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Time and International Diversification

Time and International Diversification. Global investing is expanding Mutual Funds provide a means for international diversification Types: GLOBAL FUNDS -- everywhere, including the US INTERNATIONAL FUNDS -- outside of the US REGIONAL FUNDS -- geographic areas

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Time and International Diversification

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  1. Time and International Diversification • Global investing is expanding • Mutual Funds provide a means for international diversification • Types: • GLOBAL FUNDS -- everywhere, including the US • INTERNATIONAL FUNDS -- outside of the US • REGIONAL FUNDS -- geographic areas • SINGLE COUNTRY FUNDS -- a diversified portfolio of securities from one country

  2. International Equity Returns Two major arguments for international investing 1. Higher average returns abroad • Earlier in product life cycle, population growth, etc. • Though often higher risk as measured by standard deviations 2. Broader diversification • Not perfectly correlated with the US market • Similar to diversifying over different industries, different countries, cultures, etc.

  3. Example: 1980s & Depreciating $Average Monthly (Exchange Adjusted) Returns Country Mean Std Dev Min Max Belgium .0207 .0779 -.267 +.259 Italy .0227 .0903 -.194 +.358 Spain .0234 .0760 -.313 +.316 UK .0189 .0672 -.300 +.177 US .0089.0477 -.216 +.130

  4. Risk – Return are Positively Associated Morgan Stanley Capital International (MSCI) world portfolio, the MSCI Europe and Far East (EAFE), the MSCI U.S. (very much like the S&P 500 portfolio), the International Finance Corporation (IFC) Asia emerging markets portfolio, the IFC Latin American portfolio and the IFC emerging market composite portfolio. These data begin in 1970 for the MSCI data thru 1995.

  5. Diversification & International Diversification • The concept is that RISK involves correlation with the market. • If international equities are less correlated with the US market, their “Betas” will be lower than otherwise similar domestic equities. • A portfolio of stocks from different countries would then bemore diversified than an otherwise similar portfolio of US only stocks

  6. Variance of a weighted average of two securities: Var(a•X + b•Y) = a2·Var(X) + b2·Var(Y) + 2·a·b· XY·x·y PROBLEM 2-Assets:Find the expected value, variance, standard deviation, and coefficient of variation of an equally weighted portfolio where E(X) = .12, E(Y) = .16, with standard deviations of .05, and .08, respectively. The correlation coefficient is 0.1.

  7. Answer • Expected value is .14 • Variance = .52(.0025) + .52(.0064) + 2(.5)(.5)(.05)(.08)(0.1) = .00403 • Standard deviation = SQRT(.00403) = .0634 • Coefficient of Variation is:

  8. Graph Return .16 .14 .12 Standard Deviation is SMALLER than the average of the two standard deviations (.065) Risk as Standard Deviation .05 .063 .08

  9. Variance of returns on a three asset portfolio • Let the weights, w, be: w1 + w2 + w3 = 1 and where Rp = w1·R1 + w2·R2 + w3·R3 • V(Rp) = w12·Var(R1) + w22·Var(R2) + w32·Var(R3) + 2w1·w2·Cov(R1,R2) + 2w1·w3·Cov(R1,R3) + w2·w3·Cov(R3,R2) • Or: V(Rp) = w12·Var(R1) + w22·Var(R2) + w32·Var(R3) + 2w1·w2· 12 •1·2 + 2w1·w3· 13 •1·3 + 2w2·w3·23 •2· • As the number of securities increases, the covariance terms tend to become more and more important.

  10. Beta: As Systematic Risk • The beta (ß): A measure of systematic risk with market. kiis return on asset i. Taken from a simple linear regression: • ki = i+ i·km + iMarket Model • V(ki) = i2·V(km) + V(i) • for a portfolio kp = p+ p·km + p • So, V(kp) = • p2·V(km) + i2·i2] • systematic riskunsystematic risk

  11. Unsystematic Risk Declines Through Diversification  [wi2·i2] • However, the portfolio beta, p, tends to 1, and the variance of the market does not change. Hence, systematic risk remains. Note the squared weights become tiny as N rises N securities

  12. Risk Declines Through Diversification Total Risk • Greater risk reduction with foreign equities. • Standard deviation of US market portfolio is between 15 and 20%. .182 .117 US only International systematic risk N securities

  13. Foreign BetasF • The beta on foreign stocks can be derived from knowledge about the a foreign stock’s correlation with the US market. • If we know the correlation coefficient, and std dev. of foreign and US stock markets, then:  F = • F / US • If the correlation is .2, and the foreign standard deviation is .30 and the US standard deviation is .15, then F = .2(.30/.15) = .4

