Question #1

The optimal portfolio utilizing the hedged returns was exactly the same as the optimal portfolio using the unhedged returns. Hedging foreign exchange risk provided little, if any, benefit to the expected monthly portfolio returns as evidenced by the table below and the calculated correlations:

Country / Unhedged Return / Hedged Return / Difference / Correlation
Japan / 0.51% / 3.63% / 3.12% / 87.8%
Canada / 0.77% / 0.94% / 0.17% / 93.3%
South Africa / 92.05% / 71.28% / (20.77)% / 99.9%
Indonesia / 232.61% / 212.48% / (20.13)% / 96.8%

Note: Forward exchange rates were estimated based on the interest rate parity relation of ((1+foreign treasury)/(1+30 day T-bills))*Spot Foreign Exchange Rate

Given the additional cost that would have to be taken on in hedging against foreign exchange risk, there is no value added by hedging these investments. The optimal portfolio under both the unhedged and hedged scenarios is included below. Constraints are maximum short sale weights of 20% for Japan, Canada and the US and 0% for Indonesia and South Africa. Long position constraints of 20% were also placed on Indonesia and South Africa.

Question #2

The re-optimized portfolio including the four currencies as asset classes delivers an increased level of return for the same amount of risk as just investing in the actual stocks.


Generally the expected returns, as well as the Standard Deviations, for the currencies are lower than for the stocks. This affords the portfolio the opportunity to take very strong positions in asset classes with more volatility but also increased expected returns (or losses) whilst using the lower volatility of currencies to balance the risk of the portfolio as a whole.

This can be seen from the above results where the Canadian Dollar is shorted quite severely, but as one of the lowest volatility "assets" it contributes significantly to the minimizing of portfolio risk.

This approach essentially creates another asset class with the potential to deliver returns towards portfolio growth. The overlaying method provides an opportunity to hedge the portfolio against any unfavorable currency moves, therefore minimizing risk. This procedure, although exposing the portfolio to increased downside risk due to currency fluctuations, provides an opportunity to further diversify a portfolio and generally lower risk.

This would suggest that the full currency overlay method will not always deliver the optimal portfolio. With the overlay method using the Canadian situation as an example one would believe that one is optimally invested and hedged in the Canadian market while it may in fact be better to be invested in Canadian stocks while at the same time shorting the currency, as the second method would indicate.

Question #3

The four nations for which we are trying to predict currency returns are Indonesia, Japan, South Africa, and Canada. We are US based investors and therefore are forecasting the currency levels as compared to the US Dollar. Our methodology was to predict the exchange rate and from there calculate a currency return.

The first country we examined was Indonesia. The variables that were included in our model are Lagged Exchange Rates (Rupiah/Dollar) and the Lagged spread between US and Indonesian short-term treasury bills. The regression equation is:

Exchange Rate = 7081.28+.469738*(Lagged Exchange Rate) +332.595* (T-Bill Spread)

Some key outputs from the model are below:

Adjusted R Squared / 17.9428
Exchange Rates T Statistic / 1.49312
T-Bill Spread T Statistic / 3.60268
Durbin-Watson / .216389

The second country is Canada. The variables included in the model are Lagged Exchange Rates (Canadian Dollar/ US Dollar) and the Lagged spread between US and Canadian short-term treasury bills. The regression equation is:

Exchange Rate = 1.23148+ 1.32425*( Lagged Exchange Rate) +.0303465* (T-Bill Spread)

Some key outputs from the model are below:

Adjusted R Squared / 24.7036
Exchange Rates T Statistic / 3.11379
T-Bill Spread T Statistic / 4.16602
Durbin-Watson / .374083

The next country is South Africa. The variables that we used in our model are Lagged Exchange Rates (Rand/US Dollar) and US T-bill rates. The regression equation is:

Exchange Rate =2.78608+ 1.10733*( Lagged Exchange Rate) + .285946*(US 30 day T-Bill)

