# 國際投資學第四章

Chapter 4 International Asset Pricing Introduction § In this chapter we discuss: § Efficient market hypothesis § Domestic CAPM vs. ICAPM § The relation between exchange rates and asset prices. 4 - 2 Quote Convention used in this chapter § Throughout this chapter, the direct currency quote is utilized as: Foreign currency :Domestic currency = S § The investor will pay S units of domestic currency for 1 unit of foreign currency. 4 - 3 International Market Efficiency Efficient Market Hypothesis § In an efficient market, any new information would be immediately and fully reflected in prices. § In an efficient market, the typical investor could consider an asset price to reflect its true fundamental value at all times. § The general consensus is that individual markets across the world are quite efficient. 4 - 4 Integration versus Segmentation § An integrated world financial market would achieve international efficiency, in the sense that capital flows across markets would instantaneously take advantage of any new information throughout the world. § International markets are integrated if they are efficient in the sense that securities with the same risk characteristics have the same expected return wherever in the world they are traded. § Most developed markets are considered to be integrated. 4 - 5 Integration versus Segmentation § International markets are considered to be segmented if they are inefficient in the sense that securities with the same risk characteristics sell at different exchange rate adjusted prices in different countries, thus violating the law of one price. 4 - 6 Impediments to Capital Mobility § It is sometimes claimed that international markets are not integrated but segmented because of various impediments to capital mobility. § Such impediments include: § Psychological barriers § Legal restrictions. § Transaction costs. § Discriminatory taxation. § Political risks § Foreign currency risks. 4 - 7 Impediments to Capital Mobility § The flow of foreign investment has grown rapidly over the years; thus, it does not seem that the international markets are fully segmented. § Large corporations, as well as governments, borrow internationally and quickly take advantage of relative bond mispricing between countries, thus making the bond markets more efficient. 4 - 8 Asset Pricing Theory - Domestic CAPM’s Main Assumptions § Investors are risk averse individuals who maximize the expected utility of their end-of-period wealth § Investors make portfolio decisions on the basis of mean (expected return) and variance § Investors have identical expectations about asset returns § Investors care about nominal returns in their domestic currency § Capital markets are perfect § Borrowing and lending at the riskfree rate is possible § No transactions costs or taxes. 4 - 9 Asset Pricing Theory – The Domestic CAPM § Two conclusions emerge from the domestic CAPM: § Separation Theorem § Risk-Pricing Relation 4 - 10 Separation Theorem § Separation Theorem: everyone should hold the same portfolio of risky asset, and the optimal combination of risky assets can be separated from the investor’s preferences toward risk and return. § The optimal portfolio involves a mix of the risky market portfolio and the risk-free asset 4 - 11 Risk-Pricing Relation § The relation can be expressed as: E(Ri) = R0 + RPm × βi § where E(Ri) is the expected return on asset i § R0 is the risk-free interest rate § βi is the sensitivity of asset i to market movements § RPm is the market risk premium equal to E(Rm) - R0 4 - 12 Risk-Pricing Relation § In an international context, the domestic CAPM implies that all domestic securities would be priced in line with their risk relative to the domestic market. 4 - 13 Asset Returns and Exchange rate movements § Assume S is the direct exchange rate between the two countries § Return from time 0 to time 1 shows that the DC rate of return on an foreign investment R=(V1-V0)/V0 That is R=RFC + s + (s × RFC) FC FC FC FC R =(V1 -V0 )/V0 , the FC rate of return on the investment s =(S1-S0)/S0, the percentage exchange rate movement 4 - 14 Asset Returns and Exchange rate movements § The expected return on an unhedged foreign investment is: E(R) = E(RFC) + E(s) § where E(R) is the expected domestic-currency return on the investment, E(RFC) is the expected foreign-currency investment return, and E(s) is the expected percentage currency movement. 4 - 15 Asset-Pricing Models - Definitions § The expected return on a hedged foreign investment is: FC E(R) = E(R ) + (F – S0)/S0 where E(R) is the expected domestic-currency return on the hedged investment, E(RFC) is the expected foreign-currency investment return F is the forward rate S0 is the spot exchange rate. 4 - 16 Domestic CAPM: A Reminder § Two conclusions emerge from the CAPM: § The normative conclusion where the optimal investment strategy for any investor is a combination of two portfolios: the market portfolio and the risk-free asset. § The descriptive conclusion is an equilibrium risk-pricing expression where the expected return on an asset i is the sum of the risk-free rate plus a market risk premium: E(Ri) = R0 + ?i ? RPM where ?i is the domestic market exposure of the asset and RPM is the domestic-market risk premium. 4 - 17 The CAPM Extended to an International Context § The extended CAPM is similar to the domestic CAPM, but the world market portfolio replaces the domestic market portfolio. 4 - 18 The CAPM extended to an International Context (continued) § The domestic CAPM extension can be justified only with the addition of two unreasonable assumptions: § Investors throughout the world have identical consumption baskets. § Real prices of consumption goods are identical in every country. In other words, purchasing power parity holds exactly at any point in time. 4 - 19 The CAPM extended to an International Context (continued) § With direct rates, the real exchange rate is the nominal exchange rate times the ratio of the foreign price level to the domestic price level. X = S ? (PFC/PDC) § where X is the real exchange rate § S is the nominal exchange rate § PFC is the foreign country price level. § PDC is the domestic country price level 4 - 20 § We can rewrite the mentioned equation in terms of percentage changes over a time period (1 year) x=s+ IFC-IDC = s – (IDC-IFC) Where x and s are percentage movement in the real and nominal exchange rates If PPP holds, the real exchange rate is constant, and the nominal exchange rate is equal to the inflation rate differential 4 - 21 The CAPM extended to an International Context (continued) § The real exchange rate changes in a period if the foreign exchange appreciation during the period does not equal the inflation differential between the two countries during the period. 