CFA - Derivatives

Long call option means that

right to buy back the underlying

a call option is ITM if

underlying > strike

Long put option means

right to sell the underlying

a put option is ITM if

underlying < strike

Higher volatility means option value is

higher

Shorter time to maturity means option value is

lower

What is a synthetic long forward position?

long call with a short put on the same underlying

What does a synthetic long forward position mimic the returns of?

buying a stock with money borrowed at the strike price of the put

A covered call is

long the stock and short the call

Describe the max return, max loss, and breakeven of a covered call (and where the stock price will have to be for these to occur)

max return when stock price > strike price = strike price + call premium, max loss when stock price below initial price = stock price - call premium, breakeven stock price = stock price - call premium

when would an investors want to write a covered call?

earn extra income and don’t expect large price appreciation, reducing position at a favorable price, realize a target price and happy to giveup the upside

In put call parity equation, long the stock also means

call - put + strike

In put call parity equation, short the stock also means

put - call - strike price

In put call parity equation, the strike price PV can also be thought of as

borrow/lend money at risk-free rate

What is a protective put

long the underlying and long a put

Purpose of protective puts

protects against a fall in stock price

Max profit, max loss, and breakeven stock price of a protective put (and where the stock price will have to be for these to occur)

max profit stock price higher than initial = unlimited, max loss stock price fall below strike price = stock price - strike price + put premium, breakeven stock price = stock price + put premium

What is a long collar

long the underlying, buy put, sell call

what is a zero-cost collar

long the underlying, buy put and sell call so the put and call premiums are the same

What is the maximum profit, loss, and breakeven of a long collar?(and where the stock price will have to be for these to occur)

max profit when stock price > call strike price= call strike price - initial stock price, max loss when stock price < put strike price = initial stock price - put strike price, breakeven = initial stock price

What is a long straddle

purchase the same number of calls and puts on the same underlying at the same strike price for the same expiry date

Describe the maximum profit, loss, and breakeven price of a long straddle (and where the stock price will have to be for these to occur)

max profit stock price much higher or lower than initial = unlimited for long call, long put is strike price - cost options, max loss if price don’t move = sum of call and put premiums, breakeven is either current price + call and put premium or current price - call and put premiums

What is a short straddle

sell calls and puts on same underlying, same strike, same expiry date

describe the max profit, loss, and breakeven of a short straddle (and where the stock price will have to be for these to occur)

max profit if prices don’t move = put + call premium, max loss prices well above/below initial = unlimited for short call (price - strike price - call premium), and stike price - put premium for short puts, breakeven is still current price plus or minus call and put premium

What is a bull call spread?

Long call at lower strike price, sell call at higher strike price

Describe the maximum profit, loss, and breakeven of a bull call spread (and where the stock price will have to be for these to occur)

max profit when stock price > higher strike price= difference between the strikes - net premium paid, max loss when stock price below lower strike price = net premium paid, breakeven = lower strike + net premium paid

Out of the four bull/bear spreads, which two are debt spreads?

Bull call spread, Bear put spread

Out of the four bull/bear spreads, which two are credit spreads?

bear call spread and bull put spread

What does it mean to be a debit/credit spread?

Net outflow/inflow of premiums

What is a bear put spread?

Sell a lower strike put and buy a higher strike put

Describe the maximum profit, loss, and breakeven of a bear put spread (and where the stock price will have to be for these to occur)

Max profit when price is lower than the lower strike = difference between strikes - net premiums paid, max loss when price higher than higher strike = net premiums paid, breakeven = higher strike - net premiums paid

What is a bear call spread?

Short call on lower strike and long call at higher strike

Describe the maximum profit, loss, and breakeven of a bear call spread (and where the stock price will have to be for these to occur)

max profit when price lower than lower strike = net premiums received, max loss when price higher than higher strike = difference between strike - net premiums received, breakeven = lower strike + net premium received

What is a bull put spread?

Short put on higher strike, long put on lower strike

Describe the maximum profit, loss, and breakeven of a bull put spread (and where the stock price will have to be for these to occur)

max profit when stock price higher than higher strike = net premiums received, max loss when stock price lower than lower strike = difference between strikes - net premium paid, breakeven = higher strike - net premium received

Delta measures

change in option price per one unit change in stock price

delta for calls is ___, for puts is ___

positive, negative

Gamma is

change in options delta per one unit change in stock price

gamma is __ for calls and _for puts

positive, positive

Theta is

daily change in options price (effect of tim epassing)

Theta is __for calls and _for puts

negative if long, positive is short

Vega is

change in option price per % change in volatility

the more ITM an option is, the closer absolute detla is to _

1

The more OTM an option is, the closer absolute delta is to__

0

Gamma tends to be higher when an option

is closer to ATM and close to expiration

the delta of a long position in something =

+1 * underlying delta

the delta of a short position in something =

-1 * underlying delta

The delta for long stocks, futures, and forwards are respectivly

1,1,1

The overall delta of a position =

sum of individual deltas

Describe how a protective put modifies the delta of holding a stock

When stock is up, put is OTM, so total delta around 1, but when stock is down, put is ITM with negative delta, total delta less than 1

Describe how a covered call modifies delta of holding a stock

When stock price is down, call option is OTM, total delta 1, when stock price is up, call option ITM, total delta less than 1 (shorting a call means negative delta when call is ITM)

Describe the delta of a collar

When stock price falls, put is deep ITM, delta near 0, when stock price rises, call is deep ITM, since shorting a call, negative delta, so overall delta still near 0

describe the delta of a bull call spread

When price is low, lower price call is deep OTM, higher price call is deep OTM, but since we are shorting the higher call, they even out

Describe what a long calendar spread is

buy longer dated ATM option, sell the shorter dated ATM option, same strike price and same underlining, so the premium on shorter dated option will fall faster than the longer dated option, since you are shorting the short-dated, you gain more than you lost on the long

What is the logic calendar spreads on based on?