Some key outputs from the model are below:

Adjusted R Squared / 11.2272
Exchange Rates T Statistic / 1.66898
US T-Bill T Statistic / 2.75731
Durbin-Watson / ..092583

The final country we examined is Japan. The variables that were included in our model are Lagged Exchange Rates (Yen/ US Dollar) and the Lagged spread between US and Japanese short-term treasury bills. The regression equation is:

Exchange Rate = 104.051+ .27784*( Lagged Exchange Rate) + 2.04829 *( T-Bill Spread)

Some key outputs from the model are below:

Adjusted R Squared / 5.98475
Exchange Rates T Statistic / .748642
T-Bill Spread T Statistic / 2.15184
Durbin-Watson / .150834

Question #4

In the prediction exercise, we attempted to predict the level of exchange rate and use this level to predict returns on the currencies. Our dependent variable (in all four cases) was the level of the foreign currency to the US Dollar.

The question asks if there is a difference between using exchange rate % change and currency return. We believe that there is indeed a difference between these two variables. The exchange rate % change only shows the absolute change in the foreign currency as compared to the US dollar whereas the currency return combines the change in the foreign currency (to the US dollar) with an additional return comprised of interest earned on the currency during the period being examined. We feel that the currency return is the proper one to use when building a model. The money invested in a foreign currency will have an interest component and this should not be ignored.

Question #5

We did out of sample forecasts for the four currencies for January 1999.

The results are in the table below:

Canadian Dollar / -.77 %
Japanese Yen / 2.94 %
Indonesian Rupiah / -13.38 %
South African Rand / -4.03 %

Question #6


Our predictions and weights for January 1999 are in the table below:

The results from this analysis are quite interesting. The expected monthly return is abnormally high. We attribute this figure (9.22%) to the large expected loss of the currencies of Indonesia and South Africa. Our model suggests shorting these currencies in an attempt to make some money off the anticipated continued depreciation in these markets.

Question #7

Our model currently ignores transaction costs. On a month to month basis, there can be significant swings in the percentage of the portfolio invested in any of the nine asset classes in our investment universe. Following are some recommendations on how to minimize these costs for our investment portfolio:

·  Do not change the allocation if the recommended allocation changes by less than a certain threshold percentage. This threshold can be different for different markets based on the relative transaction costs. For example, transaction costs are generally higher in Indonesia than in Canada, and the thresholds should reflect this. A sample thresh hold list is 1 % for the US, Canada, Japan and 2.5% for South Africa and Indonesia.

·  Adjust the portfolio in the futures markets instead of the cash market. Often, the futures markets are cheaper and more liquid than the cash markets and we should take advantage of this fact as we manage our investment portfolio.

·  Take advantage of the liquidity of the currency markets. Adjust the model to incorporate these costs when changing the recommended allocation.

Question #8

The MSCI and EAFE are equity only indexes. Their makeup includes equity assets in many different parts of the world. However, they do not include currencies as an asset class. One method available to minimize negative tracking error and maximize positive tracking error is to take advantage of this fact by using currencies as an available asset class. Our results from question two of this assignment show that one can increase their expected return while holding expected standard deviation constant by using currencies as an asset class to be invested in.

Question #9

(See below for graphs)

Having graphed the resultant conditional betas from the derived functions for both the stocks and the currencies it would appear that the conditional betas for stocks in terms of both pattern and movement relative to the world index returns follow the same movements with only the magnitude changing. The pattern for currencies is not quite the same with more clearly defined differences. Individual country stocks would therefore seem to be more highly correlated with movements in the world index, than are currencies.

This would suggest that in terms of tracking the world index, building a portfolio using only stocks as asset classes would not necessarily maximize the positive tracking error while minimizing the negative tracking error. Including currencies as asset classes would provide more opportunity to balance our portfolio to better track the world index whilst maximizing the positive tracking error.