International Portfolio Investment Reading: Chapter 15

Lecture Outline Basics of diversification Benefits of international diversification Measuring foreign investment performance The home bias puzzle

Basics of diversification

Benefits of international diversification

Measuring foreign investment performance

The home bias puzzle

Why Go Global? In a nutshell: Diversification!!! Potential for higher expected returns for same risk. Potential for lower portfolio risk for same return. International investing Standard deviation of return Expected return Domestic investing

In a nutshell: Diversification!!!

Potential for higher expected returns for same risk.

Potential for lower portfolio risk for same return.

International Correlations & Diversification Security returns are much less correlated across countries than within a country. This is because economic, political, institutional and even psychological factors affecting security returns tend to vary across countries, resulting in low correlations among international securities. Types of companies in each country can also vary significantly .

Security returns are much less correlated across countries than within a country.

This is because economic, political, institutional and even psychological factors affecting security returns tend to vary across countries, resulting in low correlations among international securities.

Types of companies in each country can also vary significantly .

International Stock Returns (’70 – ’04) 16.44 15.54 15.78 22.33 16.78 28.36 21.04 10.98 Std. Dev. (%, LC) 0.974 17.97 13.45 Netherlands 0.920 15.86 12.22 USA 1.065 17.73 11.94 UK 0.879 17.90 12.96 Switzerland 1.017 24.40 5.14 Japan 0.950 23.39 8.91 Germany 1.042 21.02 12.62 France 1.005 24.03 12.33 Australia β W (1970-2004) Std. Dev. (%) Mean (%)

International Correlation Structure (’70 – ’04) Stock Market AU FR GM JP NL SW UK US Australia (AU) 1 France (FR) .407 1 Germany (GM) .349 .667 1 Japan (JP) .315 .392 .362 1 Netherlands (NL) .444 .668 .738 .429 1 Switzerland (SW) .421 .638 .687 .426 734 1 United Kingdom (UK) .489 .574 .475 .373 .653 .579 1 United States (US) .508 .502 .473 .311 .620 .523 .542 1

Domestic vs. International Diversification 27 12 Portfolio Risk (%) Number of Stocks 1 10 20 30 40 50 U.S. stocks International stocks 100

International Investing The tools are Mean/Variance Analysis – same as in previous finance units. However, there are many important cross-country differences that matter when we invest internationally Country Risk Currency Risk We start out with the mathematics of portfolio optimization

The tools are Mean/Variance Analysis – same as in previous finance units.

However, there are many important cross-country differences that matter when we invest internationally

Country Risk

Currency Risk

We start out with the mathematics of portfolio optimization

Portfolio Theory Assumptions: Nominal returns are normally distributed. Investors want more return and less risk as denominated in their home currency. Let w i = proportion of wealth devoted to asset i such that  i w i = 1 Expected return on a portfolio: Portfolio Variance: where  ij =  ij  i  j

Assumptions:

Nominal returns are normally distributed.

Investors want more return and less risk as denominated in their home currency.

Let w i = proportion of wealth devoted to asset i such that  i w i = 1

Expected return on a portfolio:

Portfolio Variance:

Expected Return on a Portfolio E[R i ] σ i A American 14.3% 16.4% B British 17.6% 29.9% J Japanese 17.7% 35.7% Example : Equal weights (50%) of A and J: E[Rp] = w A E[R A ] + w J E[R J ] = (0.5x0.143)+(0.5x0.177) = 0.16 or 16%

E[R i ] σ i

A American 14.3% 16.4%

B British 17.6% 29.9%

J Japanese 17.7% 35.7%

Example : Equal weights (50%) of A and J:

E[Rp] = w A E[R A ] + w J E[R J ]

= (0.5x0.143)+(0.5x0.177)

= 0.16 or 16%

Portfolio Variance Correlation E[R i ]  i A B J A American 14.3% 16.4% 1 0.557 0.325 B British 17.6% 29.9% 0.557 1 0.317 J Japanese 17.7% 35.7% 0.325 0.317 1 Example: Equal weights of A and J  P 2 = w A 2  A 2 + w J 2  J 2 + 2 w A w J  AJ  A  J = (0.5) 2 (0.164) 2 + (0.5) 2 (0.357) 2 + 2(0.5)(0.5)(0.325)(0.164)(0.357) = 0.0481  P = (0.0481) 1/2 = 0.2190 or 21.9 percent

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. Diversification & 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. Diversification & Risk

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.

Diversification & Risk Portfolio of US stocks Total Risk = Diversifiable Risk + Market Risk (unsystematic) (systematic) 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. 20 40 60 80 Number of stocks in portfolio 10 20 30 40 50 1 100 Percent risk = Variance of portfolio return Variance of market return Total risk Systematic risk

Limitations of Domestic Investment If we only invest in domestic shares, then we are limited by the types of companies on offer in our home market. For example, the Australian market is overweight in mining companies and underweight in technology companies compared to the US and other markets. If we want to invest in IT or electronics companies, how do we do that in Australia? By investing internationally, we have a more diverse range of investment opportunities.

