**How Much to Hedge in a Volatile World?**

/ By

**Anthony Golowenko, CFA, Portfolio Manager, SSgA - Australia**

This essay is the second installment of a series of three educational pieces which closely examine the issue of strategic currency management. It extends the arguments developed in the first installment, "The Need for Currency Hedging in a Volatile World"1, by addressing the question of how much to hedge in managing foreign exposure in the current environment of volatile financial markets and more subdued expected equity returns.

Introduction

The first part of this three part series, "The Need for Currency Hedging in a Volatile World", described how currency risk is not always rewarded, heightened variability of returns increases the "Currency Volatility Drag", the impact of currency over shorter time periods is often significant and global bond managers typically insulate the underlying asset’s return. These arguments would logically lead investors to consider a fully hedged foreign currency exposure, but is this the optimal hedge ratio?

It is the intention of this essay to examine the considerations in formulating an optimal currency hedge and demonstrate why a 50% hedge ratio is a very useful starting point when developing a currency hedging policy.

**The Two Extremes: 100% and 0% Hedge Ratio**

Traditionally, there have been two schools of thought in relation to the strategic hedge ratio. The fully hedged neutralised foreign exchange risk method and the unhedged, unmanaged currency risk approach.

In their influential paper of 1988, Andre Perold and Evan Schulman2 advocate a fully hedged position on the basis of foreign currency risk not offering a commensurate return. In what they deem a "free lunch", they argue that as a result of its zero long-term expected return, currency risk can be removed without the portfolio suffering any reduction in long-term return. In relation to the often-sizable impact of unhedged currency positions, they considered transaction costs to be minimal.

At the other extreme, in his 1993 paper, HarvardUniversity’s Kenneth Froot3 argues that over long investment horizons, real exchange rates revert back to their means according to the theory of Purchasing Power Parity and investors should maintain an unhedged foreign currency position. He also concludes that, even over shorter horizons, the small transaction costs and counterparty risks associated with maintaining a currency hedge add up over time and cause the optimal hedge ratio to decline as the investment timeframe increases. However, Froot does acknowledge that real exchange rates may deviate from their theoretical fair value over shorter horizons and currency hedging in this context is beneficial in dampening volatility.

Given these two viewpoints are at opposite ends of the currency hedging spectrum, it is refreshing to know that going back as far as 1989 there has been academic research supporting an optimal hedge ratio that lies between these two extremes.

**Between the Two Extremes**

In a perfect world of frictionless trading and investment flows where all market participants are able to hedge against real exchange rates, in 1989 Fisher Black4 derived a universal formula for the optimal hedge ratio. Dependent on just three inputs, the world market portfolio’s expected return, this portfolio’s volatility and the average exchange rate volatility, Black finds the optimal hedge ratio to lie between the 0% and 100% levels suggested in the previous section. However, even with these theoretical assumptions, depending on the inputs used for the formula the author finds an optimal hedge ratio as high as 77% and, based on a different set of universal formula inputs, as low as 30%. The timeperiod sensitivity and significant variability and volatility of input parameters in the optimal hedge ratio result in a significant dispersion in what constitutes the optimal hedge ratio.

With its 'perfect world' assumptions and sensitivity to timeperiod and input parameters, the practical applications of Black’s universal optimal hedge ratio are considered by some to be limited. However, consistent with the real world practice of global bond managers as described in the first part of this series, Black’s universal formula suggests a 100% hedge ratio is most appropriate for Global Bond portfolios; thus insulating the underlying asset’s return.

**Minimising Maximum Regret – The 50% Approach**

Gardner and Wuilloud5 define 'regret' to be the difference in investor satisfaction (utility) that results when the portfolio employing the optimal mean-variance hedge ratio is outperformed by a portfolio employing an alternative hedge ratio. When the portfolio with the optimal hedge ratio is the best performing strategy, the regret is equal to zero. The authors find that a currency hedging strategy based on a mean-variance optimal hedge ratio should expect frequent and sizable regret when performance is evaluated over short time horizons and that the primary reason for this ‘sizable regret’ is the small expected value and high volatility of the expected currency surprise6.

