1. Intermediate Investments F3031 International Investments Objectives 1. Understand the case for International diversification 2. What makes determining international asset returns different from other domestic asset returns What makes international portfolio choices unique? 1. Foreign currency exposure and risks 2. Country specific risks 3. BUT it does provide additional assets in the investment opportunity set that are not perfectly correlated with the US market.

2. Intermediate Investments F3032 Foreign Currency Exposure Define:  R it = the net return on asset i at time t denominated in the Domestic currency units (i.e. USD)  R* (it) is the net return on a foreign asset i at time t denominated in the local currency units (i.e. EUR)  S(t) is the exchange rate at time t (i.e., USD/EUR)

3. Intermediate Investments F3033 Foreign Currency Exposure (cont) Consider a US investor holding a simple portfolio consisting of only the DAX index (the broad German index) The local (EUR) gross return is: 1+ R*(it) = P*(it) + D*(it) / P*(it-1) Where P*(it) is the value of the index at time t and D*(it) is the dividend it pays at time t.

4. Intermediate Investments F3034 Foreign Currency Exposure (cont) The Domestic (USD) gross return is: 1+R(it) = (P*(it) + D*(it) ) * S(t) / P*(it-1) * S(t-1) = (1+R*(it)) * (1+R(st)) Where R(St) is the percentage change in the FX rate (either up or down). So, we already said that 1+R*(it) = 1.14 from above. If the exchange rate goes up (that is the dollar depreciates) by 5% then the return will be: 1+R(it) = (1+.14) * (1+.05) 1+R(it) = 1.197 R(it) = 19.7%

5. Intermediate Investments F3035 Foreign Currency Exposure (cont) So, with International equity investments, you –Invest in the local market –Invest in the FX rate versus the domestic currency

6. Intermediate Investments F3036 Example of Foreign Currency Exposure Consider investing in a German equity portfolio which includes DAX stocks 1. To initiate the purchase change USD to EUR 2. Liquidate the German position after 1 year 3. Record profit/loss in EUR 4. Sell EUR for USD Spot rate is 1 USD = 2 EUR so.500 Invest 1,000,000 in the DAX which rises 20% over the year What is the return if the FX rate drops to.375? Rises to.625

7. Intermediate Investments F3037 The Case for International Diversification What are the implications of holding a diversified international portfolio including:  International bonds and stocks  Holdings of Foreign currencies If you remember back to mean-variance efficient portfolios the underlying assumptions about investor preferences are:  An aversion towards portfolio variance  A desire for higher portfolio return

8. Intermediate Investments F3038 The Case for International Diversification Some Background The US stock market represents about 48% of the world market Does it make sense to ignore the other 52%? Just because they simply exist is no reason to invest Some of the markets have under-performed compared to the risk (volatility) of the US market So, how much should we invest in domestic v. foreign markets?

9. Intermediate Investments F3039 The Case for International Diversification Let ‘w’ = the weight that indicates what % of our invested wealth goes to the domestic asset. If the Return on the Portfolio = R(p) then: R(p) = w*R(d) + (1- w) R(f) = w*R(d) + (1- w) (R*(f) + R(s)) Where R(d) is the domestic return, R(f) is the local return and (R*(f) + R(s)) is an APPROXIMATION of the local return + the FX return on the local investment.

10. Intermediate Investments F30310 The Case for International Diversification So, the choice of w, the weight of the domestic asset has implications for the risk and return associated with the portfolio and the portfolio return is just a weighted average of return on the domestic index and the foreign index (both in the domestic currency). Measure the variance of the portfolio utilizing the variances of the foreign market, the domestic market and rate of change in FX rates and three correlations. The correlations between: 1.The foreign market and the depreciation rate of currencies 2.The domestic and foreign stock markets 3.The domestic market and the depreciation rate of currencies

11. Intermediate Investments F30311 The Case for International Diversification Smaller values tend to bring greater gains from diversification. So, if there are low correlations between the US and other developed markets, this would imply that we could gain from international diversification by providing a higher expected return with lower risk.

12. Intermediate Investments F30312 International Asset Pricing So far, we have said that considering international investments makes sense, but we have not talked about the cost of capital in global markets and how to price foreign assets. In CAPM, risk in defined in terms of beta: the covariance of an asset with the “market” portfolio. E(Ri) = Rf + beta(i,m) [ E (Rm) – Rf ] In a perfect world with no FX risk, the natural extension of our domestic CAPM model is to apply it to the world market portfolio, so: E(Ri) = Rf + beta(i,w) [ E (Rw) – Rf ]

13. Intermediate Investments F30313 Purchasing Power Parity (PPP) The real FX risk comes from deviations from purchasing power parity (PPP). PPP states “Exchange rates should tend to equalize relative price levels in different countries”

14. Intermediate Investments F30314 Purchasing Power Parity (PPP) In a model with two countries, the asset pricing relation will be: E(Ri) – Rf = beta(iw) * [E(Rw) – Rf] + beta(i,s) [E(Rs) + R*f – Rf ] Where E(Rs) is the expected rate of depreciation of the FX rate and R*f is the foreign risk free rate. So, the risk premium is equal to the risk premium of the world market portfolio plus the risk premium resulting form the changes in FX rates. This is a simple two-factor model. Other models can be far more complex.

15. Intermediate Investments F30315 Other Risk Components Another risk component is country specific risk. The cost of capital depends on the market you are dealing in and depends on:  Market risk  Degree of integration  FX risk  Political risk  Economic risk This is much more interesting in developing countries!