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Applying Regret Theory to Investment Choices: Currency Hedging Decisions Sébastien Michenaud & Bruno Solnik Edinburg

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### Applying Regret Theory to Investment Choices: Currency Hedging DecisionsSébastien Michenaud & Bruno SolnikEdinburgh, March 2009

### Optimal Currency Hedging: The traditional approach (MV)

### Applying Regret Theory to Investment Choices: Currency Hedging Decisions

### Derivations and Results

We thank Inquire Europe VERY MUCH for their financial support

Currency Risks can be significant in the short run

- The euro was introduced in 1999 at 130 yen, two years later it was down to 90 yen, went to 167 in July 2007, and 120 in Jan 2009.
- This type of volatility is not “crisis” volatility but “normal” one for currencies. Could have taken other currency pairs (e.g. EUR:USD or GBP:USD).

There are many current and expected variables (Purchasing power, deficits, interest rates, growth, politics..) that influence exchange rates at different times.

- Short term variations of exchange rates are extremely hard to predict.

Currency changes are quite volatile.

- Currency risk can be cheaply hedged.
- Currency risk is significant in global bond portfolios but relatively smaller in well-diversified global equity portfolios. But still…
- Currency changes show low correlation with (local currency) equity or bond returns.
- Currency hedging does not materially change the correlation of domestic and foreign stocks, but increases the correlation of domestic and foreign bonds.

- Universal hedging

Full hedging

Optimized hedging

Currency Hedging

- The currency decision is basically 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)?
- Typically, one sets a strategic currency hedging position applying to all investment in the same asset class (e.g. European equity). And deviates tactically based on shorter-term expectations and risks.
- I will focus on the strategic currency benchmark.

Currency Hedging: Finance Theory

- Traditional finance relies on expected utility maximization 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. Currency risk is a “real” risk to the extent that currency movements deviates from PPP adjustments.
- Solnik (1974) and Adler and Dumas (1983) derive an international asset pricing model where all investors should invest in the same world market portfolio optimally hedged against currency risk. Hence, they should identically hedge their international investments, but the hedge ratios depend on unobservable variables such as relative risk aversion and net foreign positions.

Currency Hedging: Finance Theory

- Black (1989,1990) simplifies the equilibrium model and comes up with a universal hedging rule. He estimates that international investments should be currency-hedged with a ratio of approximately 70%.
- CONCLUSION: Everyone adopts the same hedge ratios, whatever the risk aversion, whatever their nationality.

Currency Hedging: From Theory to MV Practice

- But equilibrium results do not hold in reality: home equity bias.
- In practice, many asset managers simply conduct an asset allocation mean-variance (MV) optimization 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 optimized 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 minimizes risk is 100% (see Pérold and Schulman, 1988; Anderson and Danthine, 1981). CONCLUSION: Everyone adopts the same hedge ratios, whatever the risk aversion.

Currency Risk Premium

- Of course, the optimal hedge ratio will differ from 100% if there is correlation between asset returns and currency movements, and if the currency risk premium differ from zero.
- The case of a zero currency risk premium is an important one. As opposed to equity (where we expect a positive risk premium although its magnitude is uncertain), the naïve expectation for currencies is a zero risk premium. It should drive the long-term hedging policy. Unless we have strong beliefs that our home currency is over/undervalued and will revert to fundamentals over the long run.
- Detecting over/undervalued currencies seems “easy” (PPA, Balance of Payments,..), but it usually takes a long time for fundamentals to assert themselves and the timing of adjustments is very hard to predict.

Limits to MV analysis

- Costs (including the interest rate differential)
- Constraints
- Time horizon
- Mean reversion

A Global Survey of Institutional Investors

What is the typical currency hedging benchmark of institutional investors?

- Very diverse!

Distribution of Accounts by Base Currency and Hedge RatioRussell Mellon 2005

Nobel Prize Thinking

- “I should have computed the historical covariance of the asset classes and drawn an efficient frontier. Instead I visualized my grief if the stock market went way up and I wasn’t in it-or if it went way down and I was completely in it. My intention was to minimize my future regret, so I split my [pension scheme] contributions 50/50 between bonds and equities.”

Harry Markowitz.

As quoted in Jason Zweig, "How the Big Brains Invest at TIAA-CREF", Money, 27(1), p114, January 1998.

Regret

- 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. Ex post, one compares the investment outcome with the best outcome that could have been achieved.
- Contrary to mere disappointment (prospect Theory), which is experienced when a negative outcome happens relative to prior expectations, regret is experienced relative to the best outcome of alternative choices that could have been made (foregone alternatives).
- As the opening quote suggests, the anticipation of future regret was strong enough to turn Harry Markowitz away from his very own portfolio allocation theory when faced with a financial decision on his pension plan.

Regret (2)

- Regret is very present in life (“missed opportunities”)
- Regret influences investment choices.

