The Currency Hedging Conundrum

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

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

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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 versus Active Currency Management
Active (Expected Return ? 0)
Passive (Expected Return 0)

• Traditional Active Hedging
• Symmetrical Active Hedging
• Active Cross Hedging

• Portfolio Hedging
• Optimal Hedge Ratios

Overlay

• Alpha Strategies

Alpha
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Why is currency risk important?

• 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.
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Mechanisms for Hedging Currency Risk

• 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.

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What is the best hedge ratio for foreign currency
exposure?

• 100 - Currencies just add unwanted risk to the
  portfolio.
• 0 - Why hedge? Currencies add diversification.
• The hedge ratio that minimizes overall portfolio
  risk.
• 50 - Never 100 right, but never 100 wrong
  either!

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Why is Currency Risk Important?Schools of
Thought 100 Hedged

• Currencies simply contribute to portfolio
  volatility.

0.55 Reduction to Annualized Risk
Unhedged MSCI Switzerland
Unhedged MSCI Switzerland
Annualized Standard Deviation of Monthly Returns
The right exposure to currencies can actually
provide portfolio diversification, therefore
reducing overall portfolio risk
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Why is Currency Risk Important?Schools of
Thought 0 Hedged

• Currencies add diversification to my portfolio.

3.78 Additional Annualized Risk
Unhedged MSCI US
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!

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Why is Currency Risk Important?Schools of
Thought 50 Hedged

• Minimum regret portfolio hedging policy

• 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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Techniques for Managing Currency Risk Passive
Hedging

• Goal is to control potential exchange rate risk
• Typical hedge ratio is between 0 100
• Hedge ratios applied uniformly across all
  currencies

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Techniques for Managing Currency Risk Currency
Risk and Diversification

• 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 portfolios 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 portfolios risk.

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

• 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.

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Techniques for Managing Currency Risk Optimal
Currency-Specific Hedge Ratios

• Each currency interacts with asset markets in a
  unique way. It is not necessarily optimal to
  hedge the same proportion of every currency.

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

• 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.

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How often would we expect a 7-sigma event to
occur?

• Approximately 1 trading day in 300 years
• Approximately 1 trading day in 300,000 years
• Approximately 1 trading day in 3,000,000 years
• 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.
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Putting N-sigma events in perspective

• 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.
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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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Why do hedge ratios vary across countries?

• 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.

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Risk of Regret Multi-risk optimization to control
for regret risk
Maximizes Expected Return - Risk Aversion x
Standard Deviation2 -Tracking Error Aversion x
Tracking Error2
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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