices do not line up accurately, surely changes in prices will be related in some way?
如果價格水平不排隊準確，想必價格變動將被以某種方式相關？
• The Fisher Effect
費雪效應
• Inflation might also be expected to significantly affect relative interest rates between countries.
通脹可能也將有望顯著影響國家之間的相對利率。

The Fisher Effect
費雪效應#p#分頁標題#e#

• The Fisher effect connects interest rates to inflation, stating how ‘real’ interest rates and expected inflation jointly determine ‘nominal’ interest rates:
費雪效應連接通貨膨脹，利率說明如何“真實”的利率和通脹預期共同決定'名義利率：
• (1+r) = (1+r*)(1+i)
• (1+r) = (1+ 0.02) (1+ 0.05) = 1.071
• Where
• r = nominal interest rate (here 7.1%)
• r* = real interest rate (here 2%)
• i = expected inflation rate (here 5%)

Questions Fisher Effect
費雪效應問題

•
• Work out the nominal rate of interest that should occur under the following circumstances:
工作的名義利率應在下列情況下發生：
(1) real interest rate = 3%; expected inflation = 7%
實際利率=3％，預期通貨膨脹率= 7％
(2) real interest rate = 1%; expected inflation = 4%
實際利率=1％，預期通貨膨脹率= 7％
(3) real interest rate = 3%; expected inflation = 7%
實際利率=3％，預期通貨膨脹率= 7％

Answers Fisher Effect
費雪效應答案

• Work out the nominal rate of interest that should occur under the following circumstances:
工作的名義利率應在下列情況下發生：
(1) real interest rate = 3%; expected inflation = 7%
(1+r) = (1.03).(1.07)
r = 10.21
(2) real interest rate = 1%; expected inflation = 4%
(1+r) = (1.01).(1.04)
r = 5.04
(3) real interest rate = 3%; expected inflation = 7%
(1+r) = (1.03).(1.04)
r = 7.12

Sources
來源

• Allen, L. (1997)  Capital Markets and Institutions:  a global view.  (London:  Wiley)
• Eaker, M.R., Fabozzi, F.J., & Grant, D. (1996)  International Corporate Finance.  (International Ed., London:  Dryden) Chapters 4-5, 9