Global Asset Allocation and Stock Selection
Campbell R. Harvey
Assignment 4: Currency Overlays, Hedging and Conditional Risk Functions
Due Beginning of Class 10
To complete the global allocation problem, we must
understand the role of FX positions
in portfolio management. We must allow understand the role of conditional
risk exposure and how it evolves through time.

Create hedged equity investments in your local currency. This
is called a full currency overlay.
If forward rates are available, this would involve the forward sales of
the initial amount of principal in your equity investment. That is, being
a U.S. dollar investor, at the end of January you invest $100 million
or (Swiss Franc) CHF120 million, you do a simultaneous forward sale today for the end of the next month, February,
(sell CHF for dollars). If forward rates are not available, you will need to
approximate the forward rate by using the two local interest rates (if
onemonth Eurocurrency rates are not available, you will have to use what ever
you can find). Repeat the unconditional asset allocation in assignment 2
by matching U.S. volatility. Use maximum short sale weights of 20% for developed
markets and 0% in emerging markets. No long position constraints in
developed markets and 20% maximum constraint for any emerging market.
Run the allocation using the unhedged returns (like assignment 2) and then
run it using the hedged returns. Comment. Be sure to calculate the correlation
matrix of among the unhedged returns and the hedged returns. NOTE: If you are doing Euro countries, then you need to use the Euro which has been synthetically created by Datastream.

Create currency returns. For the U.S. investor, a
long position would involve the purchase of CHF at the end of the month
and an immediate deposit into a EuroCHF account for one month. After one
month, you collect the interest and then translate everything back to
the U.S. dollar. Add these assets to your unconditional portfolio
allocation problem. If your home currency is the U.S. dollar
and have 5 assets including the U.S. dollar, then you should have
nine total assets (5 equity/bonds and 4 currency deposits). Optimize unconditionally.
Use the same constraints as in (1). However, do not put max and min positions
on the currencies. If you get an unreasonable weight on the currencies (like
200 for CHF deposit, reoptimize with constraints). Comment. What is going
on? How is this different than the overlay? What are the advantages to this
procedure compared to the overlay. NOTE: With Euro, you may have difficulty
in getting Euro Euro rates. As a simplification use the historical EuroDM.

Run predictive regressions on the FX returns. You might try using
a combination of the same set of variables you used for the equity and bond
prediction. That is, you need not collect new data from Datastream for the
prediction part. For example, for the dollar/CHF return, you will want to consider
variables which are both U.S. and Swiss based. Interest rates (or spreads)
are top candidates. Also consider lagged FX changes.

In the prediction exercise, does it matter if you use the exchange
rate percentage change as the dependent variable or the currency return? Why?

Calculate outofsample forecasts for the FX investments
for January 2006 you already have outofsample for the equity/bond returns.

Allocate based on your outofsample forecasts for all of the
investments. Use the unconditional standard deviations and correlations
from [2]. Set the portfolio equal to the U.S. variance as in [2] with the
same constraint set. Allocate. You have now completed a real world
global asset allocation. Comment.

Comment on how you might modify your program (don't implement it)
to incorporate transactions costs. These costs are very important and
cannot be ignored. When we run this program, we get a set of investment
weights. Next month, we get another set of weights. How can our program
be modified to take into account transactions costs?

Suppose you are being benchmarked to EAFE or the MSCI world?
Describe how to modify your objective function. This is called
minimizing tracking error. Comment on how you might set the program up
to minimize the negative tracking error and maximize the positive tracking
error. You need not implement this.

Regress one of your country (or regional) returns at time t
on the world market returns at time t and the product of the the world
returns at time t and your instrumental variables at time t1. That is,
if you are predicting the U.S. with a dividend yield and a yield spread,
demean the instruments and
regress the U.S. return on the world return, the world return times
the lagged dividend yield and the world return times the lagged yield spread.
R_{it} = b_{0} + b_{1} R_{wt} + b_{2}
(R_{wt} Div_{i,t1}) + b_{3} (R_{wt}
YS_{i,t1}) + error_{it}
where Div is the Dividend yield minus the average dividend yield over the
entire sample and YS is the Yield Spread minus the average spread over the
entire sample: The conditional beta function is:
Beta_{it} = b_{1} + b_{2} Div_{i,t1} + b_{3
}YS_{i,t1}
Graph this function for this country. Repeat the exercise for the
country's currency return. Interpret the graphs.
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me
.XLS (i.e. A4_PSAM.XLS for Positive Skewness Asset Management.)
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