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the fc interest rates are above the $ rates,
and i$eq,t,T might be a little lower than it when the
fc interest rates are below the $ rates It is difficult to get statistical significance
43 CIRPT It is clear that with UIRP we are comparing
apples and oranges! The $ return is riskless The $Equivalent return is very volatile and
maybe risky St T
1 it*, T
St 1 it , T • Aside:
what is the difference between volatility and riskiness? 50 CIRPT (cnt.)
1 i t ,T E S t T
St 1 i *
t ,T What if we were to hedge the FX risk? Then
we would have
1 i t ,T Ft ,T
St 1 i 1 i
*
t ,T $ eq ,t ,T And both returns would have the same risk!
52 11 CIRPT
1 it ,T Ft ,T
St (cnt.) 1 i 1 i
*
t ,T $ eq ,t ,T In this case, if the 2 returns are not equal at any time
we can expect arbitrage to take place Buy the currency in the cheap market and
simultaneously deliver it to the expensive market 53 CIRPT (cnt.) We say that a currency is at a discount if it is
cheaper forward than spot We say that a currency is at a premium if it
is more expensive forward than spot 54 CIRPT (cnt) CIRP says that if you eliminate the FX risk by
hedging (covering) with a forward contract, the
domestic and foreign returns better be the same:
better 1 i t ,T T 360 FS 1 i
t ,T
t *
t ,T T 360 55 12 CIRPT
Ft ,T S t
St i (cnt.) t ,T i t*,T T 1 i t*,T T 360 360 Intuition: the PV of the interest differential is
completely offset by the forward discount or
premium Higher $ i means that the $ is at a discount Higher fc i means that the fc is at a discount or
the $ it at a premium
56 CIRPT (cnt.) Approximate CIRP relations They are nice for shorthand but not sufficiently accurate F t ,T S t
St i t ,T i t*,T It works OK when the fc interest rate is small
• Note the the T/360 adjustment is dropped for simplicity for both F ln t ,T ln Ft ,T ln St it ,T it*,T
S t This is the continuously compounded version of CIRP It works OK when the time interval is small 61 Examples F0 ,T 1 i0 ,T T 360 *
St
1 i0 ,T T
360 or *
i0 ,T i0 ,T T
F0 ,T S 0
360 *
S0
1 i0 ,T T...
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This note was uploaded on 01/16/2010 for the course FBE 436 at USC.
 '09
 PROTOPAPADAKIS

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