Deck 4: International Asset Pricing  

Question 1

The interest rate on one-year risk-free bonds is 5% in the United Kingdom, and 3.75% in Switzerland. The current exchange rate is £0.5 per Swiss franc. Suppose that you are a British investor and you expect the Swiss franc to appreciate by 2% over the next year.
a. Calculate the foreign currency risk premium.
b. Calculate the domestic currency return on the foreign bond, assuming that your currency appreciation expectations are met.

Answer 1

a. The interest rate differential (U.K. minus Swiss) = 0.05 - 0.0375 = 0.0125 or 1.25%. This implies that the Swiss franc trades at a forward premium of 1.25%, that is, the forward exchange rate is quoted at a premium of 1.25% over the spot exchange rate of £0.5 per franc. But the expected appreciation of the franc is higher and equal to 2%. Hence, there is a currency risk premium on the Swiss franc:
Foreign currency risk premium = 0.0200 - 0.0125 = 0.0075 = 0.75%.
b. The domestic currency (U.K. pounds) return on the foreign bond is 5.75%. This can be calculated in one of the following two ways:
Domestic risk-free rate + Foreign currency risk premium =5% + 0.75% = 5.75%.
Foreign risk-free rate+ Expected exchange rate movement= 3.75% +2% =5.75%.

Question 2

An asset has a beta of 1.20. The variance of returns on a market index, $\sigma _ { m } ^ { 2 }$ is 225. If the variance of returns for the asset is 400, what proportion of the asset's total risk is systematic, and what proportion is residual risk?

Answer 2

$\bullet$ The total risk of the asset is 400 (a $\sigma$ of 20%).
$\bullet$ Systematic risk =1.2²(225) = 324%.
Thus, the portion of total risk that can be attributed to market risk is 324/400 = 81%. The balance, 19%, can be attributed to asset specific risk.

Question 3

You are a U.S. pension fund that cares about dollar return. You believe in the "multicountry approach" to asset pricing but feel that currency premiums are equal to zero (so you do not care about currency exposures). The multicountry approach assumes that national equity markets are priced globally and that securities of each country are priced relative to their national market. In other words, each security is influenced by its national market factor, which in turn is influenced by the world market factor, and, possibly, by currency factors. This implies that the world beta of security i ( $\beta$ _iw, or sensitivity to the world market), is equal to the product of the local beta of security i ( $\beta$ _i, or sensitivity to the local market) times the world beta of its local market ( $\beta$ _lw).
In your portfolio construction, you apply a traditional two-step procedure where, you first decide on country allocation and then on security selection within each country.
The following are your forecasts for the coming year, the betas of stocks calculated relative to their domestic index, as well as the betas of the national stock markets relative to the world index. All forecasts are measured in their local currency.
Assume that you do not hedge currency risks.
a. Write the international CAPM equations that would hold for each national market and security. Express it in dollars and in the security's local currency.
b. Which national market should you under/overweight in your global portfolio? [To answer this question, you will first calculate the expected return of all three markets in dollars. You will then compare those to the theoretical expected return suggested by the international CAPM.]
c. Which are the most attractive stocks in each market? [To answer this question, you will compare the expected return of each security to its theoretical expected return suggested by the domestic CAPM.]
Assume now that you only invest in foreign stocks that are fully hedged against currency risk.
d. Which national market should you under/overweight in your global portfolio?
e. Which are the most attractive stocks?

