The diversification benefits of international investing can be significant relative to a domestically oriented portfolio.

Not only can return be enhanced but also total portfolio risk can be reduced. But we have added an additional source of risk in currency. The question is whether this risk should be managed?

Looking at the position of a German investors in unhedged and hedged portfolios, the chart below shows that with hedging of the currency risk, the efficient frontier moves upand to the left. This means that these hedged portfolios have lower risk and higher returns than the unhedged portfolios.

I have assumed that we cannot forecast exchange rates and that the hedges therefore provide no additional return. The extra return is provided by a greater exposure to higher return assets, while controlling risk through currency hedging.

#It is evident from this example that currency hedging can further benefit the portfolio by increasing return and lowering volatility (risk).

In order to understand the theory behind the interaction of the risks in an international portfolio, I am indebted to the work of Mark Kritzman, managing partner at Windham Capital Management. He has written extensively on how currency risk impacts a portfolio's returns and particularly the mathematical techniques required to calculate efficient hedging strategies.

Currency exposure influences a portfolio's risk through the interaction of the volatility it introduces to the portfolio and the diversification effects that accrue. This interaction can be ex-pressed by the formula in Fig 1.

This equation tells us how much hedging we need to employ in order to minimise the total risk of our portfolio. We can see that this is in fact the portfolio's beta with respect to the currency, hence the higher the portfolio's beta, the higher the hedge ratio that minimises the portfolio's risk.

Since we know that the standard deviations of both the portfolio and the currency must be positive, we should always hedge at least some of the currency exposure to reduce portfolio risk unless the correlation be-tween the currency and the portfolio is negative.

In determining the currency hedge that minimises portfolio risk we must be careful to estimate correlation ac-curately. Indeed, the estimation of a currency's correlation with the underlying portfolio has been the source of some confusion. Some investors focus on the correlation between currency returns and the local returns of the underlying portfolio, while other in-vestors focus on the correlation of currency returns with the base currency returns of the underlying portfolio.

Let us consider this issue from the perspective of our German in-vestor whose portfolio is invested in American stocks. The German in-vestor's return depends on both the local return of American stocks and the return of the dollar versus the deutschmark. Thus it is the deutsch-mark denominated return of American stocks that is relevant. The fact that the dollar may have a negative correlation with American stocks in America belies the direction of its relationship with those American stocks when denominated in deutschmark. Because a large part of the deutsch-mark denominated return of American stocks is the return of the dollar, the correlation between the stocks' local return and the dollar would have to be extremely negative to offset the currency component sufficiently. In order to illustrate this, we can see in the table the correlations between the currency and the local returns that correspond to the correlations of the currency with the base currency returns, as well as the resultant minimum risk currency hedge ratios (see Fig 2).

Only when the currency and the local returns are perfectly negatively correlated does currency exposure introduce sufficient diversification to obviate the need to hedge, assuming we wish to minimise the risk of the total portfolio. A more reasonable expectation is that a currency's correlation with local returns will fluctuate between -20% and +20%, in which case the minimum risk hedge ratio will range from 80% to 120%. This is borne out by the empirical analysis above demonstrating the magnitude of the reduction in risk that is available through choosing an efficient hedge portfolio. It can also be shown that: You will always reduce a foreign portfolio's risk by hedging a fraction of its currency exposure as long as the currency's standard deviation exceeds the foreign portfolio's local standard deviation.

If the currency's standard deviation is less than the foreign portfolio's local standard deviation, you will reduce a foreign portfolio's risk as long as its local correlation with the currency is greater than the following ratio:

Currency Standard Deviation

-1/2 x

Foreign Portfolio Local

Standard Deviation

The decision to invest globally is far less controversial than the decision of how to handle the consequent currency risk. We have seen that it is simple to demonstrate the benefits of global diversification for a portfolio both in terms of return as well as standard deviation and that currency risk is a necessary consequence of this pro-cess. By managing this risk through the judicious use of forward contracts we have seen that it is possible to raise returns and lower volatility considerably further. The process each fund employs will depend on its specific characteristics; we can say though that history and theory teach us that ignoring this risk is rarely the ideal strategy!

Jeremy Armitage is vice president, currency risk management at State Street Bank in London.