Global Asset Allocation and Stock Selection

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.

1. 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 one-month 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.
2. 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.
3. 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.
4. In the prediction exercise, does it matter if you use the exchange rate percentage change as the dependent variable or the currency return? Why?
5. Calculate out-of-sample forecasts for the FX investments for January 2006-- you already have out-of-sample for the equity/bond returns.
6. Allocate based on your out-of-sample 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.
7. 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?
8. 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.
9. 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 t-1. 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 = b₀ + b₁ R_wt + b₂ (R_wt Div_i,t-1) + b₃ (R_wt YS_i,t-1) + 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 = b₁ + b₂ Div_i,t-1 + b₃ YS_i,t-1 Graph this function for this country. Repeat the exercise for the country's currency return. Interpret the graphs.

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