Reading 68: International Asset Pricing-LOS i 习题精选 2011, expected, relation, capital, return

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Session 18: Portfolio Management: Capital Market Theory and the Portfolio Management Process
Reading 68: International Asset Pricing

LOS i: State the risk pricing relation and the formula for the international capital asset pricing model (ICAPM), and calculate the expected return on a stock using the model.

 

 

The international capital asset pricing model (ICAPM) expresses expected returns as:

A) E(R) = (b × MRP) + (γ1 × FCRP1) + (γ2 × FCRP2) + … + (γk × FCRPk).

B) E(R) = RF + (γ1 × FCRP1) + (γ2 × FCRP2) + … + (γk × FCRPk).

C) E(R) = RF + (b × MRP) + (γ1 × FCRP1) + (γ2 × FCRP2) + … + (γk × FCRPk).

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Where:

E(R) = asset’s expected return

R_F = domestic currency risk-free rate

b_G = sensitivity of the asset i domestic currency returns to changes in the global market portfolio

MRP_G = world market risk premium [E(R_M) – R_F]

E(R_M) = expected return on world market portfolio

γ₁ to γ_k = sensitivities of asset’s domestic currency returns to changes in the value of currencies 1 through k

FCRP₁ to FCRP_k = foreign currency risk premiums on currencies 1 through k

 

E(R) = R_F + (b × MRP) + (γ₁ × FCRP₁) + (γ₂ × FCRP₂) + … + (γ_k × FCRP_k).

The ICAPM tells us that the expected return on any asset i is equal to the investor’s domestic risk-free rate, plus a world market risk premium (which is scaled by the asset’s world market beta), plus a foreign currency risk premium for each foreign currency.

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In a two-currency world, the international capital asset pricing model expresses expected returns as:

A) E(R) = RF + (b × MRP) + (γLC × FCRPLC) + (γFC × FCRPFC).

B) E(R) = RF + (γLC × FCRPLC) + (γFC × FCRPFC).

C) E(R) = RF + (b × MRP) + (γFC × FCRPFC).

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E(R) = R_F + (b × MRP) + (γ_FC × FCRP_FC).

The relevant risk is world market risk. An additional risk premium is added for the asset’s sensitivity to changes in the foreign currency.

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Which of the following assumptions is needed to justify the international capital asset pricing model (ICAPM)? In the ICAPM, the risk-free rate is:

A) LIBOR-based, and the market portfolio is the market capitalization weighted portfolio of all risky assets in the world.

B) the investor’s domestic risk-free rate, and the market portfolio is the market capitalization weighted portfolio of all risky assets in the domestic market.

C) the investor’s domestic risk-free rate, and the market portfolio is the market capitalization weighted portfolio of all risky assets in the world.

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In the extended CAPM, the risk-free rate (R_F) is the investor’s domestic risk-free rate and the market portfolio is the market capitalization weighted portfolio of all risky assets in the world.

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Which of the following statements related to the International Capital Asset Pricing Model (ICAPM) is least accurate?

A) Investors are concerned with nominal returns in their home currency.

B) Expected return for any asset is a function of the U.S. Treasury rate, the world market risk premium, and the sensitivity of the asset to changes in all other foreign currencies.

C) All investors should hold some combination of their domestic risk-free asset and the world portfolio.

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Expected return for any asset is a function of the investor’s domestic risk-free rate, the world market risk premium, and the sensitivity of the asset to changes in all other foreign currencies. Only if the investor is from the U.S. would he use the U.S. Treasury security.

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A Japanese investor is valuing a Korean security. The risk-free rate is 2% in Japan and 3% in Korea. The world market risk premium is 6% and the securities sensitivity to the world market is 1.2. The security is sensitive to changes in the value of two foreign currencies: the Korean won and U.S. dollar. The foreign currency risk premium (SRP) for the won is 2% and the SRP for the U.S. dollar is 1%. The sensitivity to the won is estimated at 1 and the sensitivity to the dollar is estimated at 2. According to the international capital asset pricing model (ICAPM), what is the required return on the security?

A) 10.2%.

B) 3.2%.

C) 13.2%.