Taking the alternative approach of minimising the maximum expected regret, as opposed to conventional mean-variance optimisation, Gardner and Wuilloud find that moving from the mean-variance optimal hedge ratio to a 50% hedge ratio avoids extremes in regret with only a minimal reduction in expected risk adjusted return. Consistent with the Purchasing Power Parity (PPP) and Uncovered Interest Rate Parity (UIP) theories, over the long-term the authors recognise that the attractiveness of the minimising maximum regret strategy does diminish.

**What is the Optimal Hedge Ratio?**

As the previous sections describe, there has been a large amount of research conducted on the topic of currency hedging, but what is the optimal hedge ratio? As with many things in life as a result of a number of competing factors, the unfortunate answer is "It depends". There is no single ‘one size fits all’ optimal hedge ratio that will be able to simultaneously satisfy all international investors' concerns and constraints. However, we are able to examine the next best thing. Specifically, what are the major considerations in developing an appropriate foreign currency policy?

In the first part of this essay, Perold and Schulman advocated a fully hedged currency position. However, their study ignored the impact of cash flows.7

Also in the first section, Froot argued in favour of a 0% hedge. By concentrating on longer-time horizons, however, he did not have to be concerned with significant return volatility that is often experienced in the short-term.

The next two sections offered hedging ratios between these two extremes. Black's universal optimal hedge ratio and Gardner and Wuilloud’s 50% hedge ratio of ‘least regret’, offer a trade-off between the competing forces of return volatility (minimised by a 100% hedge) and cash flow volatility (minimised by a 0% hedge). The nature of return and cash flow volatility competing with one another over different hedge ratios may be seen in the schematics depicted in Figures I and II.

From Figure I it may be seen that for the investor who prefers a low level of short-term return volatility, they derive a greater level of satisfaction (utility) as the currency hedge ratio increases. For a 100% currency hedge, the international equity/bond returns are insulated from foreign currency movements. The opposite is true for the investor who prefers minimal cash flow volatility, as they will derive the least satisfaction from a 100% currency hedge. As can be seen from Figure II, these investors derive a greater level of utility from lower levels of currency hedging. The competing nature of the forces that drive the determination of the optimal currency hedge ratio are evident if we now consider an investor who prefers both a low level of return volatility and a low level of cash flow volatility. On the one hand, the return volatility is minimised by higher levels of currency hedging. On the other hand, however cash flow volatility is minimised by lower levels of hedging. This is where the 'trade-off of competing forces' comes into play. Depending on which of the preferences the investor feels most strongly about satisfying, the higher or lower the currency hedge will be. Other competing factors and their corresponding sensitivity schematics are displayed in Figure III.

James Binny8 provides a practical weighting scheme designed to convert an investor’s investment and behavioural risk preferences into an optimal hedge ratio. This involves the weighting of the major competing factors, such as those described above, on a scale of 0 to 10, where a 0 indicates that the factor is unimportant and a 10 indicates the factor is most important. An investor very concerned with return volatility and downside protection, but less concerned with cash flows, upside participation and peer group risk would have a relatively high proportion of their currency exposure hedged. Another investor who is most concerned with cash flows and upside participation, on the other hand, would have a much lower hedge ratio. Most importantly, different investors will have different priorities and this is why a customised wealth solution, as opposed to a 'one size fits all', approach to the currency hedging decision is required.

**The 50% Hedge Ratio – A Useful Starting Point**

As described in the previous section, investors investment and behavioural priorities can be quite different. Therefore, there is no single or optimal currency hedge ratio acceptable to all investors. As part of their strategic asset allocation, a thorough assessment of each investor’s preferences, needs and priorities is critical in establishing a customised currency hedging solution. From an Australian total portfolio perspective, SSgA finds the optimal hedge ratio to range between 41% and 65% over a 20-year sample period, depending on the end date and input parameters employed. A very useful starting point, however, is a 50% hedge ratio.

As indicated in a footnote to the section "What is the Optimal Hedge Ratio?", SSgA has developed a number of strategies, depending on the portfolio’s characteristics, that seek to insulate the underlying assets from the impact of cash flows that result as currency forward contracts mature. One such approach involves establishing a cash pool of 3-5% of the underlying portfolio's value, which is then equitised via appropriate futures contracts. The trading costs of accommodating cash flows through futures contracts are significantly lower than those that would be realised if physically transacting in international equities. These strategies effectively decrease the importance of "Cash Flow Volatility" in determining the optimum hedge ratio by minimising the trading frictions that can, over time, slowly erode investment returns.

