Derivatives and Currency Management

Question 1

Demonstrate how an asset’s returns may be replicated by using options.

Answer 1

Options can be used to replicate an asset’s returns, or the returns from a forward contract.
* A long call plus a short put, with the same strikes and expiration, gives a synthetic long forward—equivalent to a long position in the underlying financed by borrowing at the risk-free rate(Rf).
* A short call plus a long put, same strikes and expiration, gives a synthetic short forward, which is equivalent to a short position in the underlying plus a long bond paying Rf.
* Put-call parity links all these positions together: c0 – p0 = S0 – PV(X) or S0 + p0 = c0 + PV(X).

Question 2

Discuss the investment objective(s), structure, payoff, risk(s), value at expiration, profit, maximum profit, maximum loss, and breakeven underlying price at expiration of a covered call position.

Answer 2

An investor creates a covered call position by buying the underlying security and selling a call option.
* Covered call writing strategies can be used to generate additional portfolio income when the investor believes that the underlying stock price will remain unchanged over the short term. The calls are likely to be written OTM.
* ITM calls could be written when the investor aims to reduce a position at a favorable price.
* Marginally OTM calls could be used if the aim is to realize a target price.

Question 3

Discuss the investment objective(s), structure, payoff, risk(s), value at expiration, profit, maximum profit, maximum loss, and breakeven underlying price at expiration of a protective put position.

Answer 3

A protective put is constructed by holding a long position in the underlying security and buying a put option (usually [ATM], or somewhat OTM). You can use a protective put to limit the downside risk at the cost of the put premium.
* The purchase of the put provides a lower limit to the position at a cost of lowering the possible profit (i.e., the gain is reduced by the cost of the insurance). It is an ideal strategy for an investor who thinks the stock may go down in the near future, yet who wants to preserve upside potential.

Question 4

Compare the delta of covered call and protective put positions with the position of being long an asset and short a forward on the underlying asset.

Answer 4

The delta of a long (short) position in one unit of the underlying asset is +1 (–1). If a long position in an asset is hedged by a short forward, then the delta will be reduced to zero, whereas both covered call and protective put positions have (positive) deltas that are different than zero.
* In other words, the effect of the covered call and protective put, during the option’s life, is to reduce the asset’s delta, but not eliminate it.

Question 5

Compare the effect of buying a call on a short underlying position with the effect of selling a put on a short underlying position.

Answer 5

If an investor has a short position in the underlying, then they could:
* Hedge their exposure to the underlying rising by buying a call (analogous to hedging a long position with a protective put).
* Sell off some of the benefit from the underlying falling by selling a put (analogous to a covered call).

Question 6

Discuss the investment objective(s) of a bull option strategy.

Answer 6

Bull call spread strategy: comprises a long call and a short call. The short call has a higher exercise price, and its (lower) premium subsidizes the long call. A bull spread offers gains if the underlying asset’s price goes up, but the upside is limited.

It is a debit spread, because it involves an initial net premium payment. Particularly with American-style options. Bull put are possible.

Before expiration, bull spreads are best seen as positions giving long exposure to the underlying, but with a reduced level of delta.

Question 7

Discuss the investment objective(s), of a bear option strategy.

Answer 7

Bear put spread strategy: comprises a long put and a short put. The short put has a lower exercise price, and its (lower) premium subsidizes the long put. A bear spread offers gains if the underlying asset’s price goes down, but the upside is limited.

It is a debit spread, because they involve an initial net premium payment. Particularly with American-style options. Bear call spreads are possible.

Before expiration, bear spreads are best seen as positions giving short exposure to the underlying, but with a reduced level of delta.

Question 8

Discuss the investment objective(s) of a straddle option strategy

Answer 8

Long Straddle: is a long call plus long put with the same exercise price. The greater the move in the stock price, the greater the payoff from a straddle at expiration (with no upper limit on profit).
Before expiration, the prime focus is on volatility increasing, since a long straddle will have positive vega (but low delta, when ATM).

Short Straddle: is a short call plus short put with the same exercise price. The closer the stock price ends to the strike, the greater is the payoff from a short straddle at expiration (this is limited to the sum of the premiums).
Before expiration, the prime focus is on volatility, this time falling—a short straddle has negative vega (but low delta, when ATM).