If we only invest in domestic shares, then we are limited by the types of companies on offer in our home market.

For example, the Australian market is overweight in mining companies and underweight in technology companies compared to the US and other markets.

If we want to invest in IT or electronics companies, how do we do that in Australia?

By investing internationally, we have a more diverse range of investment opportunities.

Internationalizing a 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 portfolio opportunity set. The domestic portfolio with the minimum risk is MR DP . Domestic portfolio opportunity set •  DP R DP • Minimum risk (MR DP ) domestic portfolio MR DP DP Optimal domestic portfolio (DP) Expected Return of Portfolio, R p Expected Risk of Portfolio,  p R f Capital Market Line (Domestic)

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

Domestic vs. International Diversification 27 12 Portfolio Risk (%) Number of Stocks 1 10 20 30 40 50 U.S. stocks International stocks 100

Key Results of Portfolio Theory The extent to which risk is reduced by portfolio diversification depends on the correlation of assets in the portfolio. As the number of assets increases, portfolio variance becomes more dependent on the covariances (or correlations) and less dependent on variances. The risk of an asset when held in a large portfolio depends on its return covariance (or correlation) with other assets in the portfolio. Example – MSCI World Index & MSCI Emerging Markets Index

The extent to which risk is reduced by portfolio diversification depends on the correlation of assets in the portfolio.

As the number of assets increases, portfolio variance becomes more dependent on the covariances (or correlations) and less dependent on variances.

The risk of an asset when held in a large portfolio depends on its return covariance (or correlation) with other assets in the portfolio.

Example – MSCI World Index & MSCI Emerging Markets Index

Two Asset Case

Combinations of the two portfolios if correlation = 1

Combinations of the two portfolios if correlation = 1 Amount of risk reduction

Are Correlations Constant? Longin & Solnik estimated national stock market correlations during periods of high and low market volatility assuming constant correlations (  i,us ) between index i and the U.S. market. While, movements in volatility of various market indices are not synchronized, they nevertheless conclude that volatility is “contagious”. This means that stock markets tend to move together during BAD times. Which is not good, as it is during bad times that we really want differences across markets.

Longin & Solnik estimated national stock market correlations during periods of high and low market volatility assuming constant correlations (  i,us ) between index i and the U.S. market.

While, movements in volatility of various market indices are not synchronized, they nevertheless conclude that volatility is “contagious”.

This means that stock markets tend to move together during BAD times. Which is not good, as it is during bad times that we really want differences across markets.

The Bad News On Correlations De Santis and Gerard (1997)

Exchange Rate Risk The realized dollar return for an Australian 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 Australian dollar and the foreign currency, i.e. Uncertainty about what will happen to the foreign stock market (r foreign market ). Uncertainty about what will happen to the exchange rate (g $/FC ).

The realized dollar return for an Australian 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 Australian dollar and the foreign currency, i.e.

Uncertainty about what will happen to the foreign stock market (r foreign market ).

Uncertainty about what will happen to the exchange rate (g $/FC ).

The realized dollar return for an Australian resident investing in a foreign market is given by: Where, R i is the local currency return in the i th market. r i is the rate of change in the exchange rate between the local currency and the dollar. Exchange Rate Risk

The realized dollar return for an Australian resident investing in a foreign market is given by:

Exchange Rate Risk An example with Japanese shares: US investor takes $1,000,000 on 1/1/2002 and invests in shares traded on the Tokyo Stock Exchange (TSE) On 1/1/2002, the spot exchange rate was ¥130/$ 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 exchange rate was ¥125/$ The investor receives a 30% return on investment ($1,300,000/$1,000,000) - 1 = 30%

An example with Japanese shares:

US investor takes $1,000,000 on 1/1/2002 and invests in shares traded on the Tokyo Stock Exchange (TSE)

On 1/1/2002, the spot exchange 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 exchange rate was ¥125/$

The investor receives a 30% return on investment ($1,300,000/$1,000,000) - 1 = 30%

Exchange Rate Risk An example with Japanese shares: The total return reflects not only the rise in the yen stock price but also the appreciation of the yen. The formula for the total return is: Where: [ (1/¥125)/(1/ ¥130)]-1 = 0.04; [¥25,000/¥20,000]-1 = 0.25

An example with Japanese shares:

The total return reflects not only the rise in the yen stock price but also the appreciation of the yen.

The formula for the total return is:

Exchange Rate Risk The risk for an Australian resident investing in a foreign market will depend not only on the risk in the foreign market but also on the risk of the exchange rate between the Australian dollar and the foreign currency: This equation demonstrates that exchange rate fluctuations contribute to the risk of foreign investment through two channels: 1. Its own volatility - Var(g i ). 2. Its covariance with the local market returns - Cov(R i ,g i ).