4 - 22 International CAPM (ICAPM) § Real foreign currency risk the risk that real prices of consumption goods might not be identical in every country § Foreign currency risk premiums The foreign currency risk premium (SRP) is defined as the expected return on an investment minus the domestic currency risk-free rate. SRP? E[(S1 ?S0)/ S0]?(rDC ?rFC) 4 - 23 Foreign Currency Risk Premium (SRP) - Example § The one-year risk-free interest rates are 6 percent in DC and 3 percent in FC. The expected exchange rate appreciation of FC is 4 percent. What is the foreign currency risk premium? § Solution: SRP ? E[(S1 ? S0 ) / S0 ]? (rDC ? rFC ) SRP ? 4% ? (6% ? 3%) SRP ?1% 4 - 24 International CAPM (ICAPM) § The ICAPM is developed under the assumption that nationals of a country care about returns and risks measured in their home currency. § All assumptions of CAPM still hold. § In the ICAPM, as in the domestic CAPM, all investors determine their demand for each asset by a mean-variance optimization using their domestic currency as base currency. 4 - 25 ICAPM Conclusions § Two conclusions emerge from the ICAPM. § One conclusion is normative and indicate what should be the optimal investment strategy of investors. § The other conclusion is descriptive and indicate what should be the equilibrium risk-pricing relation for all assets. 4 - 26 ICAPM: Normative Conclusion § The normative conclusion is that the optimal investment strategy for any investor is a combination of two portfolios: § A risky portfolio common to all investors. This is the world market portfolio optimally hedged against currency risk. The optimal hedge ratios depend on variables such as differences in relative wealth, foreign investment position and risk aversion. § A personalized hedge portfolio used to reduce purchasing power risks. This is usually assumed to be the home risk-free rate 4 - 27 ICAPM: Risk-Pricing Relation § The risk-pricing expression for the ICAPM is that the expected return on an asset i is the sum of the risk-free rate plus the market risk premium plus various currency risk premiums: E(Ri) = R0 + ?iw ? RPw + ?i1 ? SRP1 +…+ ?ik ? SRPk where ? is the world market exposure of the asset and the ??’s are the currency exposures, or sensitivities, of the asset returns to the various exchange rates (1 to k). RPw is the world market risk premium and SRPk are the currency risk premiums. 4 - 28 ICAPM: Risk-Pricing Conclusion § With one foreign currency, the asset pricing equation of the ICAPM simplifies to: E(Ri) = R0 + ?iw x RPw + ?i x SRPFC 4 - 29 ICAPM: Example Assume you are a U.S. investor who is considering investments in the German (stock A) and Italian (stock B) markets. The world market risk premium is 6 percent. The currency risk premium on the Italian lira is 1.75 percent, and the currency risk premium on the euro is 1.5 percent. The interest rate on one-year risk-free bonds is 4.25 percent in the United States. In addition you are provided with the following information: Stock A B β 1 1.5 γ€ 1 -1 γIT -0.3 0.75 4 - 30 Example - Solution Use E(Ri) = R0 + ?iw ? RPw + ?i1 ? SRP1 +…+ ?ik ? SRPk E(RA) = 0.0425 + 1(0.06) + 1(0.015) -0.3(0.0175) = 11.225% E(RB) = 0.0425 + 1.5(0.06) - 1(0.015) + 0.75(0.0175) = 13.0625% 4 - 31 ICAPM versus Domestic CAPM § The ICAPM differs from the domestic CAPM in two respects: § the relevant market risk is world (global) risk, not domestic market risk. § Additional risk premiums are linked to an asset’s sensitivity to currency movements. The different currency exposures of individual securities would be reflected in different expected returns. 4 - 32 Practical Implications § Individual companies § National stock markets 4 - 33 Currency Exposure of Individual Companies § Could be estimated historically by regressing the company’s stock returns and currency returns. § The exchange rate exposure for an individual firm depends on the currency structure of its exports, imports, investments and financing. § For example, if there is a foreign currency appreciation — the importer is hurt and the exporter is helped. 4 - 34 Currency Exposure of National Stock Markets § The influence of exchange rate movements on domestic economic activity may explain the relation between exchange rate movements and stock returns. 4 - 35 Exhibit 4.2: The J-Curve Effect 4 - 36 Tests of the ICAPM § Empirical researchers have explored several questions: § Is currency risk priced? § Is domestic market risk priced beyond global market risk (segmentation)? § Are other firms’ attributes priced beyond global market risk? 4 - 37 Tests of the ICAPM (continued) § A summary of current research tends to support the conclusion that assets are priced in an integrated global financial market. § The evidence is sufficiently strong to justify using the ICAPM as an anchor in structuring global portfolios. § However, the evidence can be somewhat different for emerging smaller markets, in which constraints are still serious. 4 - 38 Estimating Currency Exposures § A local currency exposure is the sensitivity of a stock price (measured in local currency) to a change in the value of the local currency. § The currency exposure of a foreign investment is the sensitivity of the stock price (measured in the investor’s domestic currency) to a change in the value of the foreign currency. § It is equal to one plus the local currency exposure of the asset. 4 - 39 § A zero correlation between stock returns and exchange rate movements would mean no systematic reaction to exchange rate adjustments