Question 9

Discuss the investment objective(s) of a collar option strategy.

Answer 9

Collar Strategy: is simply a covered call and protective put combined to limit the downside and upside values of the position at expiration. Before expiration the collar can be seen as a way of reducing delta.

Question 10

Describe uses of calendar spreads.

Answer 10

Long calendar spread: involves the sale of a shorter-dated ATM (or near-ATM) call and the purchase of a longer-dated call with the same strike (or both could be puts). The basic motivation is to profit from the higher theta of the closer-to-expiry ATM option. At expiration the position will have a net value equal to the long put’s time value. If the options are still ATM this will exceed the net premium paid initially.

Short calendar spread: buys the shorter-dated and sells the longer-dated options. The options are either ITM or OTM, and now a large move in the underlying (so it ends up well away from the strike) is needed (and/or a decrease in implied volatility).

Question 11

Discuss volatility skew and smile.

Answer 11

Volatility smile: is where further-from-ATM options have higher implied volatilities.

Volatility skew: Relatively more common situation is , where implied volatility increases for more OTM puts, and decreases for more OTM calls.
* The skew is explained by OTM puts being desirable as insurance against market declines, while the demand for OTM calls is low.
* Deviations of the skew from historical levels could form the basis of trading strategies, a long (short) risk reversal combines long (short) OTM calls and short (long) OTM puts on the same underlying, delta-hedged using the underlying stock. A long risk reversal assumes the OTM calls are relatively underpriced.

Question 12

Demonstrate how interest rate swaps can be used to modify a portfolio’s risk and return.

Answer 12

Interest rate swaps can be used to convert floating-rate assets (or liabilities) into fixed-rate assets (or liabilities).

Interest rate swaps can be used to alter a fixed-income portfolio’s duration.
* Payer swaps (pay fixed) have negative durations.
* Receiver swaps (receive fixed) have positive durations.

Question 13

Demonstrate how Forward rate agreements (FRAs) can be used to modify a portfolio’s risk and return.

Answer 13

Forward rate agreements (FRAs): are OTC forward contracts that can be used to hedge short-term future floating lending or borrowing requirements (lock into a fixed interest rate).

FRAs can also be used to speculate on the direction of interest rates.
* Long FRA = pay fixed and receive floating. They increases in value when interest rates rise.
* Short FRA = pay floating and receive fixed. They increases in value when interest rates fall.
* The price of an FRA is a forward rate of interest determined from spot rates.

Question 14

Demonstrate how Short-term interest rate (STIR) futures can be used to modify a portfolio’s risk and return.

Answer 14

Short-term interest rate (STIR) futures: are exchange traded and, therefore, benefit from liquidity and no credit risk. They can be used to hedge short-term future interest rate risk and speculate on interest rate direction.
* STIR futures use IMM price convention = 100 − annualized interest rates.
* Long STIR futures will increase in value when rates fall.
* Short STIR futures will increase in value when rates rise.
* STIRs are typically more liquid than bond futures.
* Strips of STIRs are often used to hedge bonds with 2–3 years to maturity.

Question 15

Demonstrate how Government bond futures can be used to modify a portfolio’s risk and return.

Answer 15

Government bond futures: are used to hedge fixed-income portfolios when the constituent bonds have more than 2–3 years to maturity.
* Treasury bond futures prices are based on a notional bond (typically 6% coupon).
* Short party to the contract can deliver a range of eligible government bonds.
* One of the government bonds will be cheapest to deliver (CTD).
* The CTD bond has the highest repo rate or lowest basis.

Question 16

What is Currency Risk?

Answer 16

Currency risk is the change in value of assets and liabilities denominated in overseas currencies when converted to the domestic currency and is caused by exchange rate fluctuations.

Question 17

Demonstrate how currency swaps can be used to modify a portfolio’s risk and return.

