3XChapter 15-17 Derivatives and Currency Management

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Achieving a Target Portfolio Beta The number of contracts required to change the beta of an existing portfolio can be calculated with the following formula:

#******(BT-BP)/BF * MVP/F For contracts round-up from .5 down from .49 where: βT = target portfolio beta βP = current portfolio beta βF = futures beta (beta of stock index) MVP = market value of portfolio F = futures contract value = futures price × multiplier Note that to fully hedge the portfolio from market risk, βT = 0.

Convexity

(1) when realized volatility is below the strike, the losses on the variance swap are smaller than the losses on the volatility derivative, and (2) when realized volatility is above the strike, the gains on the variance swap are greater than the gains on the volatility derivative. With the variance swap, payoffs are increasing at an increasing rate when volatility rises and decreasing at a decreasing rate when volatility falls.

**% Probability of Rate change

(effective rate implied by futures -current funds rate) / Fed rate assuming change - current funds rate) if future = 97.9 then expected avergage rate = 2.1%

Investor's returns in [domestic] currency can be calculated as:

***Equation 1: RDC = (1 + RFC)(1 + RFX) − 1 = RFC + RFX + (RFC)(RFX) RDC ≈ RFC + RFX USE FOREIGN CURRENCY AS BASE RDC=return domestic currency RFC=return [foreign] currency

Basis risk in a currency hedge

**Basis risk exists when movement in the hedge currency is not matched by movement in the hedging vehicle *When the futures contract is longer than the desired holding period, the investor must reverse at the end of the holding period at the existing futures price. If the futures contract is shorter than the desired holding period, the investor must close the first contract and then enter another. Both the shorter-term and longer-term contracts will create basis risk. *A direct hedge will short forwards on the currency to be hedged and basis risk will therefore be low A cross hedge can range from lower to higher basis risk depending on what is used as the hedging vehicle. The MVHR depends on regressing past asset returns and currency movement to calculate a hedge ratio that would had minimized past volatility of returns to the domestic investor in a foreign asset. It is exposed to changing correlation and likely to have the highest basis risk.

Strategic Diversification Issues

**In the longer run, currency volatility has been lower than in the shorter run, reducing the need to hedge currency in portfolios with a long-term perspective. *-if the correlation between foreign currency asset returns and foreign currency returns is negative, then there may be no need to hedge all foreign currency Positive correlation between returns of the asset measured in the foreign currency (RFC) and returns from the foreign currency (RFX) increase volatility of return to the investor (RDC) and increase the need for currency hedging. Correlation tends to vary by time period, providing diversification in some periods and not in others Some investors assert that there is higher positive correlation between asset and currency returns in bond portfolios than in equity portfolios The hedge ratio (the percentage of currency exposure to hedge) varies by manager preference. Because equity is a more volatile asset class than bonds, the added risk of currency in a foreign equity investment is relatively less significant than in a foreign bond investment An unsophisticated client who does not understand currency is likely to be more confused by the incremental variability of return it adds. Hedging the currency risk will make the investment somewhat more predictable.

carry trade

**Refers to borrowing in a lower interest rate currency and investing the proceeds in a higher interest rate currency. (Buy at spot not forward) *-also look for currency pair that has the lowest implied volatility *Covered interest rate parity (CIRP) holds by arbitrage and establishes that the difference between spot (S0) and forward (F0) exchange rates equals the difference in the periodic interest rates of the two currencies. *The currency with the higher interest rate will trade at a forward discount, F0 < S0 -Rather have now than later The carry trade is based on a violation of uncovered interest rate parity (UCIRP) -UCIRP is an international parity relationship asserting that the forward exchange rate calculated by CIRP is an unbiased estimate of the spot exchange rate that will exist in the future. If this were true: -The currency with the higher interest rate will decrease in value by the amount of the initial interest rate differential. -If these expectations were true, a carry trade would earn a zero return.