The risk for an Australian resident investing in a foreign market will depend not only on the risk in the foreign market but also on the risk of the exchange rate between the Australian dollar and the foreign currency:

Where to Invest? -11.13% Nikkei Japan -7.81% MIBTEL Italy 1.31% CAC 40 France 3.53% S&P 500 U.S. 3.80% FTSE 100 U.K. 6.43% DJIA U.S. 7.16% TSE Canada 9.81% Nasdaq U.S. 11.68% IPC Mexico 16.63% ST Index Singapore 22.29% DAX 30 Germany 32.25% Seoul Comp. South Korea 39.31% HSI Hong Kong 43.65% Bovespa Brazil 47.15% BSE India 96.66% SSEC China '07 Return Index Country

Where to Invest? 2006 returns

How to Invest? Direct share investment – purchase shares in foreign markets using foreign currencies. Can be hard to do! ADRs/GDRs – purchase shares in foreign companies that are traded on your home exchange in local currency. Limited number! MNCs – why can’t we just buy shares in multinational companies to diversify internationally? Diversification benefits not as good as investing internationally! So what are the easy ways?

Direct share investment – purchase shares in foreign markets using foreign currencies. Can be hard to do!

ADRs/GDRs – purchase shares in foreign companies that are traded on your home exchange in local currency. Limited number!

MNCs – why can’t we just buy shares in multinational companies to diversify internationally? Diversification benefits not as good as investing internationally!

So what are the easy ways?

International Mutual Funds An Australian investor can easily achieve international diversification by investing in an Australian-based international mutual fund. The advantages include: Savings on transaction and information costs. Circumvention of legal and institutional barriers to direct portfolio investments abroad. Professional management and record keeping.

An Australian investor can easily achieve international diversification by investing in an Australian-based international mutual fund.

The advantages include:

Savings on transaction and information costs.

Circumvention of legal and institutional barriers to direct portfolio investments abroad.

Professional management and record keeping.

Country Funds Recently, country funds have emerged as one of the most popular means of international investment. A country fund invests exclusively in the stocks of a single country. This allows investors to: Speculate in a single foreign market with minimum cost. Construct their own personal international portfolios. Diversify into emerging markets that might be inaccessible to individual investors.

Recently, country funds have emerged as one of the most popular means of international investment.

A country fund invests exclusively in the stocks of a single country. This allows investors to:

Speculate in a single foreign market with minimum cost.

Construct their own personal international portfolios.

Diversify into emerging markets that might be inaccessible to individual investors.

Other Avenues Exchange Traded Funds – ETFs are investment companies, registered with the SEC with assets consisting of baskets of securities included in an index fund. One share in an ETF provides an investor diversification to all the constituents of the relevant index and its price and yield track the indices performance. World Equity Benchmark Shares (WEBS) / iShares – Country specific baskets of stocks designed to replicate indices of 14 countries. Low cost, convenient way for investors to hold diversified investments in several different countries.

Exchange Traded Funds – ETFs are investment companies, registered with the SEC with assets consisting of baskets of securities included in an index fund.

One share in an ETF provides an investor diversification to all the constituents of the relevant index and its price and yield track the indices performance.

World Equity Benchmark Shares (WEBS) / iShares – Country specific baskets of stocks designed to replicate indices of 14 countries.

Low cost, convenient way for investors to hold diversified investments in several different countries.

Home Bias Puzzle Home bias refers to the extent to which portfolio investments are concentrated in domestic equities. 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%

Home bias refers to the extent to which portfolio investments are concentrated in domestic equities.

Home Bias Puzzle – Possible Explanations Barriers to international investment (e.g. foreign investment not allowed in a lot of countries). restrictions on capital flows have fallen over time can use country funds International trading frictions: turnover taxes, other taxes, limited liquidity Not a huge problem for larger markets, yet home bias remains Domestic equities may provide a superior inflation hedge. Sovereign risk - repatriation of funds Exchange rate risk Information asymmetries Psychological impediments

Barriers to international investment (e.g. foreign investment not allowed in a lot of countries).

restrictions on capital flows have fallen over time

can use country funds

International trading frictions: turnover taxes, other taxes, limited liquidity

Not a huge problem for larger markets, yet home bias remains

Domestic equities may provide a superior inflation hedge.

Sovereign risk - repatriation of funds

Exchange rate risk

Information asymmetries

Psychological impediments

Conclusions Low correlations across international markets may increase the risk-return trade off Important time variations may exist that can challenge these benefits. Time horizon matters. 2 1 3 Investors might not be taking full advantage of the benefits of international diversification. This is known as the ‘home bias’ puzzle.