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International Finance International Portfolio Investments

International Finance International Portfolio Investments. Security X & Y with the following attributes Security Return Risk X 20% 10% Y 30% 16% Correlation coefficient ( ρ X,Y ) = 0.5 40% of funds invested on X Calculate the portfolio return & risk Ep = ∑ W i E i

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International Finance International Portfolio Investments

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  1. International Finance International Portfolio Investments

  2. Security X & Y with the following attributes Security Return Risk X 20% 10% Y 30% 16% Correlation coefficient(ρX,Y) = 0.5 40% of funds invested on X Calculate the portfolio return & risk Ep = ∑ Wi Ei = (.40)(.20) + (.60)(.30) = 0.26 = 26% σ2p = w21σ21 + w22σ22 + 2w1w2ρ1,2σ1*σ2 = (40%)2(10%)2+(60%)2(16%)2+2(40%)(60%)(0.5)(10%)(16%) = 12.1%

  3. International Correlation Structure and Risk Diversification • Security returns are much less correlated across countries than within a country. • This is so because economic, political, institutional, and even psychological factors affecting security returns tend to vary across countries, resulting in low correlations among international securities. • Business cycles are often high asynchronous across countries.

  4. U.S based investor takes US$1000000 on January 1, 2002, and invests in a share traded on the Tokyo Stock Exchange (TSE). On January 1, 2002, the spot exchange rate is ¥130.00/$. The investor uses his funds to acquire shares on the TSE at ¥20000 per share, and holds the shares for one year. At the end of one year, the investor sells the shares at the market price, which is ¥25000. On January 1, 2003, the spot rate is ¥125.00/$. Calculate the total return on the investment (US$1300000 – US$1000000)/ US$1000000 = 30% The total return is a combination of the return on the Japanese Yen and the return on the shares listed on the TSE

  5. R$ = [(1 + r¥/$)(1 + rshares,¥)] – 1 rshares,¥ = Percentage change in the share price r¥/$ = Percentage change in the currency value R$ = [(1 + 0.2500)(1 + 0.0400)] – 1 =30% If a U.S. resident just sold shares in a British firm that had a 15% return (in pounds) during a period when the pound depreciated 5%, his dollar return is

  6. Effects of Changes in the Exchange Rate • The realized dollar return for a U.S. resident investing in a foreign market will depend not only on the return in the foreign market but also on the change in the exchange rate between the U.S. dollar and the foreign currency.

  7. Stock Market AU FR GM JP NL SW UK US Australia (AU) .586 France (FR) .286 .576 Germany (GM) .183 .312 .653 Japan (JP) .152 .238 .300 .416 Netherlands (NP) .241 .344 .509 .282 .624 Switzerland (SW) .358 .368 .475 .281 .517 .664 United Kingdom (UK) .315 .378 .299 .209 .393 .431 .698 United States (US) .304 .225 .170 .137 .271 .272 .279 .439 International Correlation Structure Relatively low international correlations imply that investors should be able to reduce portfolio risk more if they diversify internationally rather than domestically.

  8. Domestic vs. International Diversification When fully diversified, an international portfolio can be less than half as risky as a purely U.S. portfolio. A fully diversified international portfolio is only 12 percent as risky as holding a single security. Portfolio Risk (%) Swiss stocks 0.44 U.S. stocks 0.27 0.12 International stocks 1 10 20 30 40 50 Number of Stocks

  9. Optimal International Portfolio Selection • The correlation of the U.S. stock market with the returns on the stock markets in other nations varies. • The correlation of the U.S. stock market with the Canadian stock market is 70%. • The correlation of the U.S. stock market with the Japanese stock market is 24%. • A U.S. investor would get more diversification from investments in Japan than Canada.

  10. Stock Market Correlation Coefficient Mean (%) SD (%)  CN FR GM JP UK Canada (CN) .79 5.83 0.90 France (FR) 0.38 1.42 7.01 1.02 Germany (GM) 0.33 0.66 1.23 6.74 0.87 Japan (JP) 0.26 0.42 0.36 1.47 7.31 1.22 United Kingdom 0.58 0.54 0.49 0.42 1.52 5.41 0.90 United States 0.70 0.45 0.37 0.24 0.57 1.33 4.56 0.80 Summary Statistics for Monthly Returns ($U.S.) .79% monthly return = 9.48% per year

  11. Stock Market Correlation Coefficient Mean (%) SD (%)  CN FR GM JP UK Canada (CN) .79 5.83 0.90 France (FR) 0.38 1.42 7.01 1.02 Germany (GM) 0.33 0.66 1.23 6.74 0.87 Japan (JP) 0.26 0.42 0.36 1.47 7.31 1.22 United Kingdom 0.58 0.54 0.49 0.42 1.52 5.41 0.90 United States 0.70 0.45 0.37 0.24 0.57 1.33 4.56 0.80 Summary Statistics for Monthly Returns ($U.S.) • measures the sensitivity of the market to the world market. Clearly the Japanese market is more sensitive to the world market than is the U.S.