Modified Duration

*-Receive fixed has higher modified duration because it has higher interest rate sensitivity (30 year bond vs 30 1 year bonds)

RISK The variance of RDC can be calculated using a variation of the basic formula for variance of a two asset portfolio:

*1- σ2(RDC) ≈ w^2(RFC)σ^2(RFC) + w^2(RFX)σ^2(RFX) + 2w(RFC)w(RFX)σ(RFC)σ(RFX)ρ(RFC,RFX) where: ρ = the correlation between RFC and RFX 2 -A domestic investor holds a single foreign currency denominated asset ***σ2(RDC) ≈ σ^2(RFC) + σ^2(RFX) + 2σ(RFC)σ(RFX)ρ(RFC,RFX) Example: 3^2 + 2^2 + 2*3*2*.5 3- If RFC is a Risk-Free Return σ(RDC) = σ(RFX)(1 + RFC)

*Hedges

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

The minimum-variance hedge ratio (MVHR)

*A mathematical approach to determining the hedge ratio. When applied to currency hedging, it is a [regression] of the past changes in value of the portfolio (RDC) to the past changes in value of the hedging instrument to minimize the value of the tracking error between these two variables. The hedge ratio is the beta (slope coefficient) of that regression. **jointly minimizes the volatility of the foreign market and currency. -Because this hedge ratio is based on historical returns, if the correlation between the returns on the portfolio and the returns on the hedging instrument change, the hedge will not perform as well as expected. -The hedge ratio is the beta (slope coefficient) of the regression *-A direct currency hedge is a simple 1.0 hedge ratio

Interest Rate Swaps

*A payer swap is a contract to make a series of fixed-rate payments and receive a series of floating-rate payments, If future floating rates are higher than rates expected at the initiation of a swap, a payer swap will increase in value In practice, the payments from each party to a swap are netted (the party that owes the larger amount pays the difference) to reduce credit risk.

synthetic short

*Buy put sell call Maximum profit occurs at the strike, and above. premium below the initial stock price = X Maximum loss = breakeven

*Currencies with higher relative interest rates tend to attract capital and appreciate in value. *A forward premium is caused by a relatively lower interest rate and that is associated with currency depreciation

cross-currency basis swap

*Exchange the notional amounts of each currency at the beginning and the end of the swap. *At the swap's expiration, the notional principal amounts are exchanged. The amounts are the same as those exchanged initially; changes in the exchange rate over the life of the swap do not affect these amounts, so there is no uncertainty (exchange rate risk) on the principal flows *Note that the currency received on the swap at initiation determines the currency of the interest and principal that will be paid. **If the NZD is trading at a positive cross-currency basis (NZD higher demand) to the USD, New Zealand investors can earn superior returns by lending NZD via a currency swap and investing in U.S. government bonds. *Only occurs if covered interest parity does not hold Explanation - whenever there's a higher demand for the dollar, the counterparty lending the dollar will ask for a price premium. It is this amount which is referred to as the "cross currency basis". In other words, the European company will pay out US Libor and will receive Euribor plus the cross currency basis https://www.bondvigilantes.com/blog/2017/12/29/cross-currency-basis-implications/

*Futures contracts on corporate bonds do not exist, *Futures markets are used less frequently to manage exchange rate risk since they are relatively newer than the foreign exchange forward market and provide less liquidity. *Forwards are the most frequently used method of hedging exchange rate risk in practice. 1. A forward contract is less expensive. 2. A forward contract has greater liquidity. *If own a currency, a hedge will require a forward sale of the currency and sale at a forward premium will earn positive roll yield. Positive roll yield will reduce hedging cost compared to the initial spot price. Hedging locks in the forward price as an end of period exchange rate.

Roll Yield

*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 *Roll yield for a contract held to expiration is determined by initial forward minus spot price divided by initial spot price. *Consider an investor who sells CHF 1 million six-month forward for USD 1.05 when the spot rate is 1.04. The forward price is at a premium so the roll yield on a short position will be positive. Think of it as the investor sells at a high price and the price rolls down for a gain. -Contango - futures price higher (gold now $1000 one year $1100) -backwardation - futures price lower Positive roll yield will shift the analysis toward hedging and negative roll yield will shift the analysis away from hedging.

