# FCRP calculation

A Swiss investor’s domestic risk-free rate is 9%. Japanese risk-free rates are 2%. The investor expects the Swiss Franc (SF) to depreciate by 5%. What is the foreign currency risk premium (FCRP)?

The FCRP is the expected appreciation of the foreign currency minus the interest rate differential (domestic – foreign). Hence, the FCRP is –2% (= 5% appreciation of the yen minus 7% interest rate differential). The interest rate differential is calculated as: rDC – rFC = 9% – 2% = 7%).

Under this situation, Since Swiss have higher Rf, we should expect the demand for Swiss Franc going up, hence depreciate of Yen by 7% right?

Since the Franc is depreciated 5%, then shouldn’t the FCRP be -12%?
-5-7%=-12%?

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I think this should be one of Schweser’s typo?

I would think about this material seperately from the economics material. The main thesis underlying the econ material is that real rates are the same and differences in inflation drive exchange rates. In contrast, most FCRP problems have different real Rf rates.

Think about FCRP as what you would earn above your home country’s Rf rate if you have exposure to and are invested in the FC. In this case, since you are Swiss, you would be invested in the Yen. The Yen appreciates by 5% (could be through capital flows or inflation), and the Rf asset you invested in only earned 2%. If you have kept your money in Swiss francs, you could have earned 9%.

The difference between what you could have earned in Francs (9%) and what you earned in the FC, Yen (5% + 2%) is -2%. So, for taking exposure to a FC, you lost money compared to what you could have earned on a Rf basis in Switzerland without taking the FC risk, thus the negative FCRP.

So, the FCRP formula is:

FCRP = FC Appreciation/Depreciation - (Rf DC - Rf FC), -2% = 5% - (9% - 2%)

Using the FCRP, the domestic investor who takes exposure to the FC can calculate his return 2 ways:

1) E(R) = Appreciation/Depreciation of FC + Rf of FC, 7% = 5% + 2%
2) E(R) = Rf DC + FCRP, 7% = 9% - 2%

That is a very good explanation. Thanks very much.

By FCRP = FC Appreciation/Depreciation

you mean + sign for FC Appreciation
and - sign for FC Depreciation.

Am I correct?

Yes. And just to clarify a bit from above, think about it terms of the return premium you would earn investing in the FC Rf asset (not just having exposure to the FC as I said) compared to what you would earn by holding the DC Rf asset.