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The Currency Hedging Conundrum David Turkington Portfolio and Risk Management Group State Street Associates The Currency Hedging Conundrum David Turkington Portfolio and Risk Management Group State Street Associates RESEARCH

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> Passive versus active currency management > Why is currency risk important? > Schools of thought > Optimal currency hedging: In-sample and out-of-sample results Overview

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Passive versus Active Currency Management >Currency exposure is an inescapable feature of investment in foreign markets. >The passive currency hedging policy should be driven by the volatility currency exposure introduces to a portfolio, not by the expected returns of currencies. >Views about currency returns should dictate tactical decisions, not policy decisions. >Active currency management strategies seek to generate excess return by exploiting certain characteristics of currency markets.

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Passive (Expected Return = 0) Active (Expected Return ≠ 0) Alpha Overlay >Traditional Active Hedging >Symmetrical Active Hedging >Active Cross Hedging >Alpha Strategies >Portfolio Hedging >Optimal Hedge Ratios Passive versus Active Currency Management

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> Even if currency fluctuations “wash out” in the long run, they contribute to interim risk and may substantially increase the magnitude and/or likelihood of drawdowns. This view assumes that investors are only concerned about what happens at the end of their investment horizon. In reality, most investors care about what happens along the way. Why is currency risk important?

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> Currency hedging is achieved through the use of derivative instruments. Forward contracts are often the most practical due to their high liquidity and customizable nature. > In particular, short positions in forward contracts can be used to offset exchange rate movement embedded in the portfolio. > A currency forward contract locks in a price today to buy/sell currency at a future date, taking into consideration the current spot rate, interest rate differential between two countries, and time. Mechanisms for Hedging Currency Risk

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A.100% - Currencies just add unwanted risk to the portfolio. B.0% - Why hedge? Currencies add diversification. C.The hedge ratio that minimizes overall portfolio risk. D.50% - Never 100% right, but never 100% wrong either! What is the best hedge ratio for foreign currency exposure?

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“Currencies simply contribute to portfolio volatility.” Why is Currency Risk Important? Schools of Thought – 100% Hedged Unhedged MSCI Switzerland The right exposure to currencies can actually provide portfolio diversification, therefore reducing overall portfolio risk Unhedged MSCI Switzerland EUR Standard Deviation*: 17.03% CHF Standard Deviation*: 17.58% * Annualized Standard Deviation of Monthly Returns Unhedged MSCI Switzerland 0.55% Reduction to Annualized Risk

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Why is Currency Risk Important? Schools of Thought – 0% Hedged Unhedged MSCI US EUR Standard Deviation*: 19.61% USD Standard Deviation*: 15.84% * Annualized Standard Deviation of Monthly Returns If currency returns are expected to wash out over the long run: >Expected Return = Zero >Additional volatility is uncompensated! 3.78% Additional Annualized Risk “Currencies add diversification to my portfolio.”

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“Minimum regret” portfolio hedging policy Why is Currency Risk Important? Schools of Thought – 50% Hedged Seeks to avoid: >100% hedged when foreign currencies experience periods of appreciation >0% hedged when foreign currencies experience periods of depreciation Unhedged Fully hedged

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>Goal is to control potential exchange rate risk >Typical hedge ratio is between 0% – 100% >Hedge ratios applied uniformly across all currencies Techniques for Managing Currency Risk Passive Hedging

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>Some currency exposure is beneficial, insofar as it introduces diversification to the portfolio. Hence, a 100% hedge ratio generally produces sub-optimal results. >Currency exposure affects a portfolio’s risk in two ways: >it introduces volatility, and >it introduces diversification. >The net effect of these two influences determines the optimal fraction of currency exposure to hedge in order to minimize a portfolio’s risk. Techniques for Managing Currency Risk Currency Risk and Diversification

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Percent of Portfolio Hedged Standard Deviation 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 0%20%40%60%80%100% Portfolio Volatility: 10% Currency Volatility: 12% Correlation: 60% Modern Portfolio Theory takes these factors into account to identify a single, risk-minimizing hedge ratio. β = 0.60 * (0.10 / 0.12) = 50% Techniques for Managing Currency Risk Minimum Variance Hedge Ratio

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Portfolio Volatility: 10% Currency Volatility: 12% Risk-minimizing hedge ratio Techniques for Managing Currency Risk Minimum Variance Hedge Ratio