Currency Management Strategies

*Passive hedging -rule based and typically matches the portfolio's currency exposure to that of the benchmark used to evaluate the portfolio's performance. It will require periodic rebalancing to maintain the match. The goal is to eliminate currency risk relative to the benchmark. *-High short-term income and liquidity needs **-good for bonds (more volatile than equities) ***Discretionary hedging -allows the manager to deviate modestly from passive hedging by a specified percentage. An example is allowing 5% deviations -The manager's primary duty is to protect the portfolio from currency risk and secondarily seek alpha within limited bounds. **Active currency management -allows a manager to have greater deviations from benchmark currency exposures. -The goal is to create incremental return (alpha), not to reduce risk. -if the range of hedging 70% - %130 that is active. *currency overlay -broad term covering the outsourcing of currency management (hire someone to do it for you) *Due to efficient currency markets and a long investment horizon and few immediate liquidity needs you should choose to forgo currency hedging and active management.

non-deliverable forwards (NDFs)

*The pricing of NDFs does not necessarily follow covered interest rate parity; pricing reflects the supply and demand conditions in the offshore market, which may be different than the onshore market of the specific emerging market country. **The non-controlled currency is usually the USD or some other major currency. The controlled currency is the emerging market currency. **The credit risk of an NDF is usually less than that of a regular forward contract because there is no delivery of the notional amounts required. *The pricing of NDFs reflects supply and demand conditions. *always deliver in a currency like USD so if the contract ended in a MXN1000 gain payout like $50. x

Calendar Spreads

*buying longer-dated options and selling shorter-dated options with the same strike and underlying. For options that are near to ATM, the nearer-dated options will have a higher absolute value of theta (more negative) than longer-dated options. A long calendar spread will benefit from a stable market or an increase in implied volatility.

Volatility Smile

*further-from-ATM options have higher implied volatilities, so we would see a U-shaped (smiling) curve if implied volatility were plotted against strike. This is less common, however, than volatility skew.

A volatility skew

*implied volatility increases for more OTM puts, and decreases for more OTM calls. This is explained by OTM puts being desirable as insurance against market declines (so their values are bid up by higher demand, and higher values imply higher volatility) Skew = more common

A long straddle

*involves the purchase of an equal number of calls and puts on a given underlying. The options all have the same expiry date and [strike] *If stock is 60 and have options of 58,58,62 should use both 58's only use 58 and 62 when stranggle

Gamma

*it tends to be higher the closer to ATM an option, and is at its greatest for ATM options that are close to expiration *Gamma is positive for (long) calls and for (long) puts.

VEGA

*see picture for formula or #***Variance Notional = Vega Notinial / [2 * Volatility stike price] -Vega measures the effect of a 1% increase in volatility on the value of the option

Exotic Options

-A knock-in option is a plain vanilla option that only comes into existence if the underlying first reaches some prespecified level. -A knock-out option is a standard option that ceases to exist if the underlying reaches some prespecified level. -Binary or digital options pay a fixed amount that does not vary with the difference in price between the strike and underlying price.

Because the carry trade exploits a violation of interest rate parity, it can be referred to as trading the forward rate bias. Historical evidence indicates that:

-Generally, the higher interest rate currency has depreciated less than predicted by interest rate parity or even appreciated and a carry trade has earned a profit. -However, a small percentage of the time, the higher interest rate currency has depreciate substantially more than predicted by interest rate parity and a carry trade has generated large losses.

*Fixed-income (bond) futures

-The short party can deliver any eligible Treasury bond in the delivery month. -The seller can choose when in the delivery month to deliver the bond. -Futures prices on sovereign debt are quoted for a notional bond. Each eligible bond is assigned a conversion factor (CF), computed by discounting the bond at a constant YTM regardless of the bond's actual yield. Bonds with coupon rates lower than the YTM will have conversion factors of less than 1 and bonds with coupon rates greater than the YTM will have CFs greater than 1. -The Treasury bond with the lowest basis will typically have the highest implied repo rate and be the cheapest-to-deliver.

The key determinants of an option's value are

-The strike price. -The current level of the underlying (e.g., stock price, currency rate, etc.). -The remaining time to expiration. -The volatility of the underlying (the expected annualized standard deviation of the underlying over the period to option expiration). -The annualized risk-free interest rate over the period to expiration. -The annualized yield expected from the underlying (if any) over the period to expiration. -Whether it is European- or American-style (in principle the latter might be worth more because they give the right to exercise before expiration, in addition to at expiration).

The IPS: Should Include

-The target percentage of currency exposure that is to be hedged. -Allowable discretion for the manager to vary around this target. -Frequency of rebalancing the hedge. -Benchmarks to use for evaluating the results of currency decisions. -Allowable (or prohibited) hedging tools.

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.