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In a two foreign currency world, the ICAPM becomes to: E(R_i) = R₀ + B_iw × RP_w + γ_i1 × SRP₁ + γ_i2 × SRP₂. Substituting in the numbers from the problem, we get: E(R_i) = 2% + 1.2(6%) + (1)(2%) + 2(1%) = 13.2%. Remember to use the domestic risk-free rate.

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Assume there is a German investor who is restricted to investing only in two currencies—the euro and the U.S. dollar.  The U.S. risk-free rate is 3% and the German risk-free rate is 4%.  The expected appreciation of the U.S. dollar is 2%.  The world portfolio risk premium is 8%.  The currency exposures based on euro returns and world betas for three portfolios are as follows:  > >

> >	A> >	B> >	C> >
World Beta	1.2	1.4	0.8
Currency Exposure	1.5	0.8	2.0

What is the foreign currency risk premium?

A) 2.0%.

B) 1.0%.

C) ?1.0%.

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The domestic currency is the German euro. The interest rate differential between the two countries is 1% (Domestic – Foreign). The expected appreciation of the U.S. dollar is 2%. The SRP is +1% (expected appreciation ? interest rate differential).

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What is the expected return of each security to a German investor?

E(RA)

E(RB)

E(RC)

A) 15.1% 16.0% 12.4%

B) 9.6% 11.2% 6.4%

C) 14.1% 15.0% 11.4%

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A German investor would use the German risk free rate of 4%. The world beta for each security is multiplied by the world risk premium. The currency exposure is multiplied by the euro risk premium of 1 (expected appreciation of 2% ? the interest rate differential of 1%).

E(R_A) = 0.04 + (1.2 × 0.08) + (1.5 × 0.01) = 0.04 + 0.096 + 0.015 = 0.151
E(R_B) = 0.04 + (1.4 × 0.08) + (0.8 × 0.01) = 0.04 + 0.112 + 0.008 = 0.160
E(R_C) = 0.04 + (0.8 × 0.08) + (2.0 × 0.01) = 0.04 + 0.064 + 0.020 = 0.124

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Which of the following statements regarding the International Capital Asset Pricing Model (ICAPM) is least accurate? The ICAPM:

A) assumes risk is priced similarly in all markets.

B) is very similar to the domestic CAPM in form, except for an adjustment for currency risk exposure.

C) can be applied to any financial market.

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The ICAPM applies only in a world with integrated capital markets and therefore cannot be applied to simply any financial market. If markets are segmented, risk may not be priced similarly in all markets and the ICAPM will not be applicable. The ICAPM is very similar to the domestic CAPM in form and application--the only difference is an adjustment for currency risk exposure.

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Song Lee, CFA, is a money manager for a small firm in Seoul. All of Lee’s clients are local. He is considering adding the stock of a U.S. firm, Stockco, to some of his client’s portfolios. Stockco sensitivity to the world index is 0.8 and the risk premium on the index is 6%. The risk-free rate is 3% in the U.S. and 5% in Korea. Stockco is only sensitive to changes in the value of the U.S. dollar. Lee has measured the sensitivity of Stockco to changes in the value of the U.S. dollar to be 1.2. The foreign currency risk premium on the U.S. dollar is 2%. Assuming that Lee uses the international capital asset pricing model (ICAPM), what is the required return on Stockco?

A) 12.2%.

B) 14.2%.

C) 10.2%.

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In a single foreign currency world, the ICAPM simplifies to: E(R_i) = R₀ + B_iw × RP_w + γ_i1 × FCRP₁. Substituting in the numbers from the problem, we get: E(R_i) = 5% + 0.8 × (6%) + 1.2 × (2%) = 12.2%. Remember to use the domestic risk-free rate.

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Lee Okazaki is a Japanese investor who is considering investing in the United States equity and bond market. The world risk premium is 5%. The risk-free rate is 2% in Japan and 3.5% in the U.S. The current exchange rate is 120 yen/$ and the ratio of the price levels of Japan to U.S. consumption baskets is expected to be 120 to 1 in one year. The 1-year interest rate in Japan is 2.5% and the one-year rate is 4% in the U.S. The expected inflation rate in the U.S. is 2% and in Japan the expected inflation rate is 1%.