Theta of options that are ATM lose value at a higher rate as they mature, and OTM/ITM options lose value fairly consistently

Describe a short calendar spread

sell long dated OTM or ITM option and buy shorter OTM or ITM dated, longer dated lose value more rapidly than short-dated, since you are shorting the long-dated, gain on long offsets lost on short

Vega is diminished if the option is

very ITM or very OTM

Calculating volatility of options

(days left to expiration/trading days in a year)² x implied annualized volatility

Describe the delta and vega of a long straddle

Having a call and put in a straddle is a delta-neutral neutral position. When underlying price is near strike vega is close to zero, when underlying price is far away from strike, vega increases to 1, so higher volatility will increase the price

Describe the delta and vega of a short straddle

Delta neutral, but vega is 0 when both put and call ATM, vega is negative when underlying price far from strike, so lower volatility will increase the price

What is a volatility smile?

With the strike price in the middle, implied volatility is higher when the options are OTM and ITM, lower when they are ATM

What is a volatility skew and why?

Implied volatility is higher for OTM puts and lower for OTM calls, but still follows the “smile” shape. OTM puts are more desirable insurance against market declines, which pushes up the price when markets turn bearish

which is one is more common, volatility skew or smile?

skew

When markets are more bearish, what happens to the shape of the volatility skew?

Skew level increases sharply, implied volatility of OTM puts rises fast

When markets are more bullish, what happens to the shape of the volatility skew?

less skewed with volatility of OTM calls rising sharply

Describe a long risk reversal

Long OTM call and short OTM put, belief is that implied volatility of put is too high compared to calls and markets will turn more bullish

Describe a short risk reversal

short OTM calls and long OTM puts, betting on implied volatility of call is too high compared to puts, and markets will turn bearish

The term structure of volatility refers to

Implied volatilities differ across options' maturities

In practice, when do you want to use a covered call?

client is bearish on the stocks they own, and needs cas

In practice, when do you want to write a put?

When you want to buy shares but think they are too expensive now

In practice, when do you want to long a straddle?

volatility will be high and is not priced-in yet

In practice, when do you want to long a collar?

Can’t sell the stock but want to protect the downside at “no cost”

In practice, when do you want to long a calendar spread?

Believe volatility is low but is bearish or neutral on the longer term outlook

In practice, how do you hedge against an expected increase in volatility?

Buy a call on VIX futures and sell a put on VIX futures

In practice, if you think volatility will decrease and your outlook on asset is (bearish/neutral/bullish), what should you do with options? In order

Short calls, short straddle, short puts

In practice, if you think volatility will be unchanged and your outlook on asset is (bearish/neutral/bullish), what should you do with options? In order

Short calls and buy puts, buy calendar spread, buy calls and short puts

In practice, if you think volatility will be higher and your outlook on asset is (bearish/neutral/bullish), what should you do with options? In order

Buy puts, buy straddle, buy calls

What is a payer swap and what’s the purpose of it and when does it benefit?

Pay fixed, receive floating, converting floating rate liability or fixed rate asset to fixed-rate liability or floating rate asset, benefit when floating rates rise

What is a receiver swap and what’s the purpose of it and when does it benefit?

receive fixed pay floating, converting fixed liability/floating asset to floating liability/fixed asset, benefit when floating rates fall

Calculation of swap settlement amount

Fixed payment = fixed leg unannualized * notional, floating is the same as last period ratee, net out cashflow at each settlement date

A payer swap has __ duration, in other words, a payer swap value increases when rates..

negative, rises

A receiver swap has ___ duration, in other words, a receiver swap value increases when rates..

postive, fall

Finding how much notional of swap to buy to achieve target duration of the portfolio

notional swap amount = [(target modified duration - current portfolio duration)/modified duration of swap] * market value of the portfolio

Long FRA benefits when __

market rate higher than forward rate

Short FRA benefits when__

market rate lower than forward rate

Long FRA means hedging borrowing rates __

going up

Short FRA means hedging borrowing rates __

going down

Calculating how long FRA hedges borrowing cost

Borrowing cost = (market rate + extra premium)*(unannualize)*notional; Long FRA = (actual rate - FRA forward rate)*(unannualize)*notional

Long short term interest rate futures benefits when

rates decrease

Finding total return of hedging an investment at market rate with a future position

Number of future contracts = amount to hedge/notional of futures, futures price at settlement = 100- reference rate at settlement, profit/loss on futures = settlement price - purchase

Futures price =

100- reference rate

If hold a Treasury future to maturity, …

will get a physical delivery from the short side, the bonds that can be delivered will be assigned a CF

If CF < 1, deliverable __than notional, if CF < 1, deliverable—than notional

more valuable, less valuable

Calculations for the profit/loss at delivery of a Treasury futures bond

settlement price * CF + accrued interest - (cheapest to deliver clean price + accrued interest)

Treasury futures price =

CTD future valuee/CF

Duration of Treasury futures is

negative if short, positive if long

Finding how many futures contract to hedge, or hedge ratio

(Change in portfolio value/change in CTD) x CF, or (-BPV (portfolio)/BPV(CTD)) x CF

BPV of portfolio or bond =

modified duration x 0.01% x market valuee