*Hedging results are not perfect due to three main factors:

1 - The hedge is constructed using the cheapest to deliver bond (CTD). If the level or slope of the term structure changes significantly, the bond that is CTD may change. If the CTD bond changes the duration of the Treasury bond, future will also change. 2 - The hedge ratio uses modified duration. Modified duration assumes bonds react in a symmetrical and linear fashion to interest rate changes. In reality, a bond's exposure to interest rate changes is convex. 3- Modified duration only captures parallel movements in the term structure of interest rates. The hedge ratio, therefore, does not protect a bond portfolio from shaping (structural) risk. Structural risk can be defined as non-parallel movements in the term structure such as steepening, flattening, and changes in curvature.

A long risk reversal combines long calls and short puts on the same underlying.

A quote of 0.9790/0.9810 CAD/USD has four interpretations. Deliver more CAD can be phrased as: -Buy 1.0000 USD and deliver (sell) 0.9810 CAD. -Sell 0.9810 CAD and receive (buy) 1.0000 USD. Receive less CAD can be phrased as: -Sell 1.0000 USD and receive (buy) 0.9790 CAD. -Buy 0.9790 CAD and deliver (sell) 1.0000 USD.

*Static Hedge

A static hedge (i.e., unchanging hedge) will avoid transaction costs but will also tend to accumulate unwanted currency exposures as the value of the foreign-currency assets change. The higher the degree of risk aversion, the more frequently the hedge is likely to be rebalanced back to the "neutral" hedge ratio.

Equity Swap vs. Physical Stock

Advantages -Gain exposure to equity when participation in the physical market is restricted -Avoid tax on physical ownership (i.e., stamp duty) -Avoid custody fees on physical ownership -Avoid the cost of monitoring physical positions, which may increase due to corporate actions (i.e., dividend payments, stock splits, buy-backs, M&A, etc.) Disadvantages -Equity swaps typically require collateral -Swaps are illiquid -Swaps do not convey voting rights

Currency forwards and futures

Allow users to exchange a specified amount of one currency for a specified amount of another currency on a future date Forwards are customized, while futures are standardized contracts.

strategic choices in currency management.

Arguments made for not hedging currency risk include: -It is best to avoid the time and cost of hedging or trading currencies. -In the long-run, unhedged 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. The argument for active management of currency risk is that, in the short run, currency movement can be extreme, and inefficient pricing of currencies can be exploited to add to portfolio return. -Many foreign exchange (FX) trades are dictated by international trade transactions or central bank policies. These are not motivated by consideration of fair value and may drive currency prices away from their fair value.

Economic Fundamentals

Assumes that, in the long term, currency value will converge to fair value. Increases in the value of a currency are associated with currencies: -That are more undervalued relative to their fundamental value. -That have the greatest rate of increase in their fundamental value. *-With higher real or nominal interest rates. -With lower inflation relative to other countries. Of countries with decreasing risk premiums.

*****#Fixed Income Portfolio Formula Exposure

BPVHR = {[BPV(Target)-BPV(Portfolio)]/ BPV(CTD)} then *CF BPV(Portfolio) = MD(Portfolio)*.0001*Portfolio(Market Value) BPV(CTD) = MD(CTD)*.0001*MV(CTD) MV(CTD)=Market Value CTD =contract size * (CTD bond price/100) CF=Conversion Factor (16.5 reading)

Variance swaps

Based on variance rather than volatility (standard deviation). Variance is σ2. These products are termed swaps as they have two counterparties, one making a fixed payment and the other making a variable payment The value of the swap is zero at initiation because implied volatility is the best ex ante estimate of realized volatility. Realized volatility>strike then Buyer (long) of swap makes a profit Realized volatility<strike then Buyer (long) of swap makes a loss *-If long Variance swap then return = Realized variance - Variance strike *The value of the swap is zero at initiation because implied volatility is the best ex ante estimate of realized volatility. *The value of a variance swap becomes less dependent on implied volatility and more dependent on realized volatility as time passes *The payoff of variance swaps is convex in relation to volatility due to the nonlinear (squared) nature of variance in relation to volatility.

Basis

Basis is change in futures versus change in spot price

Hedging Interest Rate Risk Using Treasury Futures

Basis point value (BPV) is the expected change in value of a security or portfolio given a one basis point (0.01%) change in yield. The starting point when hedging interest rate risk with Treasury futures is to identify the futures contract CTD security

Using Interest Rate Swaps to Alter Portfolio Duration

Because a fixed-rate note has a greater modified duration than an otherwise identical FRN, a payer swap has a negative duration (increasing in value when interest rates increase) and a receiver swap has a positive duration (decreasing in value when interest rates increase). Adding payer swap to a fixed-income portfolio will reduce portfolio duration, while adding a receiver swap to a fixed-income portfolio will increase portfolio duration.