We look at the performance of peers (competitors). It is more than looking at passive benchmarks.

Currency Hedging is a Dimension where Regret Applies

- as stressed by Statman (2005), 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 eurozone assets from late 1998 to late 2000, with a vast regret of not having fully hedged.
- Conversely a fully-hedged American 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.

Currency Hedging is a Dimension where Regret Applies

The euro was introduced in 1999 at 130 yen, two years later it was down to 90 yen, went to 167 in July 2007, and 120 in Jan 2009.

- For example, a Japanese investor who decided not to hedge currency risk would have incurred a currency loss of some 30% on its eurozone assets from 1999 to 2001, with a vast regret of not having fully hedged.
- Conversely a fully-hedged Japanese investor would have missed the huge appreciation of the euro from late 2001 to late 2007. Again, a vast regret of not having taken the "right" hedging decision (90 to 167).
- But an un-hedged Japanese investor would have lost a huge amount on the currency side from 2007 to 2009.

Others

- Could have taken the example of most currencies: GBP:EUR or USD:AUD.
- Could also take example of fuel hedging decision of airline.

Regret Theory

- where U(x,y) is the modified utility of achieving x, knowing that y could have been achieved. v(x) is the traditional utility function, also called value function or choiceless utility. It is the "value" or utility that an investor would derive from outcome x if he experienced it without having to choose.
- This value function is assumed to be monotonically increasing and concave (risk aversion) as in traditional finance.
- The difference v(x) – v(y) is the value loss/gain of having chosen x rather than a the best foregone choice y. The regret function f(.) is monotonically increasing and decreasingly concave, with f(0) = 0.

Regret Theory and Risk

- Traditional utility is only defined over the portfolio held by the investor. What matters is only what you own.
- Modified utility also “value” a comparison with other portfolios that could have been chosen. There are two risk attributes in the utility function.
- Regret theory is clearly relevant to investors who compare the performance of their portfolio to forgone alternatives that they could have chosen, or to peers and benchmark portfolios whose performance could have been achieved (this not benchmarking, because the benchmark is known only ex-post)
- Loosely speaking, traditional expected utility cares about risk in the form of the volatility of the chosen portfolio. Regret theory ALSO cares about regret risk in the form of deviation from better alternatives.

Solnik and Michenaud, “Applying regret theory to investment choices: Currency hedging decisions’, Journal of International Money and Finance, Sept 2008.

- This the first attempt to apply RT, as originally developed by Loomes and Sugden (1982) and Bell (1982), to investment choices. Technical reasons might have hindered such developments.

Currency hedging decisions are simple enough to model in the framework of RT. The ex-post optimal currency hedging choice is only one of two decisions.

- We provide normative recommendations for currency hedging that differ markedly from those of traditional utility (MV) or disappointment/prospect theory. They could explain the observed diversity in currency hedging policies.

Our Model

- We present a model of optimal currency-hedging choices based on regret theory. Investors derive utility from their global asset allocation but, in addition, they also experience regret for having chosen a currency exposure that proves, with hindsight, inappropriate.
- We derive optimal currency hedging rules as a function of the degree of regret and risk aversion.
- Regret theory is complex, but can be applied in our “simple” case of optimal currency hedging.

If the foreign currency appreciates, and whatever the positive value of s, the best hedging policy (with hindsight) would have been to stay unhedged (h=0). So for any positive s:

- If the foreign currency depreciates by any amount, the best hedging policy would have been to be fully hedged (h=1). So for any negative s:

- Simple case

- There exists a correlation between R and s

- There is some expected movement in s.

Simple case: Regret aversion dominates everything

- The optimal hedging policy should be 50%.

The 50% hedging rule is not new among investment managers

"A partial hedging policy – such as 50/50 or 70/30 – means the investor won’t ever experience the major highs of an unhedged portfolio, but won’t be subject to the lowest returns either."

To Hedge or not to hedge, Simon Segal, SuperReview.com.au, 21 march 2003

"The 50% hedge benchmark is gaining in popularity around the world as it offers specific benefits. It avoids the potential for large underperformance that is associated with "polar" benchmark, i.e. being fully unhedged when the Canadian dollar is strong or being fully hedged when it is weak. This minimizes the "regret" that comes with holding the wrong benchmark in the wrong conditions."

" Managing Currency Risk: A Canadian Perspective", Gregory Chrispin, State Street Global Advisor, Essays and Presentations, March 23, 2004.

- The 50% hedge ratio is the simplest currency hedging policy that attempts to deal with regret.

100%

- + regret term
- + speculative term
- + covariance term

Hedge ratio = 50% if regret aversion dominates risk aversion.

In Practice: Use the model to derive optimal hedging

- Expected currency return (currency risk premium?)
- Correlation between asset and currency return
- Regret aversion compared to risk aversion

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