Calculating the Return on Foreign Investments

Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved

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Calculating the Return on Foreign Investments

The return on a foreign investment is affected by the return on the assets within its own market and the change in the exchange rate between the security’s own currency and the currency of the purchaser’s home country.

Therefore, the return on a foreign investment can differ according to the domicile of the purchaser.


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From the viewpoint of an American investor, assume the following information :

Année Taux de change $/peso

(1)

Valeur des actifs étrangers en pesos

(2)

Valeur en $

(1 fois 2)

0 0,091 $ 40 pesos 0,091 X 40 = 3,64 $

1 0,073 $ 45 pesos 0,073 X 45 = 3,28 $


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The return to a Mexican investor expressed in his home currency (pesos) is :

451 1,125

400,125 ou 12,5%

MEX

MEX

R

R

The return to a US investor on Mexican stocks is :

0,073 45 3,2851 0,9

0,091 40 3,64

d'où : 0,1 ou 10%

US

US

MEX

MEX

R

R


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Dividing the return to the American investor into a component due to return in the Mexican market and the return due to exchange gains or losses gives :

1 1 1US

MEXMEX xR R R


where Rx is the exchange return C’est-à-dire la variation en % du taux de change

0,0731 0,8 d'où 0,2 (soit 20%)

0,091

451 1,125 d'où 0,125 (soit 12,5%)

40

1 1 0,2 1 0,125 0,9 d'où 0,10 (soit 10%)US US

x x

MEX MEX

MEX MEX

R R

R R

R R


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Calculating the Return and Risk on Foreign Investments

Restating the preceding equation :

1 1 1US

MEXMEX xR R R

Simplifying : 0,1 0,2 0,125 0,025

MEXUS x MEX x MEXR R R R R

By approximation, we have the following expressions for expected return and standard deviation of return on a foreign security :

1/ 22 2

,2

MEXUS x MEX

MEXUS x MEX x MEX

E R E R E R

NB : la formule qui permet de calculer ici le risque d’un actif financier étranger est identique à celle qui nous a permis de calculer le risque d’un portefeuille composé de deux actifs (cf. Chapitre 2, slides 25 - 28)

0


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Usually, there is a very low correlation between exchange returns (gains or losses expressed as %) and market returns in a country. Therefore, the covariance between exchange returns and market returns is close to zero, so :

, x,MEX

1/ 22 2

0 (or 0)

and

x MEX

MEXUS x MEX


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Let :

, ,

0,2

0,3

0 or 0

x

MEX

x MEX x MEX

Then : 1/ 2 1/22 20,2 0,3 0,13 0,36MEXUS

Thus, the standard deviation of the return expressed in dollars is considerably less than the sum of the standard deviation of the exchange return and the standard deviation of the return of the security in its home currency (here, in pesos)

0,36 0,50MEXUS x MEX


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The Rationale of Holding Foreign Securities in a Portfolio

Holding foreign (Mexican) securities - from the US standpoint - as long as :

,

,.

MEXUS F US F

MEX USMEXUS US

MEXUS MEX USMEX

US F US FUS

E R R E R R

or E R R E R R

Where :

,

( ) :

:

:

:

:

:

MEXUS

US

MEXUS

US

MEX US

F

E R

E R

R

Expected return on Mexican securities in dollars

Expected return on US securities

Standard deviation of the Mexican securities in dollars

Standard deviation of US securities

Coefficient of correlation between US securities returns and Mexican securities

US Risk free rate of interest

=MEX

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Calculating the Return on Foreign Investments