Answer 17

Cross-currency swaps = synthetic overseas borrowing.
* Borrow in cheap currency (often domestic).
* Use to exchange domestic borrowing for overseas currency.
* Principal exchanged using the spot rate at initiation at the start and end of the swap’s life.
* Counterparties pay the interest on the currency received at initiation.
* Negative basis means the cost of synthetic $ borrowing > the cost of direct $ borrowing (lenders of the $ receive a premium).
* Negative basis means that the $ lender will pay less than overseas LIBOR on their interest payments (overseas LIBOR – basis).
* Negative basis allows U.S. fixed-income managers to lend dollars via a swap, invest the foreign currency in a foreign bond market, and generate a higher return (due to the basis) than if they invested domestically.

Question 18

Demonstrate how currency forwards and futures can be used to modify a portfolio’s risk and return.

Answer 18

Currency forwards: allow a participant to lock in a guaranteed exchange rate for converting a fixed amount of one currency into another at a future delivery date.

Currency futures: are exchange-traded currency forwards.

Question 19

Demonstrate how equity swaps, forwards, and futures can be used to modify a portfolio’s risk and return.

Answer 19

Equity swaps can be used to create synthetic exposures to equity market return.

There are three main types of equity swaps:
* Pay fixed, receive equity return.
* Pay floating, receive equity return.
* Pay one equity return, receive another equity return.

Equity return may be based on:
* A stock index.
* A basket of stock.
* A single stock.

Return may be computed as price return or total return (including dividends).

The equity payer in an equity swap pays the return if positive and receives the return if negative.

Question 20

What are the Benefits of equity futures?

Answer 20

Benefits of equity futures include:
* Low transaction costs.
* Implementing tactical asset allocation without transactions in the physical securities.
* Selling futures: reduces equity exposure.
* Buying futures: increases equity exposure.
* Diversification of portfolios.
* Gain exposure to a different equity market.
* To achieve a target beta.

Question 21

What is the VIX?

Answer 21

VIX = volatility index (CBOE Volatility Index):
* Measures implied volatility of the S&P 500 over a forward period of 30 days.
* Implied volatility computed from call and put options on the index.
* Volatility mean reverts over time.
* Market participants cannot directly invest in VIX.

VIX level and equity returns are negatively correlated.

Question 22

Demonstrate the use of volatility derivatives and variance swaps.

Answer 22

VIX futures:
* Term structure of futures allows us to view the market’s expectation of volatility for different contract maturities.
* Typically, the market is in contango when implied 30-day forward volatility is low.
* VIX futures can be used to offset tail risk in equity portfolios.

Based on realized vs. implied volatility over the swap’s life:
* NVEGA = profit or loss for a 1% change in volatility
* NVAR = multiplier that converts (σ2 − K2) into a payoff
* K = implied volatility over the swap period
* σ = realized volatility over the swap period

Volatility options and futures have linear payoffs with respect to volatility.

Question 23

What are Variance Swaps?

Answer 23

Variance swaps have convex payoffs with respect to volatility.

Convexity makes variance swaps more attractive for hedging tail risk because, as volatility rises and equity returns fall, the payoffs on variance swaps increase at an increasing rate.

Question 24

Demonstrate the use of derivatives to achieve targeted equity and interest rate risk exposures.

Answer 24

Use an equity swap to reduce equity exposure by entering into a pay total return equity swap receive fixed.
Invest surplus cash by purchasing equity index futures.

Question 25

Analyze the effects of currency movements on portfolio risk and return.

Answer 25

An investment in assets priced in a currency other than the investor’s domestic currency (a foreign asset priced in a foreign currency) has two sources of risk and return:
1. the return on the assets in the foreign currency.
2. the return on the foreign currency from any change in its exchange rate with the investor’s domestic currency.

Question 26

Discuss strategic choices in currency management.

Answer 26

Passive hedging: is rule-based and typically matches the portfolio’s currency exposure to the portfolio’s benchmark in order to eliminate currency risk relative to the benchmark.

Discretionary hedging: allows the manager to deviate modestly from passive hedging. The primary goal is currency risk reduction while seeking some modest value added return.

Active currency management: allows wider discretion to selectively hedge or not hedge and to deviate substantially from the benchmark. The goal is value added, not risk reduction. At the extreme, an active manager can treat currency as an asset class and take positions independent of the portfolio assets. For example, a manager who is bearish on the Swedish krona (SEK) can short the SEK even if no SEK assets are owned.