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The extent to which currencies introduce volatility and/or diversification to a portfolio depends on: >the asset/liability composition of the portfolio, >the base currency of the investor, and >the specific currencies to which the portfolio is exposed. Techniques for Managing Currency Risk Optimal Passive Hedge

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> Each currency interacts with asset markets in a unique way. It is not necessarily optimal to hedge the same proportion of every currency. Techniques for Managing Currency Risk Optimal Currency-Specific Hedge Ratios

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Standard Deviation Expected Return The Modern Portfolio Theory framework can be extended to identify a set of currency-specific hedge ratios that jointly minimize portfolio risk. Techniques for Managing Currency Risk Hedge Ratios and Portfolio Efficiency Without Currency Hedging With Currency Hedging

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Optimal Hedge Ratios: In-Sample Results Source: Kinlaw, W. and M. Kritzman. “Optimal currency hedging in- and out-of-sample” The Journal of Asset Management, Vol 10, No 1, 22-36.

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Optimal Hedge Ratios: Out-of-Sample Results Source: Kinlaw, W. and M. Kritzman. “Optimal currency hedging in- and out-of-sample” The Journal of Asset Management, Vol 10, No 1, 22-36.

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Black Swan Events?

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>A “1-sigma” event is a one standard deviation move, a “2-sigma” event is a two standard deviation move, and so forth. >When investors describe events using sigma, they are implicitly assuming that returns follow a normal, “bell curve” distribution. >On average, we would expect: >a 1-sigma event to occur on 1 trading day out of 8, >a 2-sigma event to occur on 1 trading day out of 44, and >a 3-sigma event to occur on 1 trading day out of 741. >In the summer of 2007, a high-profile hedge fund announced that it had experienced two 25-sigma events in a row. A digression on “sigma”

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A.Approximately 1 trading day in 300 years B.Approximately 1 trading day in 300,000 years C.Approximately 1 trading day in 3,000,000 years D.Approximately 1 trading day in 3,000,000,000 years Source: Dowd, K., J. Cotter, C. Humphrey, and M. Woods. “How Unlikely Is 25-Sigma?” The Journal of Portfolio Management, Summer 2008. How often would we expect a 7-sigma event to occur?

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>“A 5-sigma event corresponds to an expected occurrence of less than just one day in the entire period since the end of the last Ice Age,” or approximately 1 day every 14,000 years. >“A 7-sigma event corresponds to an expected occurrence of just once in a period approximately five times the length of time that has elapsed since multi-cellular life first evolved on this planet,” or approximately 1 day every 3 billion years. >An 8-sigma event corresponds to an expected occurrence of once in “a period that is considerably longer than the entire period since the Big Bang.” >“The probability of a 25-sigma event is comparable to the probability of winning the lottery 21 or 22 times in a row.” Source: Dowd, K., J. Cotter, C. Humphrey, and M. Woods. “How Unlikely Is 25-Sigma?” The Journal of Portfolio Management, Summer 2008. Putting N-sigma events in perspective

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Out-of-Sample Results: 5-Year Drawdowns Source: Kinlaw, W. and M. Kritzman. “Optimal currency hedging in- and out-of-sample” The Journal of Asset Management, Vol 10, No 1, 22-36.

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>For both German and Canadian investors, commodities are negatively correlated with a capitalization-weighted foreign currency basket. These coefficients are -0.10 and -0.14, respectively. On average, when commodity prices rise, a basket of foreign currencies falls. >The German stock market (net consumers of commodities) is negatively correlated with commodities; this coefficient is -0.20. For Germans, an increase in commodity prices impacts domestic stock returns and foreign currency returns in the same way: both fall. Hence, foreign currencies do not diversify German equities. >The Canadian stock market (net producers of commodities) is positively correlated with commodities; this coefficient is 0.10. Hence, for Canadians, an increase in commodity prices impacts domestic stock returns and foreign currency returns differently: stocks rise and foreign currencies fall. Hence, foreign currencies do diversify Canadian equities. Why do hedge ratios vary across countries?

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Maximizes: Expected Return - Risk Aversion x Standard Deviation 2 -Tracking Error Aversion x Tracking Error 2 Risk of Regret Multi-risk optimization to control for regret risk

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Implementation Considerations >Contract tenor >Rebalance frequency >Market volatility and cash flows

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Summary >There is no single hedging policy that applies to all investors >The strategic hedging decision depends on a number of factors: >base currency of investor >underlying portfolio holdings >currencies to which portfolio is exposed >Out-of-sample tests highlight statistically significant benefits of hedging

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