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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