Riskless Profit on the Swiss Franc

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```					 Five Parity Conditions                       Theoretical basis of the parity conditions

1.    Purchasing Power Parity (PPP)     1. Arbitrage- Law of one price
2.    The Fisher Effect (FE)
3.    The International Fisher Effect   2. Risk adjusted expected returns on all
(IFE)                               assets equal.
4.    Interest Rate Parity (IRP)
5.    Unbiased Forward Rate (UFR)

What is an arbitrage - Riskless profit         The price of a Big Mac in Britain was BP
or as Dire Straits put it " Money for            1.27 BP on March 30, 1999.
Nothing "                                      In the US, it was \$2.43. On that day, the
exchange rate was \$1.61 per BP.
THE LAW OF ONE PRICE
Identical goods sell for the                Does this conform to the law of one price?
same price worldwide.                       Is there an arbitrage?

PARITY                                          POWER PARITY
Price levels adjusted for exchange rates
should be equal between countries.             states that the exchange rate of one currency
against another will adjust to reflect
changes in the price levels of the two
countries.

1
In mathematical terms:                           If the US is expected to have a inflation
of 5% for the next year and
et/e0 = (1+ih)t/(1+i f)t                Switzerland 3% for the next year, and
where                                           the current exchange rate is \$0.75 per
et = expected spot rate in HC per FC at time t     Swiss Franc, what is the expected spot
e0 = spot rate rate in HC per FC today             rate in \$ per SFr after one year?
ih =expected home inflation between 0 and t
if =expected foreign inflation between 0 and t
t = the time period

Suppose problem gives you e0 as 1.33             Since the US has higher expected
SFr / USD as asks you to calculate et in        inflation, it depreciates with respect to
SFr per USD, the easiest to solve               the SFr.
problem assuming Switzerland is
home.                                         If the difference in expected inflation is
et = 1.33 * 1.03 / 1.05 = 1.3079 Sfr/USD           expected to persist for 3 years, then the
expected spot rate three years from
1/ .7645 = 1.3080.                                 now would be
.75 * (1.05/1.03)3 = \$.7945

Another way of stating the PPP.                  PPP states that real exchange rates
Define: Real Exchange Rate is                        stay the same.
the nominal rate adjusted for changes in         Assume PPP is valid. Then,
the relative purchasing power of each            et/e0 = (1+ih)t/(1+i f)t
currency over some base period.                Therefore,
et' = et * (1+if)t/(1+ih)t            et ' = et * (1+i f)t/(1+ih)t
= et * Pf / Ph                          = e0 * [(1+ih)t /(1+i f)t ] * [(1+i f)t/(1+ih)t]
= e0

2
From 1980 to 1995, the Yen moved from             We first have find percentage inflation over
226.63 Yen/\$ to 93.96 Yen/\$. In this period,     this period.
the US Consumer price index (CPI) rose          US - 152.4 / 82.4 = 1.8495
from 82.4 to 152.4 and the Japanese CPI         Japan 119.2 / 91 = 1.3098
rose from 91 to 119.2.
To find change in value of Yen express rate in
Yen per \$, therefore, et = 1/93.96
Calculate change in real value of yen over this   Then, e t' = 1/93.96 * (1.3098/1.8495)
period.
= .007538.

The initial exchange rate over this period is
1/226.63 = .004412 \$ / Yen.
Therefore, Yen appreciated in real terms by
71% = (007538 - .004412)/ .004412

If PPP were true, exchange rate for Yen / \$
should have been 226.63 * 1.3098/ 1.8495
= 160.51 Yen / \$

3

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