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# Introduction to International CAPM

Investing in any asset has risks that can be minimized by using financial tools to determine expected returns. The capital asset pricing model (CAPM) is one of these tools. This model calculates the required rate of return for an asset using the expected return on both the market and a risk-free asset, and the asset's correlation or sensitivity to the market.

Some of the problems inherent in the model are its assumptions, which include: no transaction costs, no taxes, investors who can borrow and lend at the risk-free rate and investors who are rational and risk averse. Obviously these assumptions are not fully applicable to real-world investing. Despite this, CAPM is useful as one of several tools in estimating the return expected on an investment.

The unrealistic assumptions of CAPM have led to the creation of several expanded models that include additional factors and the relaxing of several assumptions used in CAPM. International CAPM (ICAPM) uses the same inputs as the CAPM but also takes into account other variables that influence the return on assets on a global basis. As a result, ICAPM is far more useful than CAPM in practice. However, despite relaxing some assumptions, ICAPM does have limitations that impact its practicality.

## Understanding ICAPM Calculations

Since ICAPM introduces additional variables or factors to the CAPM model, investors first need to understand CAPM's calculations. CAPM simply states investors want to be compensated for:

1. The time value of money, which they expect to be more than the risk-free rate and
2. Taking market risk so they require a premium over the return of the market, less the risk-free rate, times the correlation with the market.

ICAPM expands on CAPM by further saying that in addition to getting compensated for the time value of money and the premium for taking market risk, investors need to be paid for direct and indirect exposure to foreign currency. ICAPM allows investors to add currency effects to CAPM to account for the sensitivity to changes in foreign currency when investors hold an asset. This sensitivity accounts for changes in a currency that directly and indirectly affects profitability and, thus, returns.

For example, if a company domiciled in the United States buys parts from China and the U.S. dollar strengthens relative the yuan, then the costs of those imports goes down. This indirect currency exposure impacts the profitability of a company and the returns generated by the investment. To determine these effects, investors need to calculate the difference between the expected future spot exchange rate and the forward rate and divide that difference by today's spot rate, the result of which is the foreign currency risk premium (FCRP). Then, multiply that by the sensitivity of the domestic currency returns to changes in foreign currencies. ICAPM provides investors with a way of calculating expected returns in local currency terms by accounting for variables as stated below:

﻿ \begin{aligned} &\text{Expected Return} = \text{RFR} + \beta ( \text{R}_m -\text{R}_f ) + \beta ( \text{FCRP} ) \\ &\textbf{where:}\\ &\text{RFR} = \text{Domestic risk-free rate} \\ &\beta = \text{Beta} \\ &\text{R}_m = \text{Expected return of market} \\ &\text{R}_f = \text{Risk-free rate} \\ &\text{R}_m - \text{R}_f = \text{Premium for global market risk measured} \\ &\text{in local currency} \\ &\text{FCRP} = \text{Foreign currency risk premium} \\ \end{aligned}﻿

## Assumptions

While ICAPM improves upon the unrealistic assumptions of CAPM, several assumptions are still required for the theoretical model to be valid. The most important assumption is that international capital markets are integrated. If this assumption fails and international markets are segmented, then there will be pricing discrepancies among assets with similar risk profiles but in different currencies. As a result, segmented markets will cause investors to make higher allocations to specific assets in specific countries, resulting in inefficient asset pricing. ICAPM also assumes unlimited lending and borrowing at the risk-free rate.

## Practical Uses

ICAPM's usefulness in stock selection and portfolio management is only as good as understanding the assumptions as stated above. Despite these limitations, portfolio selection can be influenced by the model. Understanding the impact of currency movements on a particular company's operations and profits will help investors choose among two assets with similar characteristics in different countries.

For example, if an investor in the U.S. wants to calculate the expected return from holding asset A and compare that to the expected return from holding asset B, he needs to determine the inputs for the last two components of the model, which are to determine the direct currency impact and the indirect currency impact. The first two variables in the equation will be the same for both assets. Therefore, the practical usefulness of the ICAPM is in understanding how one currency affects a company in the foreign country and how translating it to the investor's local currency will impact the return on the asset.

For example: An investor is deciding to invest in one of the following assets:

• Company A: Japanese company that derives all of its profits and input costs in yen
• Company B: Japanese company that derives all its profits in U.S. dollars but has input costs in yen

Both assets have similar betas, or sensitivity to changes in world market portfolio. In a macroeconomic environment where the U.S. dollar is weakening relative to the yen, an investor will determine that the profits for company B would decline, as it would cost more U.S. dollars to buy the products. As such, the required return would increase for company B, relative to company A, to offset the additional currency risk.

## The Bottom Line

ICAPM is one of several models used to determine the required return on an asset. Used in conjunction with other financial tools, it can assist investors in selecting assets that will meet their required rate of return. ICAPM, like CAPM, makes several assumptions, including that global markets are integrated and efficient. If this assumption fails, then stock selection is critical; allocating more resources toward investments in countries that have a currency advantage should result in alpha. Currency advantages tend to disappear quickly as exploited market inefficiencies close, but the fact that these inefficiencies occur argues that active portfolio management is key to providing superior returns over the market portfolio.

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