The change of a portfolio value in absolute domestic currency terms Equation 1. The change in the value of the currency future is analyzed separately

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1 READING 35: CURRENCY RISK MANAGEMENT A- Hedging with Futures or Forward Currency Contracts 1- The Basic Approach: Hedging the Principal Hedging with futures is very simple. An investor takes a position with a foreign exchange contract that offsets the currency exposure associated with the principal being hedged. The notations in the reading are: V t V t S t F t Value of the portfolio of foreign assets to hedge, measured in foreign currency at time t Value of the portfolio of foreign assets measured in domestic currency Spot exchange rate: domestic currency value of one unit of foreign currency quoted at time t Futures exchange rate: domestic currency value of one unit of foreign currency quoted at time t R Rate of return of the portfolio measured in foreign currency terms, (V t V 0 )/V 0 R Rate of return of the portfolio measured in domestic currency terms, (V t V 0 )/V 0 s Percentage movement in the exchange (S t S 0 )/S 0 The change of a portfolio value in absolute domestic currency terms V t V 0 = V t S t V 0 S 0 Equation 1 The change in the value of the currency future is analyzed separately Realized gain/loss = V 0 ( F t + F 0 ) Equation Therefore, the net profit on the hedged position is: Profit loss = V t S t V 0 S 0 V 0 (F t F 0 ) Equation 3 The rate of return in domestic currency on the hedged position, R H, can be found by dividing the profit in Equation 3 by the original portfolio value V 0 S 0. We find R H = V ts t V 0 S 0 V 0 S 0 F t F 0 S 0 = R R F Equation 4 where R F is the futures price movement as a percentage of the spot rate F t F 0 S 0. The exact relationship between domestic and foreign returns is R = R + s(1 + R) Equation 5 - Minimum-Variance Hedge Ratio A problem appears when the foreign currency value of a foreign investment reacts systematically to an exchange rate movement. One objective is to search for minimum variability in the value of the hedged 1

2 portfolio. Investors usually care about the rate of return on their investment and the variance thereof. So, if they decide to hedge, investors would like to set the hedge ratio h to minimize the variance of the return on the hedged portfolio. Recall that the hedge ratio is the ratio of the size of the short futures position in foreign currency to the size of the currency exposure (value of the portfolio in foreign currency). It is easy to show that the rate of return on a hedged portfolio, R H, is equal to the rate of return on the original portfolio (unhedged), R, minus h times the percentage change on the futures price, R F : R H = R h R F Equation 6 The optimal hedge ratio h, which minimizes the variance of R H, is equal to the covariance of the portfolio return to be hedged with the return on the futures, divided by the variance of the return on the futures: h = cov(r, R F ) σ F Equation 7 This optimal hedge ratio is sometimes called the regression hedge ratio because it can be estimated as the slope coefficient of the regression of the asset, or portfolio, return on the futures return: R = a + h R F + Error term Equation 8 where R is the return on the asset or portfolio measured in the investor s domestic currency, R F is the return on the futures, and a is a constant term. To get a better understanding of this minimum-variance hedge ratio, it is useful to substitute the value of R given in Equation 5 into Equation 6. From now on, we will further assume that the cross-product term of Equation 5 is small and will drop it. We find R H = R + s hr F Equation 9 The futures exchange rate differs from the spot exchange rate by a basis equal to the interest rate differential. Let s first assume that the basis is zero (interest rates equal in the two currencies) and remains so over time. Hence, the futures exchange rate is equal to the spot exchange rate. Then the rate of return on a futures contract, R F = (F t F 0 ) S 0, is equal to the spot exchange rate movement, s = (S t S 0 )/S 0. Equation 9 can now be written as follows: R H = R + s(1 h) Equation 10 and the minimum-variance hedge ratio is equal to h = cov(r, R F ) σ F cov(r + s, s) = σ s cov(r, s) = 1 + σ s Equation 11

