### PowerPoint Slides 7

```IBUS 302:
International Finance
Topic 7–Interest Rate Parity II
Lawrence Schrenk, Instructor
1 (of 20)
Learning Objectives
1.
2.
Describe and calculate covered interest
arbitrage. ▪
Discuss reasons for a deviation from
interest rate parity.▪
2 (of 20)
Interest Rate Parity (IRP)

Recall, for no arbitrage, the following
relationship must hold:
1  i \$ 
FIRP  \$ / x   S  \$ / x  

1  i x 
Both in American Terms

This is the interest rate parity (IRP)
requirement.

FIRP is the forward rate predicted by IRP.
3 (of 20)
Two Connections
1  i \$ 
FIRP  \$ / x   S  \$ / x  

1  i x 

A Connection:
FIRP  \$ / x   S  \$ / x 
1  i\$ 
iff 
 1
1  i x 
iff i \$  i x

And the reverse.
4 (of 20)
Two Connections (cont’d)

The Two Connection:
FIRP  \$ / x   S  \$ / x  , iff i \$
 ix
FIRP  \$ / x   S  \$ / x  , iff i \$  i x

In words


If the dollar is depreciating (FIRP(\$/x) > S(\$/x)), the
dollar interest return must be higher (i\$ > ix).
If the dollar is appreciating (FIRP (\$/x) < S(\$/x)), the
dollar interest return must be lower (i\$ < ix).
5 (of 20)
FX/Interest Rate Relationships

If dollar is at a forward discount, i.e.,





FIRP (\$/£) > S (\$/£)
There will be less demand for the dollar,
It will cost more dollars to buy one pound
The dollar will depreciate against the pound
Then



i\$ > i£
The interest rate on dollars must be higher to offset
the depreciation.
Otherwise the two strategies would not yield the
same dollar value.
6 (of 20)
Example 1 Revisited


To capture the arbitrage opportunity, do you
borrow or lend dollars?
If the FX market is efficient, what should
happen to the rates in example 1?




S(£/\$) = 0.6000
F12(£/\$) = 0.5800 (→ F12(\$/£) = 1.7241)
i£ = 9%
i\$ = 10%
7 (of 20)
Example 1: An Arbitrage
Opportunity
Strategy 1
≠
\$1.13
£0.6540
F12(\$/£) = 1.7241
i£ = 9%
i\$ = 10%
\$1.10
Strategy 2
S(£/\$) = 0.6000
\$1.00
\$1.00
£0.6000
8 (of 20)
Practice

Is arbitrage possible if...
S(\$/€) = 1.4900, so S(€/\$) = 0.6711
F(\$/€) = 1.4975
i\$ = 6%
i€ = 7%

Exercise:


Calculate the two strategies.
Does the IRP requirement hold?
9 (of 20)
Practice (cont’d)

We could tell that covered interest arbitrage
is possible, since

The dollar is at a forward discount



FIRP (\$/£) > S (\$/£)
1.4975 > 1.4900
But the dollar interest is less


i\$ < i€
6% < 7%
10 (of 20)
Capturing the Arbitrage Profit


If arbitrage is possible,
To capture the profit

Go short in the less valuable strategy


Go long in the more valuable strategy


Here, borrow at the lower return
Here, lend (invest) at the higher return
Net the difference
11 (of 20)
Practice (same numbers)

We now know arbitrage is possible if...
S(\$/€) = 1.4900, so S(€/\$) = 0.6711
F(\$/€) = 1.4975
i\$ = 6%
i€ = 7%

How do you exploit covered interest arbitrage?



Borrow at the lower return (i\$ = 6%)
Lend (Invest) at the higher return (i€ = 7%)
Do it.
12 (of 20)
Implications

Recall the IRP requirement:
1  i \$ 
FIRP  \$ / x   S  \$ / x  

1

i

x 

So, if there is no arbitrage, the forward
rate is strictly a function of...
1.
2.
The spot rate
The two risk free rates of interest
13 (of 20)
Key Idea: Differentials


Forward rates are determined by differentials
in the risk free return (i).
If the risk free rates are equal, i\$ = i€,



FIRP(\$/€) = S(\$/€)
FIRP(€/\$) = S(€/\$)
If the risk free rates are not equal, i\$ ≠ i€,


FIRP(\$/€) ≠ S(\$/€)
FIRP(€/\$) ≠ S(€/\$)
14 (of 20)
Deviations form
Interest Rate Parity
15 (of 20)
Transaction Costs



Transaction costs are central in we can, in
practice, get an arbitrage profit.
Arbitrage is only practical if the arbitrage profit
exceeds the transaction costs required to get
it.
You cannot exploit small deviations from IRP.▪
Arbitrage Practical▪
16 (of 20)
Capital Controls

If governments limit the flow of capital across
political borders,


There are capital controls.
If the demand for a currency increases


The currency appreciates
But capital controls may limit the supply of the
currency.
17 (of 20)
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