Okazaki is considering buying common stock in a U.S. firm that has a world beta of 1.1 and an estimated sensitivity of yen-denominated returns to changes in the U.S. dollar of 0.7. What is the required return for this investment?

A) 7.55%.

B) 7.85%.

C) 9.55%.

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The International Capital Asset Pricing Model (ICAPM) for a two world currency is:

E(R) = R_f + β_gMRP_g + γ_$(FCRP_$).

R_f is the domestic risk free rate, in this example Japan. β_g is the World beta. MRP_g is the world market risk premium. γ_$ is the domestic currency sensitivity. Foreign currency risk premium (FCRP) is the foreign currency risk premium calculated by taking the expected appreciation minus the interest rate differential. Note the first part of this is the expected appreciation of the exchange rate. Using relative purchasing power parity (PPP) the expected spot rate is 120 × (1.01 / 1.02) = 118.8. The exchange rate is currently 120yen/$, and a year from now it will be 118.8 yen/$.

FCRP = [E(S₁) ? S₀] / S₀ – (r_DC ? r_FC) = [(118.8 – 120) / 120] – (0.02 ? 0.035) = 0.005

E(R) = 0.02 + 1.1(0.05) + 0.7(0.005) = 0.02 + 0.055 + 0.0035 = 0.0785

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Okazaki is also considering the purchase of a United States one-year bond. If the real exchange rate remains constant over the next period, what is Okazaki’s expected return over the next year on the U.S. one-year bond?

A) 4%.

B) 2%.

C) 3%.

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As long as the real rate remains constant, the expected return on the bond is equal to the U.S. (foreign) interest rate of 4% plus the inflation differential of –1% (inflation in domestic ? inflation in U.S.). The expected return to Okazaki is 3% (= 4% ?1%).

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What will the return be for Okazaki on the 1-year bond if the end-of-period exchange rate is 110:1 instead of the beginning-of-period exchange rate of 120:1?

A) ?1.33%.

B) 8.33%.

C) ?4.33%.

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This indicates that the yen has appreciated over the time period and the real rate has changed. The dollar has depreciated compared to the yen over the time period. The depreciation is (110 / 1) / (120 / 1) ? 1 = 0.9167 ? 1 = –8.33%. The return to Okazaki is foreign interest rate plus the currency appreciation (in this example, depreciation) = 4% – 8.33% = –4.33%.

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Jaro Sumzinski, who lives in Poland, is applying the international capital asset pricing model (ICAPM) to determine the value of a German security. The German currency (Euro) has a risk premium of 1% and the security has a local currency sensitivity of 0.5. The risk-free rate in Poland is 8% and the risk-free rate in Germany is 4%. The world market risk premium is 7% and the securities sensitivity to the world market is 2. What is the required return of the security?

A) 23.5%.

B) 18.5%.

C) 12.5%.

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In a single foreign currency world, the ICAPM simplifies to: E(R_i) = R₀ + B_iw × RP_w + γ_i1 × SRP₁. Substituting in the numbers from the problem, we get: E(R_i) = 8% + 2(7%) + (1 + 0.5)(1%) = 23.5%. Remember to use the domestic risk-free rate.

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Paul Wilkes, a U.S. investor, is interested in investing in securities in the Caribbean country of Grenada. He is convinced that current market conditions make the securities of Grenada very attractive relative to those securities of other countries. Wilkes’ current portfolio is composed entirely of domestic securities, with an allocation of 60% equity and 40% fixed income. Wilkes has little experience in global investing, but has decided that the timing is right to invest at least 10% of his portfolio in foreign assets. Wilkes is particularly attracted to the high rate of return attainable in the Grenada market, but first needs to determine if the additional risk outweighs the return. 