**Collar

Buy stock Buy put sell call call can be higher than stock and put can be low. example: stock $30 sell $31 call and buy $29 put

To synthetically create the risk/return profile of an underlying common equity security:

Buy the corresponding futures contract and invest in a T-bill.

If short a stock

Buying a call (probably above the current stock price) would provide a hedge against the stock rising The sale of a put (probably below the current stock price) sells off (part of) the benefit of the stock falling

*Example

Calculate the notional principal of the swap [MD(target)-MD(portfolio)] / MDswap all times market value.

put-call parity relationship

Call premium (paid initially) − put premium (received initially) = initial stock price paid − PV(X) received assumes no yield

The Greeks

Delta (Δ) = change in option price per +1 change in stock price. Delta is positive for (long) calls and negative for (long) puts. Gamma (Γ) = change in option delta per +1 change in stock price. Gamma is positive for (long) calls and for (long) puts. Theta (θ) = daily change in option price (effect of time passing). Theta is negative for (long) calls and (long) puts. Vega (ν) = change in option price per +1% change in volatility. Vega is positive for (long) calls and for (long) puts.

Managing Emerging Market Currency

Emerging market currencies return distributions are non-normal with higher probabilities of extreme events and negative skew of returns. Many trading strategies and risk measures assume a normal distribution and are, therefore, flawed. *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. -Rather have currency now than later *The relatively high interest rates of emerging market economies leads to an inverted pricing curve with forward prices of the emerging market currencies below their spot prices. This raises hedging cost for sellers of the currency, not buyers; sellers receive negative roll yield while buyers receive positive roll yield. EM currencies do have relatively high bid/asked spreads which increase in periods of crisis. Contagion and tail risk refer to infrequent events. Contagion refers to all EM currencies tending to decline together in periods of crisis, and tail risk to the downside in those periods of crisis being large in relation to typical upside movement in the currencies.

Equity Futures

Equity futures are exchange traded, standardized, require margin, have low transaction costs, and are available on indexes and single stocks. They enable market participants to do the following: -Implement tactical allocation decisions (alter the exposure to equity of a portfolio). -Selling futures (short position) reduces equity exposure. -Buying futures (long position) increases equity exposure. -Achieve portfolio diversification. -Gain exposure to international markets. -Make directional bets on the direction of the market.

Equity Swaps

Equity swaps can be used to create a synthetic exposure to physical stocks, allowing market participants to increase or decrease their exposure to equity returns. Equity swaps enable users to achieve the economic benefits of share ownership without the cost and expense of ownership. The three main types of swaps include the following: -Pay fixed, receive equity return. -Pay floating, receive equity return. -Pay another equity return, receive equity return.

European-style options may only be exercised at the point of expiration, while American-style options may be exercised on any trading day up to and including the point of expiration.

Generalized At-Expiration Formulas for Spreads

For debit spreads (bull call and bear put): Maximum loss = net premium Maximum profit = difference between strikes - net premium For credit spreads (bear call and bull put): Maximum loss = net premium Maximum profit = difference between strikes - net premium For Bull spreads, breakeven = lower strike + net premium For Bear spreads, breakeven = higher strike - net premium

Cross-Currency Basis

For the three decades leading up to the great financial crisis in 2008/2009, the covered interest rate parity (CIRP) relationship held quite well. When CIRP holds, borrowing directly in USD should have the same cost as borrowing in a foreign currency and hedging exchange rate risk with a currency swap. Since the financial crisis, USD lending via swaps has attracted a premium.

The hedge ratio for futures can be calculated as:

Hedge Ratio = amount of currency to be exchanged / futures contract size

Strategic Cost Issues:

Hedging is not free and benefits must be weighted versus costs. The bid/asked transaction cost on a single currency trade is generally small, but repeated transaction costs add up. Full hedging and frequent rebalancing can be costly. Hedging every currency movement is costly and managers generally chose partial hedges.

**Bear Put Spread

Here we sell a lower strike put and buy a higher strike put. -Assume a bear spread is puts unless stated to use calls.

