Last updated March 1, 1999

INTEREST RATE PARITY

NINE BASICS

  1. ROR = %DI = [I1 - I0]/I0 = tup(I) - one
    where I = value of the investment
  2. %DVODM = [VODM1 /VODM0 ] - 1
  3. VODM1 /VODM0 = 1 + %DVODM
  4. %DVODM = AODM
  5. -%DVODM = DODM
  6. RG = EV(DM)/BV(DM) - 1
    where RG = rate of return in Germany, EV = ending value, and BV = beginning value
  7. [RUS(in ROW) ]= EV($)/BV($) - 1
  8. I0(1 + R) = I1
    Simple Interest Formula
  9. RUS(in ROW) = RUS(DOM) = RUS
    where DOM= domestic investment
    (equilibrium condition)

EXAMPLE #1

Given::

Find:

  1. RUS
  2. %DVODM

Solution:

Step 1 Convert the $1000 to DM

$1000(2DM/$1) = 2000DM = BV(DM)
Step 2 earn interest in Germany for one year
2000DM(1 + .05) = 2100DM = EV(DM)
Step 3 Convert the 2100DM to $
2100DM($.625/1DM) = $1,312.50 = EV($)
RUS = 1312.50/1000 - 1 = 31.25%
%DVOD = -20%
%DVODM = 25%

DISCUSSION

The fundamental aspect of Interest Rate Parity (IRP) is very similar to Purchasing Power Parity which applies the direct exchange rate to the value of a commodity in Germany in order to see what the price should be in dollars in a frictionless world:

PPP:
PUS = ( P G)(VODM)

tup(PUS ) = tupPG tup(VODM)

1 + %DPUS = (1 + %DPG)(1 + %D(VODM))

1 + PUS = (1 + PG)(1 + AODM)

IRP:
IUS = (IG )(VODM)

tupIUS = tupIG tup(VODM)

1 + %DIUS = (1 + %DIG)(1 + %D(VODM))

1 + RUS = (1 + RG)(1 + AODM)

RUS = RG + AODM + (RG)(AODM)

EXAMPLE #1 Redux

The IRP formulas above can be confirmed from the results obtained from Example #1:

RUS = RG + AODM + (RG)(AODM)
.3125 = .05 + .25 +(.05)(.25)

EXAMPLE #2

You take $800 to Germany where it becomes 1400DM. After one year, the 1400DM becomes worth 1580DM at which time the exchange rate is $.80/1DM.

Find the following (answers are in Column 2 of table below):

ending value in $
$1264
dollar return
$464
ROR (rate of return)
58.00%
initial VOD
1.75DM/$1
initial VODM
.57143/1DM
%DVODM
40%
AODM
40%
RG
12.85714%
RUS (in ROW)
58.00%
%DVOD
-28.57%
DOD
28.57%

EXAMPLE #3

You take $2000 to Germany where it becomes 3200DM. After one year, the 3200DM becomes worth 3680DM at which time the exchange rate is $.9375/1DM.

Find the following (answers are in Column 2 of table below):

ending value in $
$3450
dollar return
$1450
ROR (rate of return)
72.50%
initial VOD
1.60DM/$1
initial VODM
$.625/1DM
%DVODM
50%
AODM
50%
RG
15%
RUS (in ROW)
72.50%
%DVOD
-33.33%
DOD
33.33%

INTEREST RATE PARITY AND PURCHASING POWER PARITY:
A UNIFIED THEORY

PPP
1 + PUS = (1 + PG)(1 + AODM)

  • if PG < PUS, then AODM>0 and VODM will go up

  • if PG> PUS, then AODM<0 and VODM will fall

  • if PG = PUS, then AODM = 0 and VODM will stay the same
IRP
1 + RUS = (1 + RG)(1 + AODM)

  • if RG < RUS, then AODM>0 and VODM will go up
  • if RG > RUS, then AODM<0 and VODM will fall
  • if RG = RUS, then AODM = 0 and VODM will stay the same
Purchasing Power Parity examines inflation rates in the two countries and is able to explain why they might be equal and why they might be different -- it depends on the direct exchange rate. Interest Rate Parity examines interest rates and is able to explain why they might be equal and why they might be different -- it depends on the direct exchange rate.

The ceteris paribus of PPP is that interest rates in the two countries need to be held constant and for IRP the requirement is that the respective inflation rates need to be held constant. In a unified theory, these two assumptions can be relaxed by allow ing the one rate to be higher, lower or the same as the other rate.

THE UNIFIED THEORY OF INTEREST RATE PARITY AND PURCHASING POWER PARITY

 

IRP


PPP
RG < RUS
RG > RUS
PG < PUS
IRP: AODM > 0

PPP: AODM > 0

AGREE
IRP: AODM < 0

PPP: AODM > 0

DISAGREE

PG > PUS
IRP: AODM > 0

PPP: AODM < 0

DISAGREE
IRP: AODM < 0

PPP: AODM < 0

AGREE

Page created June 1, 1998