Answer 3

Note to the Instructor: This is a rather complex problem whose purpose is to engage in discussion about active portfolio construction using deviation from the international CAPM. The solution proposed is only a discussion guideline to introduce concepts .It is important to use the linear approximation throughout (e.g., the dollar expected return on a Japanese security is the sum of the yen expected return plus the expected percentage currency movements of the yen against the dollar).Otherwise it
is a bit messy and we have to introduce the fact that currency risk premiums are zero.
This problem is already challenging, so, I often only assign to my students questions (a) through (c). Question (d) and (e) involve currency hedging and I deal with them in class if I have the time.
a. Let's first review the implication of the multicountry approach (often used in global asset management) if the international CAPM holds.
For each security, the international CAPM dictates:
E_T(R_i) =R₀ + $\beta$ _iw (E(R_w) -R₀) = R₀ + ( $\beta$ _i * $\beta$ _lw) *(E(R_w) - R₀).
Where all returns are measured in the same currency; for example in dollars with R₀ being the U.S. risk-free rate (or in yen, with R₀ being the Japanese risk-free rate). In risk premium terms
we have:
RP_i= $\beta$ _i * $\beta$ _lw *RP_w.
Again, note that this equation is independent of the currency used to measure returns. This is because a risk premium is the difference of two returns in the same currency, so currency movements will cancel out. What is important is to use as the risk-free rate R₀, the interest
rate of the currency used to measure returns.
For a given local market l, we have:
E_T(R_l) =R₀ + $\beta$ _lw (E(R_w) - R₀)
or:
RP_l = $\beta$ _lw *RP_w.
Hence, there is also a risk pricing relation for each security relative to its local market:
RP_i = $\beta$ _i * $\beta$ _lw *RP_w = $\beta$ _i *RP_l.
As an active manager believing that expected returns are not fully consistent with market equilibrium, your choice will be in a risk/return framework, trying to capitalize on my forecasts while maintaining a good diversification. As forecasts are, by nature uncertain, my neutral position will be a well-diversified global portfolio (possibly with market capitalization weights). You will over/underweight markets and securities based on your forecasts. To do so, you compute the alpha of securities based on the difference between the forecasted return and the theoretical return.
Here are my total dollar return forecasts for the markets (including currency gains or losses with a linear approximation).
$$\begin{array} { l c c c } & \begin{array} { c } \text { United } \\\text { Statas }\end{array} & \text { France } & \text { Japan } \\\hline \text { Risk-Free Rate } & \text { go/ } & 5 \% & 11 \% \\\text { Stack Market } & 10 \% & 6 \% & 19 \% \\\text { Compary A } & 13 \% & & \\\text { Compary B } & 9 \% & & \\\text { Compary C } & 11 \% / 6 & & \\\text { Compary D } & & 7 \% & \\\text { Compary E } & & 7 \% & \\\text { Compary F } & & 6 \% & \\\text { Compary G } & & & 21 \% \\\text { Compary H } & & & 23 \% \\\text { Compary I } & & & 17 \% \\\hline\end{array}$$ b. Assume that we start from a passive benchmark such as the world index. Based on forecasts,
I would tend to overweight Japan (expected market return of 19%) and underweight France (expected market return of 6%) in my portfolio. France is clearly not an attractive place to invest, as its world beta is 1.2, while its expected dollar return is below the dollar risk-free rate. On the other hand, Japan has a huge risk premium (19 -8 =11%) compared to its world beta of 1.3.
The alpha of each local market is given by the equation:
$\alpha$ _l =E(R_l) -E_T(R_l) =E(R_l) -(R₀ + RP_l).
Where all returns are in dollars and R₀ is the U.S. risk-free rate. Using a world risk premium
of 2%, I have an alpha of -4.4% for France and +8.4% for Japan. The U.S. stock market seems properly priced.
You would overweight or underweight markets but not put all your money in a single market
(or security) because you know that forecasts can turn wrong and you wish to keep a well-diversified global portfolio (we do not have sufficient data on this very simple case to say much more on diversification).
c. In each market, I would then turn to the security selection on a risk/return basis. For each company, I can calculate its local $\alpha$ from the following equation:
E(R_i) = R₀ + $\beta$ _i (E(R_l) - R₀) + $\alpha$ _i
where E(R_i) and E(R_l) are the expected (forecasted) returns in local currency terms on company i and on the local market. R₀ is the local risk-free rate, $\beta$ _i is the beta of company i relative to its domestic (local) market, and $\alpha$ _i is the extra return due to an inefficient pricing in the local market, given the risk of the company.
The local $\alpha$ _s are given below:
$\begin{array}{lrrrrr}\text { United States } &{\text { France }} &{\text { Japan }} \\\hline \text { A: } 2.6 \% & \text { D: } 1.2 \% & \text { G: } 0 \% \\\text { B: } -0.8 \% & \text { E: } 0 \% & \text { H: } 3.2 \% \\\text { C: } 0 \% & \text { F: } -0.1 \% &{\text { I: }} -1.2 \%\end{array}$ In their respective countries, the best companies in which to invest are: A (United States),
D (France), and H (Japan).
Note that these local $\alpha$ measure mispricing relative to the local market, not relative to the world. This is what we want to do in this two-step portfolio construction approach. We first look at mispriced markets and then at mispriced securities relative to their local markets. We could also compute a world $\alpha$ for all securities, but these would reflect both the mispricing of the local market relative to the world and the mispricing of the security in its local market. These world alphas would be given by the equation:
$\alpha _ { i } ^ { t }$
= E(R_i) +(R₀ + $\beta$ _i * $\beta$ _lw*RP_w).
All French (Japanese) securities would have a very negative (positive) alpha simply because the national market is strongly overvalued (undervalued).
If I did not care about risk, I would only invest in the asset expected to perform best, that is, company H in Japan with an expected return of 23% (assuming a linear approximation rather than the compounding of stock market and currency returns). Because of risk, my strategy will rather be to overweight countries such as Japan and companies such as A, D, and H, while still maintaining a good diversification. Also Japanese bills might be attractive.
d. If I hedge my investments, the French stock market expected return is:
11% + (8% -10%) = 9%.
The Japanese stock market expected return is:
14% + (8% -6%) = 16%.
So, I would still tend to overweight Japan and underweight France in my portfolio.
e. The results are the same as in the solution to Question (b).

Question 4

Consider two Thai firms listed on the Bangkok stock exchange:
$\bullet$ Thai A is a mining company that exports a large part of its minerals production. Much larger competitors can be found in Latin and North America. The market price of its production is largely determined in dollars on the world market.
$\bullet$ Thai B imports various engine parts from Europe and the United States. The demand for its product is highly price elastic. A significant rise in baht prices lowers the demand.
a. What will happen to the earnings and stock prices of the two companies if there is a sudden and large devaluation of the Thai baht against major currencies?
b. What can you say about the currency exposures of the two companies ( $\gamma$ 's)

Question 5

Consider an asset that has a beta of 1.20. If the risk-free rate is 3.5% and the market risk premium
is 3%, calculate the expected return on the asset.

