International Portfolio Theory

Portfolio Diversification and Risk

Portfolio diversification and risk

The risk of a portfolio is measured by the ratio of the variance of a portfolio’s return relative to the variance of the market return (portfolio beta)

As an investor increases the number of securities in a portfolio, the portfolio’s risk declines rapidly at first, then asymptotically approaches the level of systematic risk of the market

The total risk of any portfolio is therefore composed of systematic risk (the market) and unsystematic risk (the individual securities)

Increasing the number of securities in the portfolio reduces the unsystematic risk component leaving the systematic risk component unchanged.

A portfolio that is fully diversified would have a beta of 1.0

Optimal portfolio

 Assuming a typical investor is risk-averse

The typical investor is therefore in search of a portfolio that maximizes expected portfolio return per unit of expected portfolio risk

Portfolio opportunity set (exhibit).

The efficient frontier

Optimal portfolio

Calculation of portfolio risk and return

Portfolio return

Portfolio risk

Portfolio performance measurements

The Sharpe ratio

The Treynor ratio

International Diversification and Risk

The case for international diversification of portfolios can be decomposed into two components

The first is the potential risk reduction benefits of holding international securities

The second component of the case for international diversification addresses foreign exchange risk

The foreign exchange risks of a portfolio, whether it be a securities portfolio or the general portfolio of activities of the MNE, are reduced through international diversification

Purchasing assets in foreign markets, in foreign currencies may alter the correlations associated with securities in different countries (and currencies)

The risk associated with international diversification, when it includes currency risk, is very complicated when compared to domestic investments.

International diversification benefits induce investors to demand foreign securities

If the addition of a foreign security to the portfolio of the investor aids in the reduction of risk for a given level of return, or if it increases the expected return for a given level of risk, then the security adds value to the portfolio

A security that adds value will be demanded by investors, bidding up the price of that security, resulting in a lower cost of capital for the issuing firm

Internationalizing the domestic portfolio

Domestic portfolio opportunity set (exhibit).

The efficient frontier.

The internationally diversified portfolio opportunity set

The internationally diversified portfolio opportunity set is of lower expected risk than comparable domestic portfolios. The gains arise directly from the introduction of additional securities and/or portfolios that are of less than perfect correlation with the securities and portfolios within the domestic opportunity set

An investor can reduce investment risk by holding risky assets in a portfolio

The International Capital Asset Pricing Model

The capital asset pricing model (CAPM) states that the expected return on an equity by an investor is the sum of two components, a risk-free rate of interest and a risk-premium component (which is based on the perceived riskiness of the individual security relative to the market)

The International Capital Asset Pricing Model

The CAPM formula is as follows:

ke = krf + βi(km – krf)

Where:

ke = expected (required) rate of return on equity i

krf = rate of interest on risk-free bonds (Treasury bonds, for example)

βi = coefficient of systematic risk for the firm

km = expected (required) rate of return on the market portfolio of stocks

βi = ρimσi

In theory, the primary distinction in the estimation of the cost of equity for an individual firm using an internationalized version of the CAPM is the definition of the “market” and a recalculation of the firm’s beta for the market

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