In their paper of 2000, Gorman & Qian9 (from a U.S. perspective) find that over the twenty-year period from January 1978 to December 1997, a 50% currency hedge delivers roughly 75% of the total equity volatility reduction on an EAFE portfolio and around 66% of the total bond volatility reduction on the equivalent Fixed Income portfolio. Over this representative sample period, the authors find the benefits of volatility reduction in implementing a currency hedge to be clearly non-linear. The implication of this non-linearity to the Investor Sensitivity Schematics of the previous section would lead to a revised Return Volatility Schematic as depicted in Figure IV.

Returning to the practical weighting scheme provided by Binny, the non-linear volatility reduction of Figure IV as the currency hedge ratio increases would effectively provide greater satisfaction, at lower levels of currency hedging, for the investor who prefers minimal short-term return volatility.

A very compelling argument in favour of implementing a 50% currency hedge is provided by Gorman and Qian. Moving from an unhedged benchmark to a 50% hedged benchmark reduces volatility or, viewed differently, makes additional room available for larger allocations to international stocks and bonds, or even an active currency overlay, in a fund's total volatility space. As described in the first part of this series, "Currency Hedging in a Volatile World", holding a foreign currency over a long time-horizon provides an expected return of zero. Unlike an unmanaged currency exposure, however, international stocks and bonds and active currency overlays provide a more dependable means of diversification and offer positive expected returns over time. This represents a variation on Perold and Schulman’s ‘free lunch’ analogy, and involves a zero expected return volatility being substituted for volatility that is compensated by positive long-term expected returns.

Conclusion

There is no single hedge ratio that satisfies the needs of all international investors. This essay has shown that:

- Academic research exists in support of fully hedged, unhedged and ‘in between’ hedge ratios.
- Significant short-term ‘regret’ is minimised by a 50% hedge ratio.
- Investors must trade-off competing factors to arrive at their optimal hedge ratio.
- A 50% hedge ratio represents a useful starting point in creating a customised wealth solution.

Having presented "Currency Hedging in a Volatile World" in the first part of this series and "How Much to Hedge in a Volatile World" in this essay, the next part will continue the close examination of currency management by focusing on pertinent considerations in the development of an active currency overlay, so please stay tuned.

1 For more details please refer to this essay dated 12/9/02 in ssga.com.

2 Perold, A. and Schulman, E. (1988) "The Free Lunch in Currency Hedging: Implications for Investment Policy and Performance Standards", Financial Analysts Journal, May-June, 45-50

3 Froot, K. (1993) "Currency Hedging over Long Horizons", National Bureau of Economic Research, Cambridge, MA

4 Black, F. (1989) "Universal Hedging: Optimising Currency Risk and Reward in International Equity Portfolios", Financial Analysts Journal, July-August

5 Gardner, G. and Wuilloud, T. (1995) "Currency Risk in International Portfolios: How Satisfying is Optimal Hedging?", Journal of Portfolio Management, 21(3)

6 Where currency surprise is the gain or loss on a long foreign currency position relative to the beginning-of-period forward rate.

7 In implementing a currency hedging program, SSgA has developed a number of strategies to minimise the impact of cash flows, resulting when forward contracts mature, on the underlying portfolio.

8 Binny, J. (2001) "The Optimal Benchmark for a Currency Overlay Mandate", Journal of Asset Management, Vol. 2

9 Gorman, S. and Qian, E. (2000) "International Benchmarks: In Support of a 50% Hedge Ratio", Journal of Investing, Vol. 9, No. 2

*This material is for your private information. The views expressed are the views of Anthony Golowenko only through the period ended March 14, 2003 and are subject to change based on market and other conditions. The opinions expressed may differ from those with different investment philosophies. The information we provide does not constitute investment advice and it should not be relied on as such. It should not be considered a solicitation to buy or an offer to sell a security. It does not take into account any investor's particular investment objectives, strategies, tax status or investment horizon. We encourage you to consult your tax or financial advisor. All material has been obtained from sources believed to be reliable, but its accuracy is not guaranteed. There is no representation nor warranty as to the current accuracy of, nor liability for, decisions based on such information. Past performance is no guarantee of future results.*

March 14, 2003