Currency overlay management: is a broad term referring to the use of a separate currency manager. The asset manager first takes positions in the markets considered most attractive, without regard to the resulting currency exposures. The overlay manager then adjusts the currency exposures. The overlay manager’s mandate can be passive, discretionary, or active.

Arguments made for not hedging currency risk include the following:
* Avoid the time and cost of hedging or trading currencies.
* Currency effects are a “zero-sum game”; if one currency appreciates, another must depreciate.
* In the long run, currencies revert to a theoretical fair value.

Arguments for active currency management include the following:
* In the short run, currency movement can be extreme.
* Inefficient pricing of currencies can be exploited to add to portfolio return. Inefficient pricing of currency can arise as many foreign exchange (FX) trades are dictated by international trade transactions or central bank policies.

Question 27

Formulate an appropriate currency management program given financial market conditions and portfolio objectives and constraints.

Answer 27

Factors that favor a benchmark neutral or fully hedged currency strategy are:
* A short time horizon for portfolio objectives.
* High risk aversion.
* High short-term income and liquidity needs.
* Significant foreign currency bond exposure.
* Low hedging costs.
* Clients who doubt the benefits of discretionary management.
* A client who is unconcerned with the opportunity costs of missing positive currency returns.

Question 28

Compare active currency trading strategies based on economic fundamentals, technical analysis, carry-trade, and volatility trading.

Answer 28

Economic fundamentals assume that purchasing power parity (PPP) determines exchange rates in the very long run. In the shorter run, currency appreciation is associated with:
* Currencies that are undervalued relative to fundamental value (based on PPP).
* Currencies with a faster rate of increase in fundamental value.
* Countries with lower inflation.
* Countries with higher real or nominal interest rates.
* Countries with a decreasing country risk premium.

Technical analysis:
* Overbought (or oversold) currencies reverse.
* A currency that declines to its support level will reverse upward unless it pierces the support level, in which case, it can decline substantially.
* A currency that increases to its resistance level will reverse downward unless it pierces the resistance level, in which case, it can increase substantially.
* If a shorter term moving average crosses a longer term moving average, the price will continue moving in the direction of the shorter term moving average.

The carry trade exploits the forward rate bias (i.e., forward exchange rates are not a valid predictor of currency market movement).
* Borrow the lower interest rate currency (often a developed market).
* Convert it to the higher rate currency (often an emerging market) at the spot exchange rate.
* Invest and earn the higher interest rate.
This is a risky, not a hedged, trade. If the higher interest rate currency appreciates or depreciates less than “implied” by the forward rate, the trade will be profitable. In times of severe economic stress, the carry trade can be very unprofitable as the higher interest rate (and riskier) currency collapses.

Volatility trading profits from changes in volatility.
* If volatility is expected to increase, enter a straddle (purchase a call and put with the same strike price, typically using at-the-money options). A strangle (buy an out-of-the-money call and put) can also be used. The strangle will cost less but will have less upside if volatility increases.
* If volatility is expected to decline, enter a reverse straddle or strangle (i.e., sell the options).

Question 29

Describe how changes in factors underlying active trading strategies affect tactical trading decisions.

Answer 29

Relative currency:
* Appreciation: Reduce the hedge (short position) on OR increase the long position in the currency
* Depreciation: Increase the hedge on or decrease the long position in the currency

Volatility:
* Rising: Long straddle (or strangle)
* Falling: Short straddle (or strangle)

Market conditions:
* Stable: A carry trade
* Crisis: Discontinue the carry trade

Question 30

Describe how forward contracts and FX (foreign exchange) swaps are used to adjust hedge ratios.

Answer 30

Typically, forward contracts are preferred for currency hedging because:
* They can be customized, while futures contracts are standardized.
* They are available for almost any currency pair, while futures trade in size for only a limited number of currencies.
* Futures contracts require margin, which adds operational complexity and can require periodic cash flows.
* Trading volume of FX forwards and swaps dwarfs that of FX futures, providing better liquidity.