Higher volatility means higher option premiums (both for calls and puts). Less time to expiry means lower option premiums (both for calls and puts).

Cash Equitization

Holding cash balances will increase the risk that the portfolios will underperform the benchmark. *-Cash equitization refers to purchasing index futures to replicate the returns that would have been earned by investing the cash in an index with risk and return characteristics similar to those of the portfolio. -The major advantages of futures, in this application, are their liquidity and low transaction costs relative to direct investment in the equity markets. Cash equitization is also known as cash securitization or cash overlay.

If hedging both the foreign currency exposure and market risk then return = domestic risk-free rate If hedge a foreign position by shorting it then return = foreign risk-free rate

Mechanics of Fixed-Income Futures

In practice, the majority of bond futures are closed out prior to settlement (the delivery date) by entering an offsetting trade. For futures held until settlement, bond futures include delivery options for the short party. For example, with U.S. Treasury bond futures, the short party may deliver any U.S. Treasury bond with a maturity between 15 and 25 years at contract maturity. This practice ensures availability of government bonds for the short to deliver. Each eligible bond that can be delivered by the short party is assigned a conversion factor (CF) to reflect its value relative to the notional bond in the contract.

In the case of a call option, the short has undertaken to deliver the underlying if the buyer chooses to exercise (receiving the strike price in exchange). In the case of a put option, the short has undertaken to take delivery of the underlying if the buyer chooses to exercise (paying the strike price).

Index futures have a multiplier. The actual futures price is the quoted futures price (in points) × the multiplier. For S&P 500 Index futures, the multiplier is $250; for FTSE 100 Index futures, the multiplier is £10.

Bear Call and Bull Put Spreads

It is also possible, of course, to use calls to create a bear spread, or puts to create a bull spread. In both cases there would be a net inflow of premium (since the relatively more valuable option is sold) and they are referred to as credit spreads.

Tips

It is easier to work with FX quotes when the foreign currency is the base currency. If quotes are given as B/P, take the reciprocal to make it P/B. Assume any statements or directions refer to the base currency

Fixed-Income Futures

Liquidity of interest rate futures decreases for forward rates further in the future. Longer-maturity bonds are most often hedged with fixed-income futures (bond futures), which have very good liquidity.

Contango

Longer-dated futures contracts have higher prices than short-dated futures contracts.

Module 15.10: Theta and Vega

Module 15.11: Volatility Skew and Smile

Module 15.12: Applications

Module 15.1: Options Basics—Value at Expiration and Profit at Expiration

Module 15.2: Synthetic Positions Using Options

Module 15.3: Covered Calls

Module 15.4: Protective Puts

Module 15.5: Options as a Hedge of a Short Position

Module 15.6: Collars

Module 15.7: Straddles

Module 15.8: Spreads

Module 15.9: Delta and Gamma

Module 16.1: Managing Interest Rate Risk—Interest Rate Swaps, Forward Rate Agreement, and Interest Rate Futures (MAYBE REDO WAS HARD)

Module 16.1: Managing Interest Rate Risk—Interest Rate Swaps, Forward Rate Agreement, and Interest Rate Futures. (Slide 354 - 2:00)

Module 16.2: Managing Currency Exposure (maybe redo)

Module 16.2: Managing Currency Exposure

Module 16.3: Managing Equity Risk

Module 16.4: Derivatives on Volatility

Module 16.5: Uses of Derivatives in Portfolio Management

Module 17.1: Managing Currency Exposure

Module 17.2: Active Strategies: Fundamentals and Technical Analysis

Module 17.3: Active Strategies: Carry and Volatility Trading

Module 17.4: Implementation and Forwards

Module 17.5: Implementation and Options

Module 17.6: More Advanced Implementation Issues

Number of Futures Contracts needed

Monetary value of position to be hedge / Futures price * Multiplier

currency swap

One party agrees to make periodic interest rate payments on a notional amount in one currency, while the other party agrees to make period interest payments on a notional amount in another currency

**Payoff to variance buyer

Payoff to variance buyer = variance notional × (realized variance - variance strike) -Note realized variance is simply the time-weighted average of realized variance to date and implied variance over the remaining life of the contract. Example= 263 × (21^2 - 19^2) = $21,040

At the delivery date, the bond that is cheapest-to-deliver (CTD) will generate the greatest gain or lowest loss on settlement.

