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 ($\beta$_l_w). 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?

Question

Quizplus · Accepted Answer

The Answer is 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 } ext { United } \ ext { Statas }\end{array} & ext { France } & ext { Japan } \\hline ext { Risk-Free Rate } & ext { go/ } & 5 \% & 11 \% \ ext { Stack Market } & 10 \% & 6 \% & 19 \% \ ext { Compary A } & 13 \% & & \ ext { Compary B } & 9 \% & & \ ext { Compary C } & 11 \% / 6 & & \ ext { Compary D } & & 7 \% & \ ext { Compary E } & & 7 \% & \ ext { Compary F } & & 6 \% & \ ext { Compary G } & & & 21 \% \ ext { Compary H } & & & 23 \% \ ext { 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} ext { United States } &{ ext { France }} &{ ext { Japan }} \\hline ext { A: } 2.6 \% & ext { D: } 1.2 \% & ext { G: } 0 \% \ ext { B: } -0.8 \% & ext { E: } 0 \% & ext { H: } 3.2 \% \ ext { C: } 0 \% & ext { F: } -0.1 \% &{ ext { 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).

You Are a U β\betaβ iw, or Sensitivity to the World Market), Is Equal to Return

You Are a U $\beta$ _iw, or Sensitivity to the World Market), Is Equal to Return