  12. The Optimal International Portfolio OIP Efficient set 1.53 JP UK US FR GM Rf CN 4.2%

  13. OIP ODP Mean Return 1.53% 1.33% Standard Deviation 4.27% 4.56% Gains from International Diversification • For a U.S. investor, the risk-return tradeoff for the optimal international portfolio and optimal domestic portfolio are shown below and at right. return OIP 1.53% 1.33% ODP 4.27% 4.56% risk

  14. An investor is considering investing in two different risky assets, an index of the U.S equity markets and an index of the German equity markets. Expected return Expected risk U.S equity index 14% 15% German equity index 18% 20% Correlation coefficient (ρUs-GER) 0.34 40% of investment on U.S Calculate the return & risk on international portfolio

  15. Country E(Ri) σi Wi A 0.12 0.20 0.60 B 0.08 0.10 0.30 C 0.04 0.03 0.10 ρAB = 0.25 ρAC = -0.08 ρBC = 0.15 Calculate the international portfolio expected return & risk E(Rp) = (0.60)(0.12) + (0.30)(0.80) + (0.10)(0.04) = 10% σ2p = ∑W2iσ2j + ∑∑WiWjCovij σ2p = [W2Aσ2A+W2Bσ2B+W2Cσ2C]+[2WAWBσAσBρAB+2WAWCσAσCρAC + 2WBWCσBσCρBC] = 13.6%

  16. Investors should examine returns by the amount of return per unit of risk accepted, rather than in isolation. To consider both risk and return in evaluating portfolio performance, Sharpe measure (SHP) Treynor measure (TRN) SHPi = ( Ri – Rf ) / σi Where, Ri = Average return for portfolio i during a specified time period Rf = Average risk free rate of return σi = risk of portfolio i TRNi = (Ri – Rf) / βi Assume that therisk free is 5% per year for Hong Kong, calculate SHP and TRN

  17. Assume the U.S dollar returns (monthly averages) shown below for three Baltic republics. Calculate the SHP and TRN measures of market performance. Country M.Ret SD Rf Beta Estonia 1.12% 16% 0.42% 1.65 Latvia 0.75% 22.8% 0.42% 1.53 Lithuania 1.6% 13.5% 0.42% 1.20

  18. International Mutual Funds: A Performance Evaluation • A U.S. investor can easily achieve international diversification by investing in a U.S.-based international mutual fund. • The advantages include: • Savings on transaction and information costs. • Availability of legal and institutional barriers to direct portfolio investments abroad. • Professional management and record keeping.

  19. The Capital Asset Pricing Model – CAPM The CAPM is an equation that expresses the equilibrium relationship between a security’s expected return and it’s systematic risk. E(ri) = rf + βi(rM - rf) Nestle, is a Swiss-based multinational firm. A prospective Swiss investor might assume a risk-free return of 3.3% (index of Swiss government bond issues), an average return on a portfolio of Swiss equities of 10.2% (Financial Times Swiss Index), and a βNestle of 0.885. Calculate the expected rate of return on Nestle equity. 9.41%

  20. The International Capital Asset Pricing Model The international version of the CAPM includes risk premium for multi-country exposure. The general form of international CAPM is given as: E(ri) – rf = βi[E(rM) – rf] + ∑ γi,k[E(Sn) + rnf – rf] rf = Continuous compounded risk-free rate in the domestic country Sn = Exchange rate of country k rnf = Continuous compounded risk-free rate in country k n = Number of countries considered βi and γi = regression coefficients

  21. In the case of Nestle, for the same period as before, a global portfolio index such as the Financial Times index would show a market return of 13.7%. In addition, a beta for Nestle estimated on Nestle’s returns versus the global portfolio index would be 0.585. Calculate the expected return of an internationally diversified Swiss investor.

  22. Why Home Bias in Portfolio Holdings? • Home bias refers to the extent to which portfolio investments are concentrated in domestic equities.

  23. Country Share in World Market Value Proportion of Domestic Equities in Portfolio France 2.6% 64.4% Germany 3.2% 75.4% Italy 1.9% 91.0% Japan 43.7% 86.7% Spain 1.1% 94.2% Sweden 0.8% 100.0% United Kingdom 10.3% 78.5% United States 36.4% 98.0% Total 100.0% The Home Bias in Equity Portfolios

  24. Why Home Bias in Portfolio Holdings? • Three explanations come to mind: • Domestic equities may provide a superior inflation hedge. • Home bias may reflect institutional and legal restrictions on foreign investment. • Extra taxes and transactions/information costs for foreign securities may give rise to home bias.

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