Profit/(loss) on delivery = [(Settlement price × CF)+ AIT] − (CTD clean price + AIT)

Equity Forwards

Provide many of the same advantages but lack liquidity and are not subject to mark-to-market margin adjustments. Because there is no clearinghouse, the credit quality of the counterparties is a concern. The major advantage of forward contracts is they can be customized.

**Seagull spread

Put spread combined with selling a call (ex. buy 35-delta put, sell a 25-delta put and sell a 35-delta call). Same downside protection as Put Spread but lower cost and less upside potential. A 40-delta strangle is more in-the-money than the 10-delta strangle and would therefore, be more expensive with a better payoff structure.

Variance

Realized variance is calculated by taking the natural log of the daily price relatives, the closing price on day t, divided by the closing price on day t − 1: Ri = ln(Pt / Pt-1) Ri/SQRT(N) If we have N days of traded prices, we can compute N − 1 price relatives (R): annualized variance = daily variance × 252; 252 = assumed trading days in a year This has the advantage of making the variances perfectly additive (i.e., one-year variance can be split into two equal six-month periods). profit/(loss) = NVAR × (σ2 − K2) where: σ = realized volatility K = strike volatility (implied volatility)

**cross hedge

Refers to hedging with an instrument that is not perfectly correlated with the exposure being hedged. Hedging the risk of a diversified U.S. equity portfolio with S&P futures contracts is a cross hedge when the portfolio is not identical to the S&P index portfolio.

Short-Term Interest Rate (STIR) Futures

STIR futures are conceptually very similar to FRAs. The futures price is forward interest rate on deposits starting at the expiry of the future and lasting for 30 days. The pricing convention means that futures prices will rise when forward rates fall. The forward interest rate is calculated from current spot LIBOR rates in the same way the forward price of an FRA is established.

*synthetic long put position

Sell short stock + buy call

*Synthetic stock portfolio

T-Bills + stock index futures

Technical Analysis

Technical analysis of currency is based on three principals: -Past price data can predict future price movement and because those prices reflect fundamental and other relevant information, there is no need to analyze such information. -Fallible human beings react to similar events in similar ways and therefore past price patterns tend to repeat. -It is unnecessary to know what the currency should be worth (based on fundamental value); it is only necessary to know where it will trade. At both support and resistance levels, the price becomes "sticky." However, if the market moves through the sticky resistance levels, it can then accelerate and continue in the same direction.

*Forward Rate Agreements (FRAs)

The key point is that long FRA positions will increase in value when future interest rates rise. (pay fixed receive floating) short positions will increase in value when interest rates fall.

Delta

The more ITM is an option, the higher is its (absolute) delta (closer to 1). The more OTM is an option, the lower is its (absolute) delta (closer to 0). The delta of a long position in one unit of the underlying is +1. *Delta is positive for (long) calls and negative for (long) puts. **Straddles and strangles are delta-neutral strategies since the underlying calls and puts have equal but opposite deltas.

The value of an option can be decomposed into its intrinsic value and its time value, the total premium being the sum of these two. *-Intrinsic value is the value of immediate exercise. It reflects the degree to which the option is in the money (ITM). -Time value is the additional value reflective of what might happen between now and the point of expiration (i.e. over the option's remaining life).

Forward Points

There is a myth that the forward points are always divided by 10,000. That is only true if the spot quote is given to four decimal places. To continue the pattern, if the spot quote shows five decimals on the right, move the forward point decimal five places to the left (i.e., forward points / 100,000) .

There is a term structure of volatility, where implied volatilities differ across option maturities (contango is quite common, with longer-dated options having higher implied volatilities). An implied volatility surface uses a three-dimensional graph, with implied volatility on the z-axis, to examine the joint influence of maturity (x-axis) and strike price (y-axis).

Theta

Theta measures how quickly an option loses value as time passes. *All negatives Options that are close to ATM have the highest thetas (in absolute terms), and these increase as expiration approaches (all other factors being held constant)

Base Vs Pricing Currency

Think of a currency quote as a base currency in the denominator and a pricing currency in the numerator The base currency is the denominator of the exchange rate and it is priced in terms of the numerator sell spot 1,000,000 at CAD/USD 0.9800 is assumed to mean sell for "immediate delivery" 1,000,000 U.S. dollars and buy 980,000 Canadian dollars.

