Prepared by Shafiq Jadallah

Chapter 19 International Portfolio Theory & Diversification Prepared by Shafiq Jadallah To Accompany Fundamentals of Multinational Finance Michael H. Moffett, Arthur I. Stonehill, David K. Eiteman

Chapter 19International Portfolio Theory & Diversification • Learning Objectives • Separate total risk of a portfolio into two components, diversifiable and non-diversifiable • Demonstrate how both the diversifiable and non-diversifiable risks of an investor’s portfolio may be reduced through international diversification • Explore how foreign exchange risk impacts the individual investor investing internationally • Define the optimal domestic portfolio and the optimal international portfolio

Chapter 19International Portfolio Theory & Diversification • Learning Objectives • Review the recent history of equity market performance globally, including the degree to which the markets are more or less correlated in their movements • Examine the question of whether markets appear to be more or less integrated over time • Explore whether international portfolio theory may be extended to the estimation of a company’s cost of equity using the international CAPM

International Diversification & Risk • Portfolio Risk Reduction • The risk of a portfolio is measured by the ratio of the variance of the portfolio’s return relative to the variance of the market return • This is defined as the beta of the portfolio • As an investor increases the number of securities, the portfolio’s risk declines rapidly at first and then asymptotically approaches the level of systematic risk of the market • A fully diversified portfolio would have a beta of 1.0

Percent risk Variance of portfolio return Variance of market return = 100 80 60 40 Total risk 20 Systematic risk 1 10 20 30 40 50 Number of stocks in portfolio International Diversification & Risk Total Risk = Diversifiable Risk + Market Risk (unsystematic) (systematic) Portfolio of U.S. stocks By diversifying the portfolio, the variance of the portfolio’s return relative to the variance of the market’s return (beta) is reduced to the level of systematic risk -- the risk of the market itself.

Percent risk Variance of portfolio return Variance of market return = 100 80 60 40 20 1 10 20 30 40 50 Number of stocks in portfolio International Diversification & Risk Portfolio of U.S. stocks Portfolio of international stocks By diversifying the portfolio, the variance of the portfolio’s return relative to the variance of the market’s return (beta) is reduced to the level of systematic risk -- the risk of the market itself.

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 diversification • Internationally diversified portfolios are the same in principle because the investor is attempting to combine assets which are less than perfectly correlated, reducing the risk of the portfolio

Foreign Exchange Risk • An illustration with Japanese equity • US investor takes $1,000,000 on 1/1/2002 and invests in stock traded on the Tokyo Stock Exchange (TSE) • On 1/1/2002, the spot rate was ¥130/$ • The investor purchases 6,500 shares valued at ¥20,000 for a total investment of ¥130,000,000 • At the end of the year, the investor sells the shares at a price of ¥25,000 per share yielding ¥162,500,000 • On 1/1/2003, the spot rate was ¥125/$ • The investor receives a 30% return on investment ($300,000/$1,00,000 = 30%)

Foreign Exchange Risk • An illustration with Japanese equity • The total return reflects not only the appreciation in stock price but also the appreciation of the yen • The formula for the total return is Where: ¥130/¥125 = .04 ¥25,000/¥20,000 = .25

Internationalizing the Domestic Portfolio • Classic portfolio theory assumes that a typical investor is risk-averse • The typical investor wishes to maximize expected return per unit of expected risk • An investor may choose from an almost infinite choice of securities • This forms the domestic portfolio opportunity set • The extreme left edge of this set is termed the efficient frontier • This represents the optimal portfolios of securities that possess the minimum expected risk per unit of return • The portfolio with the minimum risk among all those possible is the minimum risk domestic portfolio

Capital Market Line (Domestic) Expected Return of Portfolio, Rp Optimal domestic portfolio (DP) DP • R DP Minimum risk (MRDP ) domestic portfolio • MRDP Domestic portfolio opportunity set Rf Expected Risk of Portfolio,p  DP Internationalizing the Domestic Portfolio An investor may choose a portfolio of assets enclosed by the Domestic portfolio opportunity set. The optimal domestic portfolio is found at DP, where the Security Market Line is tangent to the domestic portfolio opportunity set. The domestic portfolio with the minimum risk is MRDP.

Internationalizing the Domestic Portfolio • If the investor is allowed to choose among an internationally diversified set of securities, the portfolio set of securities shifts to upward and to the left • This is called the internationally diversified portfolio opportunity set

Capital Market Line (Domestic) Expected Return of Portfolio, Rp DP • R DP Internationally diversified portfolio opportunity set Domestic portfolio opportunity set Rf Expected Risk of Portfolio,p  DP Internationalizing the Domestic Portfolio An investor may choose a portfolio of assets enclosed by the Domestic portfolio opportunity set. The optimal domestic portfolio is found at DP, where the Capital Market Line is tangent to the domestic opportunity set. The domestic portfolio with the minimum risk is designated MRDP.

Internationalizing the Domestic Portfolio • This new opportunity set allows the investor a new choice for portfolio optimization • The optimal international portfolio (IP) allows the investor to maximize return per unit of risk more so than would be received with just a domestic portfolio

Optimal international portfolio Expected Return of Portfolio, Rp CML (International) CML (Domestic) • IP R IP DP • R DP Internationally diversified portfolio opportunity set Domestic portfolio opportunity set Rf Expected Risk of Portfolio,p  IP  DP Internationalizing the Domestic Portfolio An investor may choose a portfolio of assets enclosed by the Domestic portfolio opportunity set. The optimal domestic portfolio is found at DP, where the Security Market Line is tangent to the domestic portfolio opportunity set. The domestic portfolio with the minimum risk is MRDP.

