Portfolio investors have progressively accepted the argument that international diversification provides risk/return benefits. However, the currency dimension has remained an emotional issue and currency hedging is a sensitive decision. Attractive local-currency returns on foreign asset market can be swamped by a depreciation of the foreign currency. Conversely, the return on foreign currency can provide a major portion of the total return of international investments when the domestic currency is weak. The currency hedging decision is a simple one: what currency hedge ratio (proportion of foreign asset value hedged against currency risk) should be adopted? In other words, should international assets be fully hedged against currency risk, not hedged, or partially hedged (hedge ratio between zero and one)?
The currency hedging policy adopted by investors seems diverse. Data from a worldwide survey of institutional investors (Harris 2004) conducted in 2004 by Mellon/Russell, indicates that 39% of investors adopt a no hedging policy, 34% of investors adopt a 50% hedging policy, 14% of investors adopt a 100% hedging policy and 13% of investors adopt some other hedge ratio. Because these numbers reflect long-term policy benchmarks, they cannot be explained by short-term expectations on currency movements, but primarily by risk considerations or some behavioural attitude. The wide diversity in hedge ratios is puzzling.
Traditional finance relies on expected utility maximisation and uses the expected return/risk paradigm to search for an answer. Some researchers have developed global market equilibrium models to derive optimal currency hedging rules. Solnik (1974) and Adler and Dumas (1983) derive an international asset pricing model where investors from different countries use their own currency as numéraire. Therefore investors from different countries view asset expected returns and risks differently because of foreign exchange uncertainty. Global equilibrium models conclude that all investors should hold a combination of their own risk-free asset (risk-free in home currency) and the world market portfolio partly hedged against currency risks. Hence the risky portfolio is identical for all investors and made of the equity market-capitalisation-weighted portfolio optimally hedged against currency risk. Investors attain their desired risk level by adjusting the combination between their home risk-free asset (cash or bond) and this risky portfolio. A major result is that all investors should identically hedge their international investments, whatever their nationality of their level of risk aversion. The optimal hedge ratio applies to all investors independently of their risk aversion and nationality, and is therefore ‘universal’. Unfortunately, the equilibrium hedge ratios depend on unobservable variables such as relative risk aversion and net foreign positions. Black (1989,1990) simplifies this equilibrium model and estimates that international investments should be currency-hedged with a ratio of approximately 70%. Unfortunately, it is observed worldwide that investors exhibit a strong home bias in their equity portfolios, so the normative implications of the global equilibrium model do not seem verified in the real world.
In practice, many asset managers simply conduct an asset allocation mean variance optimisation based on expected returns and risk. Typically a two-step approach is implemented. The asset allocation to international asset markets is determined in a first step, and the amount of currency hedging is then decided for this specific asset allocation. So currency hedging is optimised assuming that the global asset allocation is fixed. In its most simple form, this is typically a mean-variance exercise. If currency risk premia are nil and if asset returns are uncorrelated with currency movements; then the optimal hedge ratio that minimises risk is 100% because currency risk is pure noise (see Pérold and Schulman,1988).
So the currency-risk-minimising strategy is a hedge ratio of 100%. Again, this hedge ratio obtains for any (positive) level of risk aversion and should therefore be ‘universal’. According to portfolio theory, deviations from this full-hegded policy can only be explained by beliefs in currency risk premia, or correlation between asset returns and currency movements. For example, some investors believe that equity is a real asset so that the correlation between asset returns and currencies is strong.
Behavioural finance claims that investors do not follow the traditional mean-variance paradigm and this is clearly applicable to the currency hedging decision (see Fisher and Statman, 2004). Agents tend to experience regret when their investment yields, ex-post, a poor performance relative to an obvious alternative decision that they could have chosen. Regret is such a powerful negative emotion that the prospect of its future experience may lead individuals to make seemingly sub-optimal, non-rational decisions relative to the mean-variance paradigm. Regret is defined as a cognitively-mediated emotion of pain and anger when, with hindsight, we observe that we took a bad decision in the past and could have taken one with better outcome.
Contrary to mere disappointment, which is experienced when a negative outcome happens relative to prior expectations, regret is an emotion strongly associated with a feeling of responsibility for the choice that has been made based on a comparison of the actual outcome with the best outcome that could have been achieved.
Currency hedging is a dimension where regret clearly applies. For example, an American investor who decided not to hedge currency risk would have incurred a currency loss of some 40% on its Euro-zone assets from late 1998 to late 2000, with a vast regret of not having fully hedged. Conversely a fully-hedged investor would have missed the 50% appreciation of the euro from late 2001 to late 2004. Again, a vast regret of not having taken the ‘right’ hedging decision. Furthermore, selling short an appreciating foreign currency leads to cash losses on the forward position that have to be covered by the sale of securities. A forced decision that is not lightly accepted by a board of trustee. The experience of regret in currency hedging is not news for the investment world. Several practitioners have justified a 50% naive hedge ratio on intuitive grounds. The 50% hedge ratio is the simplest currency hedging policy that attempts to deal with regret. With unpredictable exchange rates, an unhedged or hedged policy will be wrong 50% of the time, and often by a large amount. A naive 50% hedging policy will always be wrong and exhibit regret ex-post, but the maximum amount of regret will be cut in half. But oversimplistic rules that forget about mean-variance and solely focus on regret are wrong.
Developing a quantified approach that considers both volatility and regret in the optimisation is not technically easy. The problem is that regret is not the return deviation from a passive preset benchmark but from a ‘moving’ benchmark, the best ex-post hedge ratio. But currency hedging lends itself to the application of regret theory because with hindsight, the optimal hedging decision can only be one of two possible choices. If the foreign currency appreciated by any amount, it would have been better to be unhedged. If the foreign currency depreciated by any amount, it would have been better to be fully hedged. We developed 1 a model of optimal hedging where investors can have different levels of traditional risk aversion and of regret aversion. The optimal hedging policy varies drastically depending on the type of risk that an investor privileges. Much of the diversity in observed hedging policies can be explained.
1Michenaud and Solnik: ‘Optimal currency hedging: A regret-theoretic approach’. HEC working paper 2005