A hedge can be a static hedge, which is established and held until expiration, or a dynamic hedge, which is periodically rebalanced.

The choice of hedging approach should consider:
* Shorter term contracts or dynamic hedges with more frequent rebalancing tend to increase transaction costs but improve the hedge results.
* Higher risk aversion suggests more frequent rebalancing.
* Lower risk aversion and strong manager views suggest allowing the manager greater discretion around the strategic hedging policy.

Hedging also exposes the portfolio to roll yield or roll return. Roll yield is a return from the movement of the forward price over time toward the spot price of an asset. It can be thought of as the profit or loss on a forward or futures contract if the spot price is unchanged at contract expiration.

Question 31

Describe trading strategies used to reduce hedging costs and modify the risk–return characteristics of a foreign-currency portfolio.

Answer 31

The cost of hedging a currency exposure:
Positive roll will reduce and negative roll will increase hedging costs.
* Hedging with forward (or futures) has no explicit option premium cost, but it has implicit cost; it removes upside as well as downside.
* Active managers can selectively over- or under-hedge. Buy more or sell less of the currency expected to appreciate.
* An at-the-money (ATM) put (a protective put or portfolio insurance) is the most expensive (upfront premium cost) form of option hedging (e.g., buy a 50 delta put).

Option hedging costs can be reduced by decreasing upside potential or increasing downside risk. To hedge an existing currency exposure:
* Buy an out-of-the-money (OTM) put.
* Use a collar; buy an OTM put and sell an OTM call.
* Use a put spread; buy an OTM put and sell a further OTM put.
* Use a seagull spread; buy an OTM put, sell a further OTM put, and sell an OTM call.
* Use exotic options that require additional conditions before they can be exercised or which can expire early.

Question 32

Describe the use of cross-hedges, macro-hedges, and minimum-variance-hedge ratios in portfolios exposed to multiple foreign currencies.

Answer 32

A cross hedge (sometimes called a proxy hedge): uses a hedging vehicle that is different from, and not perfectly correlated with, the exposure being hedged.

A macro hedge: is a type of cross hedge that addresses portfolio-wide risk factors rather than the risk of individual portfolio assets. One type of currency macro hedge uses a derivatives contract based on a fixed basket of currencies to modify currency exposure at a macro (portfolio) level.

The minimum-variance hedge ratio (MVHR): is a mathematical approach to determining the hedge ratio. Regress past changes in value of the portfolio (RDC) to the past changes in value of the hedging instrument (the foreign currency) to find the hedge ratio that would have minimized standard deviation of RDC.

The hedge ratio: is the beta (slope coefficient) of that regression.
* Positive correlation between RFX and RFC; MVHR > 1.
* Negative correlation between RFX and RFC; MVHR < 1.

Question 33

Discuss challenges for managing emerging market currency exposures.

Answer 33

Transactions in a lesser developed country’s currency poses challenges because of (1) higher transaction costs and (2) the increased probability of extreme events. Examples of these problems include the following:
* Low trading volume leads dealers to charge larger bid/asked spreads.
* Liquidity can be lower and transaction costs higher to exit trades than to enter trades.
* Transactions between two emerging market currencies can be even more costly.
* Emerging market currencies return distributions are non-normal with higher probabilities of extreme events and negative skew of returns.
* The higher yield of emerging market currencies will lead to large forward discounts. This produces negative roll yield for investors who need to sell such currencies forward.
* Contagion is common during periods of financial crisis; the correlations of emerging markets with each other and their currencies tend to converge toward +1.0. At the very time diversification is needed most, it tends to disappear.
* Tail risk exists when the governments of emerging markets actively intervene in the markets for their currencies producing long periods of artificial price stability followed by sharp price movements when market forces overwhelm the government’s capacity to intervene. These negative events occur more frequently than would be assumed with a normal distribution.
Nondeliverable forwards (NDFs): are forward contracts in which the exchange of the notional amounts of the currencies is not required. NDFs are an alternative to deliverable forwards and allow for the gains or losses of an emerging market’s restricted currency to be settled in a developed market currency, which lowers credit risk. Only the gains to one party are paid at settlement.