3 where σ s is the variance of the exchange rate movement. Equation 11 shows the minimum-variance hedge ratio as the sum of two components, h 1 and h, linked to different aspects of currency risk: Translation risk h 1 = 1 Economic risk h = cov(r,s) σ s a. Translation Risk Translation risk comes from the translation of the value of the asset from the foreign currency to the domestic currency. It would be present even if the foreign currency value of the asset were constant (e.g., a deposit in foreign currency). The hedge ratio of translation risk is 1. This is usually taken to mean that a currency hedge should achieve on a foreign asset the same rate of return in domestic currency as can be achieved on the foreign market in foreign currency terms. Creating a perfect currency hedge is equivalent to nullifying a currency movement and translating a foreign rate of return directly into a similar domestic rate of return. Considering only translation risk, the optimal amount to hedge is determined by finding the value of h such that the hedged return in domestic currency terms R H closely tracks the return in foreign currency terms R. Equation 10 can be written as R H R = s(1 h) Equation 1 To minimize the variance of R H R, we must obviously set a hedge ratio of 1. This is basically the strategy of hedging the principal outlined previously. b. Economic Risk Economic risk comes when the foreign currency value of a foreign investment reacts systematically to an exchange rate movement. This is in addition to translation risk. The hedge ratio required to minimize this economic risk can be estimated by cov(r, s) σ s. This is the slope that we would get on a regression of the foreign currency return of the asset on the exchange rate movement. c. Hedging Total Currency Risk If an investor worries about the total influence of a foreign exchange rate depreciation on her portfolio value, measured in domestic currency, she should hedge both translation and economic currency risk. In this approach, the objective is to minimize the overall influence of an exchange rate movement, whether direct or indirect, on the asset return in domestic currency. The objective is not to try to minimize the tracking error between R H and R (translation risk). Most portfolio managers care only about translation risk, so they adopt a unitary hedge ratio if they try to minimize the impact of currency risk. From a portfolio accounting standpoint, currency loss is simply stated as the difference in return when measured in domestic and foreign currencies, R R. So, minimizing accounting currency losses is an objective choice. Also, the sensitivity of an asset value to an 3

4 exchange rate movement has to be estimated from some economic model and/or from historical data. Even though estimates might be imprecise and unstable, hedging only translation risk might not be optimal from an economic viewpoint. 3- The Influence of the Basis a. Basis Risk Forward (or swap) and futures exchange rates are directly determined by two factors: the spot exchange rate and the interest rate differential between two currencies. The forward discount, or the premium which is the percentage difference between the forward and the spot exchange rates equals the interest rate differential for the same maturity as the forward contract. In futures jargon, we say that the basis equals the interest rate differential. If we express the exchange rate as the dollar value of one pound and call r $ and r the interest rates in dollars and pounds, respectively, with the same maturity as the futures contract, the relation known as interest rate parity is F S = 1 + r $ F S and = r $ r 1 + r S 1 + r Equation 13 Note that the interest rates in Equation 13 are period rates, not annualized. They equal the annualized rates multiplied by the number of days until maturity and divided by 360 days. Because interest rate parity is the result of arbitrage on very liquid markets, it technically holds at every instant. Changes in the basis have an impact on the quality of the currency hedge. Although currency risk is removed by hedging, some additional risk is taken in the form of basis risk. But this basis risk is quite small. The correlation between futures and spot exchange rates is a function of the futures contract term. Futures prices for contracts near maturity closely follow spot exchange rates because at that point the interest rate differential is a small component of the futures price. Another factor that can affect the quality of the hedge is that movement in the interest rate differential (basis) could be correlated with movement in the spot exchange rate itself. b. Expected Hedged Return and the Basis We have so far focused on minimizing risk. A hedge ratio of 1 will minimize transaction risk. But in the long run, the return on the hedged portfolio will differ from the portfolio return achieved in foreign currency by the interest rate differential, even with a hedge ratio of 1. Although we can minimize, or even eliminate, the variance of R H R, it is impossible to set them equal. This is because we can hedge only with futures contracts with a price F different from S. Over time, the percentage movement in the futures price used in the hedge, R F, will differ from the percentage movement in the spot exchange rate, s, which affects the portfolio by the interest rate differential. 4

5 4- Implementing Hedging Strategies Short-term contracts track the behavior of the spot exchange rates better, have greater trading volume, and offer more liquidity than long-term contracts. On the other hand, short- term contracts must be rolled over if a hedge is to be maintained for a period longer than the initial contract. For long-term hedges, a manager can choose from three basic contract terms: 1) Short-term contracts, which must be rolled over at maturity ) Contracts with a matching maturity, that is, contracts that match the expected period for which the hedge is to be maintained 3) Long-term contracts with a maturity extending beyond the hedging period Another consideration in choosing a hedging strategy is transaction costs. Rolling over short-term contracts generates more commissions because of the larger number of transactions involved. It must also be stressed that the market value of the investment to be hedged varies over time. To maintain a desired hedge ratio, the hedge amount should be adjusted frequently to reflect changes in asset market prices. Practically, this cannot be done on a continuous basis because of transaction costs. Forward contracts of small size can be expensive to arrange and will entail a staggering of maturity dates difficult to manage because they are arranged for a fixed duration (e.g., one month or six months). Futures are easier to use for frequent adjustments because they are of small size and traded with a few fixed maturity dates rather than a fixed duration. Longer hedges can be built using currency swaps, which can be arranged with horizons of up to a dozen years. However, currency swaps are used primarily by corporations in the currency management of their assets and liabilities. Portfolio managers usually take a shorter horizon. 5- Hedging Multiple Currencies Cross-hedges are sometimes used for closely linked currencies. Some investment managers fear the depreciation of only one or two currencies in their portfolios and therefore hedge currency risk 5