After carefully developing his investment criteria and researching the financial markets of Grenada, Wilkes has narrowed his potential investments down to one choice. The secondary markets for equities issued in Grenada are more illiquid than Wilkes had previously thought. This lack of liquidity in the equities market leads Wilkes to determine that equities would be an inappropriate investment for his portfolio. However, bonds issued by the government of Grenada seem to have a history of good liquidity as well as steady returns, both of which are qualities Wilkes is seeking for his portfolio. Wilkes must now use various methods to determine expected returns for these bonds, given a one-year time horizon, expected changes in the U.S./Grenada exchange rates, and inflation rates. Wilkes also must consider the foreign currency risk premium of the issue, and decide if it is appropriate given the additional exposure. 

The currency of Grenada is the Eastern Caribbean Dollar (ECD). The current exchange rate is 2.50 USD/ECD. The ratio of the price levels of American goods to Grenadian goods is also 2.50. Inflation in the U.S. is expected to be 2% and 3% in Grenada. The end-of-year expected spot exchange rate is 2.75 USD/ECD. The one-year U.S. (risk free) interest rate is 4%, and in Grenada it is 8%. 

Also assume that these two currencies are the only ones that exist. The world portfolio risk premium is 6%. The security Wilkes is interested in is a government issue that has a world beta of 1.25 and currency exposure of 0.80.

What is the beginning of period real exchange rate and the end of period real rate, respectively?

A) 2.50; 2.55.

B) 1.00; 1.11.

C) 6.25; 6.94.

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Beginning of period real exchange rate:
X₀ = S × P_F / P_D = (2.5USD/ECD)(1.0P_Grenada / 2.50P_US) = 1.0 USD/ECD

End of period real exchange rate:
X₁ = (2.75 USD/ECD)(1.03P_Grenada / 2.55P_US) = 1.11 USD/ECD

P_Grenada = 1 × 1.03 = 1.03
P_US = 2.50 × 1.02 = 2.55

(Study Session 18, LOS 66.g)

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Has there been a change in the real exchange rate?

A) Yes, purchasing power has changed.

B) No, inflation remained constant.

C) No, the inflation differential compensated for the change in the spot rate.

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The real exchange rate was 1.00 at the beginning of the period, and at the end it is 1.11. (Study Session 18, LOS 66.g)

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For this question, assume the real exchange rate is expected to be constant. What is the expected exchange rate?

A) 2.52.

B) 2.40.

C) 2.48.

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If the real rate remains constant, the change in the exchange rate will be the inflation differential. Since the differential is 1%, we would expect to see the ECD depreciate by 1% against the dollar. Hence, the expected exchange rate is = 2.50USD/ECD / (1.01) = 2.475USD/ECD. (Study Session 18, LOS 66.f)

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For this question, assume the real exchange rate is expected to be constant. If the U.S. investor wants to buy a bond in Grenada, what would be the approximate expected return of this bond?

A) 7%.

B) 8%.

C) 9%.

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The return on the bond should be approximately equal to the foreign interest rate minus the depreciation of the foreign currency = 8% + (–1%) = 7%. (Study Session 18, LOS 66.f)

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What is the foreign currency risk premium (SRP)?

A) 14.0%.

B) 10.0%.

C) 6.0%.

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SRP = (E(S₁) ? S₀) / S₀ ? (r_DC ? r_FC)
The expected foreign currency appreciation is = (2.75 ? 2.50) / (2.50) = 0.10.
The SRP is the expected foreign currency appreciation minus the interest rate differential:

SRP> >	= 10% ? (4% ? 8%)> >
>>	= 10% + 4%> >
>>	= 14.0%

(Study Session 18, LOS 66.h)

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Using the international CAPM (ICAPM), what is the approximate expected return on this security?

A) 22.7%.

B) 12.2%.

C) 14.0%.

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The ICAPM in this case would be:

E(R_i) = R_f + (β_g × MRP_g) + (γ_iECD × FCRP_iECD)

The ECD risk premium is:

FCRPECD	= (E (S1) ? S0) / S0 ? (rDC ? rFC)
	= 10% ? (4% ? 8%)
	= 10% + 4%
	= 14.0%

Substituting in values, we get:

E(Ri)	= 0.04 + (1.25 × 0.06) + (0.80 × 0.14)
	= 0.04 + 0.075 + 0.112
	= 0.2270 or 22.70%

(Study Session 18, LOS 66.j)