Calculating Portfolio Risk and Return • The two-asset model consists of two components • The expected return of the portfolio • The expected risk of the portfolio • The expected return is calculated as Where: A = one asset B = second asset w = weights (respectively) E(r) = expected return of assets

Calculating Portfolio Risk and Return • The expected risk is calculated as Where: A = first asset B = second asset w = weights (respectively) σ = standard deviation of assets  = correlation coefficient of the two assets

Calculating Portfolio Risk and Return • Example of two-asset model Where: US = US security GER = German security wUS = weight of US security – 40% wGER = weight of German security – 60% σUS = standard deviation of US security – 15% ρ = correlation coefficient of the two assets – 0.34

Calculating Portfolio Risk and Return • Example of two-asset model Where: EUS = expected return on US security – 14% EGER = expected return on German security – 18% wUS = weight of US security wUS = weight of German security E(r) = expected return of portfolio

Expected Portfolio Return (%) • 18 17 • Maximum return & maximum risk (100% GER) Initial portfolio (40% US & 60% GER) 16 • Minimum risk combination (70% US & 30% GER) 15 • Domestic only portfolio (100% US) 14 13 12 Expected Portfolio Risk ( ) 0 11 12 13 14 15 16 17 18 19 20 Calculating Portfolio Risk and Return

Calculating Portfolio Risk and Return • The multiple asset model for portfolio return

Calculating Portfolio Risk and Return • The multiple asset model for portfolio risk

National Equity Market Performance

Sharp and TreynorPerformance Measures • Investors should not examine returns in isolation but rather the amount of return per unit risk • To consider both risk and return for portfolio performance there are two main measures applied • The Sharpe measure • The Treynor measure

Sharp and TreynorPerformance Measures • The Sharpe measure calculates the average return over and above the risk-free rate per unit of portfolio risk Where: Ri = average portfolio return Rf = market return σ = risk of the portfolio

Sharp and TreynorPerformance Measures • The Treynor measure is similar to Sharpe’s measure except that it measures return over the portfolio’s beta • The measures are similar dependant upon the diversification of the portfolio • If the portfolio is poorly diversified, the Treynor will show a high ranking and vice versa for the Sharpe measure Where: Ri = average portfolio return Rf = market return β = beta of the portfolio

Sharp and TreynorPerformance Measures • Example: • Hong Kong average return was 1.5% • Assume risk free rate of 5% • Standard deviation is 9.61%

Sharp and TreynorPerformance Measures • Example: • Hong Kong average return was 1.5% • Assume risk free rate of 5% • beta is 1.09

Sharp and TreynorPerformance Measures • For each unit of risk the Hong Kong market rewarded an investor with a monthly excess return of 0.113% • The Treynor measure for Hong Kong was the second highest among the global markets and the Sharpe measure was eighth • This indicates that the Hong Kong market portfolio was not very well diversified from the world market perspective

Are Markets Increasingly Integrated?

The International CAPM • Recall that CAPM is • The difference for the international CAPM is that the beta calculation would be relevant for the equity market for analysis instead of the domestic market Where: β = beta of the security  = correlation coefficient of the market and the security σ = standard deviation of return

The International CAPM

Summary of Learning Objectives • The total risk of any portfolio is composed of systematic (the market) and unsystematic (individual securities) risk. Increasing the number of securities in a portfolio reduces the unsystematic risk component • An internationally diversified portfolio has a lower beta. This means that the portfolio’s market risk is lower than that of a domestic portfolio; this arises because the returns on the foreign stocks are not closely correlated with returns on US stocks

Summary of Learning Objectives • Investors construct internationally diversified portfolios in an attempt to combine assets which are less than perfectly correlated, reducing the total risk of the portfolio. In addition, by adding assets outside the home market, the investor has now tapped into a larger pool of potential investments • International portfolio construction is also different in that when the investor acquires assets outside their home market, the investor may also be acquiring a foreign-currency denominated asset

Summary of Learning Objectives • The investor has actually acquired two assets – the currency of denomination and the asset subsequently purchased with the currency – two assets in principle but two in expected returns and risks • The foreign exchange risks of a portfolio are reduced through international diversification • The individual investor will search out the optimal domestic portfolio which combines the risk-free asset and a portfolio of domestic securities found on the efficient frontier

Summary of Learning Objectives • This portfolio is defined as the optimal domestic portfolio because it moves out into risky space at the steepest slope – maximizing the slope of expected return over expected risk – while still touching the opportunity set of domestic portfolios • The optimal international portfolio is found by finding that point on the capital market line which extends from the risk-free rate of return to a point of tangency along the internationally diversified efficient frontier

Summary of Learning Objectives • The investor’s optimal portfolio possesses both higher than expected portfolio return and lower expected risk than the purely domestic portfolio • Risk reduction is possible through international diversification because the returns of different stock market around the world are not perfectly positively correlated • The relatively low correlation coefficients among returns of 18 major stock markets in the 20-year period indicates great potential for international diversification

Summary of Learning Objectives • The overall picture is that the correlations have increased over time • Nevertheless, 91 of the 153 correlations had overall means still below 0.5 in 1987-1996, thus markets are increasingly integrated • However, although capital market integration has decreased some benefits of international portfolio diversification, the correlations between markets are still far from 1.0 • In theory, the primary distinction in the estimation of the cost of equity for an individual firm using CAPM is the definition of the “market” and a recalculation of the firm’s beta for that market

Prepared by Shafiq Jadallah