Federal funds rate

This is the interest rate that deposit institutions (banks and credit unions) charge other deposit institutions for loans in the overnight interbank markets. The federal funds effective (FFE) rate is the weighted average of interest rates charged on overnight interbank loans. Note that the Fed does not directly control the FFE rate, but it influences the rate through its monetary policy tools with the goal of keeping it within the target range.

Federal funds target rate

This is the rate set by governors of the Federal Reserve in Federal Open Market Committee (FOMC) meetings. The FOMC meets eight times a year to set the target rate based on current and forecasted macroeconomic variables. The most important considerations when setting the target rate are inflation rates and GDP growth rates. When market participants refer to the central bank (Fed) changing interest rates, it is typically this target rate they are referring to. The target rate is typically set as a range (e.g., 2.25%-2.50%).

Josh Young Bid Ask

Up the Bid and multiply Down the Ask and Divide **Sell bid Buy ask

Vega

Vega measures the effect of a 1% increase in volatility on the value of the option *Vegas are always positive: a more volatile underlying makes all the options on it more valuable All other factors constant, vega is higher the more time there is to expiry, but it diminishes the further ITM or OTM the option is.

**Currency Management Hints

Work with Foreign currency as the base Assume question is referring to base currency Be explicit in answer and make sure you are stating which currency you are referring to. Buying futures, forwards, or calls on base currency increase exposure on base currency. A call on the foreign currency is a put on the domestic currency. Currency forwards preferred over futures because customizable, available in any currency, more liquid Domestic currency or home currency is the currency of the investor (or the currency in which portfolio results are reported and analyzed). Domestic asset is an asset denominated in the investor's domestic currency. Foreign currency and foreign asset are a currency other that the investor's domestic currency and an asset denominated in that foreign currency. These are sometimes called the local currency and local market, respectively. Foreign-currency return (RFC) is the return of the foreign asset measured in its local (foreign) currency. It can be called the local market return. The percentage change in value of the foreign currency is denoted as RFX. It can be called the local currency return. Domestic-currency return (RDC) is the return in domestic currency units considering both the foreign-currency return (RFC) and the percentage change in value of the foreign currency (RFX).

macro hedge

a type of cross hedge that addresses portfolio-wide risk factors rather than the risk of individual portfolio assets.

**Covered Call

buy stock, sell call

*To create a synthetic cash position:

buy the common equity and sell short the corresponding futures contract.

VIX Options

cash-settled European-style options. VIX options can only be exercised at contract maturity

*Sell Forward

if want to hedge a Euro portfolio then SELL Euros forward and BUY USD. You would then earn the US rfr and pay the Euro rfr

VIX

implied volatility As a rule of thumb, a value lower than 20 represents a low-risk environment and values above 30 represent a high-risk environment *empirical studies have shown a negative correlation between the VIX and stock returns *VIX is a measure of expected volatility of the S&P 500 Index over the forthcoming 30 days. *The VIX Index level is the annualized standard deviation of implied volatility on the S&P 500. *-so if VIX 40 then 68% that the S&P 500 will stay within a range of +/− 40% over one year. When levels of the VIX Index are low, it is common for the futures market to be in contango. *The strategy of buying the second-month future and selling the VIX spot is unfeasible as the VIX spot cannot be directly invested in.

short straddle

involves selling, instead of buying, and is a neutrality play. It makes more profit the closer to the strike the underlying ends up, with no limit on potential loss.

**Protective Put

long stock and long put Maximum loss at expiry = S0 - X + p0 Breakeven stock price at expiry = S0 + p0 Maximum profit = unlimited

*dynamic hedges

require periodic rebalancing -more risk averse

cheapest-to-deliver (CTD) bond

the cheapest security that can be delivered in a futures contract to a long position to satisfy the contract specifications.

**Bull spreads

use long options on the lower strike (Bull = Buy Low) and short options on the higher strike. In general, for a bull call spread: Maximum loss = net premium paid Breakeven = lower strike + net premium paid Maximum profit = difference between strikes - net premium paid

Bear spreads

use short options on the lower strike and long options on the higher strike. Bear spreads are just short bull spreads, in fact.

**strangle

will provide similar but more moderate payoffs to a straddle. Out of-the-money calls and puts with the same absolute delta are purchased. The out-of-the-money options require larger movement in the currency value to create intrinsic value but will cost less. Both the initial cost and the likely profit are lower than for the straddle.

3XChapter 15-17 Derivatives and Currency Management

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