Question 6

You are a money manager of French stocks. Your research department prepared the table below. According to the domestic CAPM for French securities, which stocks would you recommend for purchase and sale?
$$\begin{array} { l c c } & & \text { Domasic } \\\text { Security } & \text { Forec-asted Return (€) } & \text { Beta } \\\hline \text { Risk-Free Rate (€) } & 10 \% &0\\\text { French Market } & 15 \% & 1 \\\text { PARIHO } & 12 \% & 0 .7 \\\text { SPOUTNIK } & 20 \% & 1.5 \\\text { KLUB } & 9 \% & 1.2 \\\text { POUPOU } & 14 \% & 0.8\end{array}$$

Question 7

Thailand limits foreign ownership of Thai companies to a maximum percentage of all the shares issued. The limit in 2002 was generally 49%, but could be lower for some industries or firms. Once a company has reached this limit, it starts to be traded on two different boards. Foreigners trade on the Alien Board, while, Thai investors must still trade in the same share on the Main Board. Thai investors are allowed to purchase shares on the Alien Board, but not to sell them. Main and Alien Board shares are identical in all other respects.
a. Why does this segmentation ensure that the limit on foreign ownership is respected?
b. Shares listed on the Alien Board trade at a fairly large premium over their Main Board counterparts. Give some likely explanations.

Question 8

Assume that you are a U.S. investor who is considering investments in the German (Stocks A and
B) and British (Stocks C and
D) stock markets. The world market risk premium is 4.5%. The currency risk premium on the euro is 1%, and the currency risk premium on the pound is -1%. In the United States, the interest rate on one-year risk-free bonds is 4%. In addition, you are provided with the following information:
$$\begin{array} { c c c c c } \text { Stack } & \mathbf { A } & \mathbf { B } & \mathbf { C } & \mathbf { D } \\\hline & & & \text { United } & \text { United } \\ \text { Country } & \text { Germany } & \text { Germany } & \text { Kingdam } & \text { Kingdam } \\\beta _ { w }& 1.5 & 0.90 & 1 & 1.5 \\\gamma _ { € } &1 & 0.80 & - 0.25 & 1.0 \\\gamma _ { €} &-0.25&0.75&1.0&-0.5 \\\hline\end{array}$$ Calculate the expected return for each of the stocks. The U.S. dollar is the base currency.

Question 9

Consider two European firms listed on Euronext:
$\bullet$ Company I: Its stock return shows a consistent positive correlation with the value of the euro.
The stock price of Company I (in euros) tends to go up when the euro appreciates relative to the U.S. dollar.
$\bullet$ Company II: Its stock return shows a consistent negative correlation with the value of the euro. The stock price of Company II (in euros) tends to go down when the euro appreciates relative to the U.S. dollar.
An American investor wishes to buy European stocks but is unsure about whether to invest in Company I or Company II. She is afraid of a depreciation of the euro relative to the U.S. dollar. Which of the two investments would offer some protection against a weakening U.S. dollar?

Question 10

Suppose that you are an investor based in Denmark, and you expect the U.S. dollar to depreciate by 3% over the next year. The interest rate on one-year risk-free bonds is 4.5% in the United States, and 3.75% in Denmark. The current exchange rate is DKr 6.35 per U.S. dollar. You buy some U.S. stocks with an expected return of 7% in dollars.
a. Calculate the foreign currency risk premium from the Danish investor's viewpoint.
b. Calculate the expected return on the U.S. stock from the Danish investor's viewpoint, that is, in Danish krone.
c. Calculate the risk premium on the U.S. stock from a U.S. viewpoint and from the Danish investor's viewpoint.
d. Calculate the expected return on the U.S. stock from the Danish investor's viewpoint, assuming that the Danish investor hedges the currency risk. Calculate the risk premium on the hedged
U.S. stock from the Danish investor's viewpoint.

Question 11

Assume that you are a British investor who is considering investments in the German (Stocks A and B) and Swiss (Stocks C and D) stock markets. The world market risk premium is 4.5%. The currency risk premium on the Swiss franc is 0.5%, and the currency risk premium on the euro is 1%. The interest rate on one-year risk-free bonds is 4% in the United Kingdom. In addition, you are provided with the following information:
$$\begin{array} { c c c c c } \text { Stack } & \mathbf { A } & \mathbf { B } & \mathbf { C } & \mathbf { D } \\\hline \text { Country } & \text { Germany } & \text { Germany } & \text { Switzerland } & \text { Switzerland } \\\beta _ { w } & 1 & 0 .90 & 1 & 1.5 \\Y_{ €}& 1 & 0.80 & - 0.25 & - 1.0 \\Y_{SF} & -0 .25 & 0.75 & 1.0 & - 0.5\end{array}$$ Calculate the expected return for each of the stocks. The British pound is the base currency.