6 selectively. Other managers fear that their domestic currency will appreciate relative to all foreign currencies. In a portfolio with assets in many currencies, the residual risk of each currency is partly diversified away. Optimization techniques can be used to construct a hedge with futures contracts in only a few currencies. Although the residual risk of individual currencies is not fully hedged, the portfolio is well protected against a general appreciation of the home currency. Another alternative is to use contracts on a basket of currencies as offered by some banks. The stability of the estimated hedge ratios is crucial in establishing effective hedging strategies, especially when cross-hedging is involved. Empirical studies indicate that hedges using futures contracts in the same currency as the asset to be hedged are very effective but that the optimal hedge ratios in cross-hedges that involve different currencies are somewhat unstable over time. In practice, a diversified international portfolio can be hedged using only the futures contracts available in a few currencies by following this procedure: Select the most independent major currencies with futures contracts available. Calculate the hedge ratios jointly by running a multiple regression of the domestic currency returns of the portfolio (U.S. dollar return for a U.S. investor) on the futures returns in the selected currencies. With the example of three currencies, we have R = a + h 1 R F1 + h R F + h 3 R F3 + Error term Equation 14 Use the estimates of the regression coefficients h1, h, and h3 as the hedge ratios in each currency. Because the spot currency movement is the major component of futures volatility, the hedge ratios obtained would be fairly close if we used currency movements in the regression instead of futures return. Of course, this procedure requires historical data on the portfolio and will work well only if the estimated regression coefficients are stable over time. B- Insuring and Hedging with Options 1- Insuring with Options For starters, a good hedge implies buying options (puts or calls), not selling or writing them. The advantage of buying options rather than futures is that options simply expire if the pound appreciates rather than depreciates. Of course, investors must pay a price for this asymmetric risk structure, namely, the premium, which is the cost of having this insurance. Note that the cost of the premium prevents a perfect hedge. If we call V 0 the number of pounds, P 0 the premium per, and K the strike (or exercise) price, the net dollar profit on the put at the time of exercise t is 6

7 Net dollar profit = V 0 (K S t ) V 0 P 0 when K > S t Equation 15 = V 0 P 0 otherwise That is, when K > S t, we have Net dollar profit = quantity (Exercise price Spot price) quantity Premium per pound, but the investor loses the premium otherwise. An alternative solution is to buy out-of- the-money puts with a lower exercise price and a lower premium. But with those, exchange rates would have to move that much more before a profit could be made on the options. In general, what is gained in terms of a lower premium is lost in terms of a lower strike price for the put option. - Dynamic Hedging with Options Listed options are traded continually, and positions are usually closed by reselling the option in the market instead of exercising it. The profit is therefore completely dependent on market valuation. The dynamic approach to currency option hedging recognizes this fact and is based on the relationship between changes in option premiums and changes in exchange rates. We know that an option premium is related to the underlying exchange rate, but in a complex manner. Exhibit 4 shows the relationship we usually observe for a put. Beginning with a specific exchange rate, say, :$ =.00, a put premium can go up or down in response to changes in the exchange rate. The slope of the curve at point A denotes the elasticity of the premium in response to any movements in the dollar exchange rate. In Exhibit 4, the premium is equal to 6 cents when the exchange rate is 00 U.S. cents per pound, and the slope of the tangent at point A equals 0.5. This slope is usually called delta (δ). 7

8 In this example, a good hedge would be achieved by buying two pound puts for every pound of British assets. One pound put is defined here as a put option on one unit of British currency. One contract includes several pound puts, depending on the contract size. If the pound depreciated by 1 U.S. cent, each put would go up by approximately 0.5 cents, offsetting the currency loss on the portfolio. In general, if n pound put options are purchased, the gain on the options position is Option gain = n(p t P 0 ) Equation 16 where P t is the put value at time t, and P 0 is the put value at time zero. For small movements in the exchange rate, P t P 0 = δ(s t S 0 ) Equation 17 Hence, the gain on the options position is Option gain = n(p t P 0 ) = n δ (S t S 0 ) Equation 18 Assuming that the value of the portfolio in foreign currency remains constant at V0, the gain (loss if negative) on the portfolio in domestic currency is equal to Portfolio gain = V 0 (S T S 0 ) Equation 19 A good currency hedge is obtained by holding n = V 0 /δ options. The hedge ratio is equal to 1/δ. The profit on the options position offsets the currency loss on the portfolio. In the example, the hedge ratio is equal to two as δ = 0.5. One should buy two pound puts for every pound of portfolio value. We must emphasize that δ and the hedge ratio vary with the exchange rate, so that the number of options held must be adjusted continually. This strategy is called the delta hedge. 3- Implementation A hedging strategy can combine futures and options. Futures markets are very liquid and have low transaction costs. Options offer the advantage of an asymmetric risk structure but have higher costs, in terms of both the fair price for this insurance risk structure and their transaction costs. If a hedging decision is necessary because an investor faces an increasing volatility in exchange rates and doesn t have a clear view of the direction of change, currency options are a natural strategy. Where the direction of a currency movement is clearly forecasted, currency futures provide a cheaper hedge. In setting the hedge, however, investors should take into account the expected return on the portfolio and its correlation with currency movements. C- Other Methods for Managing Currency Exposure Futures and options on foreign assets reduce currency exposure as long as an investor does not already own the assets in question. In addition, costs involved in taking such positions are less than those for 8