  14. Correlations Across Countries • Monthly correlations (exchange rate adjusted, lagged one month) for 1981-1989 are quite low. Australia .0524 Austria .0674 Belgium -.0155 Germany .0448 Japan .0782 New Zealand .0010 Switzerland .0730

  15. Time Diversification • Suppose returns are independent and normally distributed, with E(Ri) = for one period, and V(Ri) = 2. • Returns grow proportionally with time: E(Rn) = N·E(Ri) No compounding. • Variance:Var(Rn) = N·2 for N periods. • Hence, the standard deviation grows only by the square root of the time period, n = 1·N • Hence, the C.V. declines in N. • This is know as time diversification

  16. The Coefficient of Variation DECLINES in the length of period, • C.V. = 1· N / N·E(Ri) • Nevertheless, total variability INCREASES in the length of the period • n2 =N•12 • Ex: If  = .05 for one month, then 12 months the standard deviation would be .0512 =.17321

  17. Risk and Time Horizons Total Risk Annual • As the length of the time horizon grew, the “advantage” of diversification flattened and risk increased. • Marcus, R.D., Solberg, D., and Zivney, T.L., "A Reexamination of the Benefits to International Diversification," Recent Developments in International Banking and Finance, Vol. 4 and 5 (Amsterdam: Elsevier Science Publishers B.V., 1991), 315-340. Six Months One Month N securities

  18. Mean International Correlation Coefficients By TIME HORIZONS average correlation coefficients Tests over 120 pairs of countries .42 .42 .31 .14 weekly monthly six months annual

  19. Moving from monthly to 60 months to 120 months smooths returns. Ten Year Holding Periods Five Year HoldingPeriods

  20. LDCs and Emerging Markets CIS • Diversification doesn’t mean investing only in STABLE countries. • Often highly volatile markets offer greater risk reduction as they tend to be less correlated with the US market • Emerging Markets offer the greatest risk and the greatest rewards. • Correlations with LDCs are lower than developed countries.

  21. Modes for Investing Abroad • Several hundred foreign firms are listed on the AMEX and NYSE in US dollars. • Exchange listing requires extensive disclosure, which are required of all US publicly traded firms • GAAP accounting • 10-Ks, Quarterly reports to shareholders and the SEC (Security & Exchange Commission). • But foreign firms get access to US capital. • Examples: Hanson PLC, Nestle

  22. ADRsAmerican Depository Receipts • A substitute for a direct purchase of shares is a certificate to shares held by a US Bank. • A bank buys foreign shares and offers ADRs to the public. • The public owns their share of those shares held by the bank (like a closed-end mutual fund of one company’s shares). • Dividends are passed through to shareholders. • About a 1,000 ADRs available. • Investors absorb a handling cost.

  23. American Shares • The capital stock of some firms involves different classes of shares • Some firms issue a special stock offering in the US of American shares. • Whereas ADRs are certificates to the same shares as trade in the parent country, the American shares are a different category. They may differ with regard to: • voting rights • dividends • Nippon Telephone or Nike B (NYSE), for example

  24. International Asset Allocation: Bonds • Asset allocation involves determining the percentage of different types of assets: stocks, bonds, real estate, money market accounts, etc. • We will concentrate only on Bonds & Stocks. • A “Balanced” portfolio is often 50:50 stocks and bonds. We’ll look first at Bonds only: asset allocation of Foreign & US bond portfolios • Suppose we try differing percentages, we achieve higher return for the same risk as a US only portfolio.

  25. Risk - Return Tradeoff: Bonds Only RETURNS 100% Foreign Bonds .11 .08 .07 Least Risk at 70% US Bonds and 30% Foreign Bonds 100% US Bonds standard deviation as the measure of risk

  26. Asset Allocation with Stocks & Bonds • Investment horizons affect appropriate portfolios. • Stocks are long durationassets. Time horizons of at least five years is recommended. • Age of the investor or the use of the funds affects the prudent asset allocation. • The efficient frontier appears in the next graph.

  27. Efficient Frontiers NOTE:Can do better than just using an index of the World Market values. RETURNS STOCKS & BONDS .30 .20 .10 STOCKS ONLY EAFE Balanced EAFE (Europe, Australia, & Far East) Stocks Only World Stocks Only WorldBalanced US Stocks Only US Balanced standard deviation as the measure of risk

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