9 actually buying foreign assets and hedging them with currency futures or options. On the other hand, if the assets are already part of a portfolio, more conventional methods of currency hedging are probably better, especially for assets that will remain in the portfolio for a long time. 9

10 D- Strategic and Tactical Currency Management 1- Strategic Hedge Ratio a. Total Portfolio Risk It is often claimed that currency risk does not add a significant amount of uncertainty to the total portfolio when the international allocation is small (typically 10%). So the optimal passive hedge ratio is likely to depend on the proportion of international assets in the total portfolio: The lower the proportion of international assets, the lower the benchmark hedge ratio. b. Asset Types Stock prices from emerging countries are more sensitive to the value of the local currency than stock prices from developed countries. International bond portfolios could justify a different benchmark hedge ratio than international equity portfolios. The lower the correlation between portfolio return and currency movements, the lower the benchmark hedge ratio should be. c. Investment Horizon It is often stated that exchange rates revert to fundamentals over the long run, so currency risk tends to diminish over long horizons. Hence, long-term investors should worry less about currency risk and possibly adopt a no-hedging policy. But empirical work indicates that it might take a very long time for exchange rates to revert to fundamentals. The longer the investor s time horizon, the lower the benchmark hedge ratio should be. d. Prior Beliefs on Currencies Some investors believe that their own base currency is structurally weak (strong). This would lead them to adopt a lesser (higher) hedge ratio. e. Costs There are two components in hedging cost. The first one is related to trading, namely, transaction costs in the form of fees, commissions, and bid ask spreads. Currency hedging entails rather small transaction costs but poses a cumbersome administrative burden. The administrative and monitoring tasks should not be underestimated. The second cost component is the interest differential, as described in earlier chapters. To hedge, one has to sell foreign currencies forward at their forward price, which differs from the spot exchange rate used to value assets. This is not a transaction cost, but it is still a sure cost to be borne by a hedger. Hedging will become attractive only if the actual dollar depreciation is larger than this basis. 10

11 f. Is Regret the Proper Measure for Currency Risk? Ex post, if the foreign currency depreciates by any amount, the best hedging alternative would have been to be fully hedged. If the foreign currency appreciates by any amount, the best hedging alternative would have been to be unhedged. To minimize regret risk, a simple hedging rule would be to hedge 50 percent. Such a decision will turn out to be almost always wrong ex post, but the amount of regret would be minimized. - Currency Overlay The currency management of the international portfolio is often delegated to a specialized manager called the currency overlay manager. This decision is based on the assumption that the primary manager of the international assets does not have the currency expertise of the currency overlay specialist. The composition of the portfolio is periodically transferred to the currency overlay manager, who decides on the positions taken in currencies and manages currency risk. a. Management of the Currency Risk Profile Exchange rate movements are assumed to be unpredictable and no attempt is made to forecast future returns. But currency risk is managed through dynamic hedging or option-based approaches. The strategy attempts to create an asymmetric risk profile protecting from downside losses while allowing capture of some upside potential. This is pure active risk management. b. Technical Approach In many cases, the supply and demand for currencies that affect the exchange rate are non-profit-driven and may result in some temporary market inefficiencies in the price quoted for currencies. Some currency overlay managers claim that they can exploit these inefficiencies. They develop models that attempt to identify predictable price patterns in exchange rates and in their volatility. These technical models are used to generate superior returns within controlled currency risk management. c. Fundamental Approach Economic analysis could help detect undervalued or overvalued currencies. A fair value is determined for each currency, and the hedge ratio is adjusted upward (downward) when a foreign currency trades above (below) its fair value. Ultimately, the success of these strategies depends on the predictability of exchange rates. Having discussed currency overlay, it should be stressed that an investment management approach that separates the asset allocation decision from currency exposure decisions is not ideal. 3- Currencies as an Asset Class Currency overlay is restricted to the management of the currency exposure of an existing portfolio. The next step is to offer funds that specialize in currency management. 11