CFA level 3 CFA level 3 CFA level 3 CFA level 3 CFA level 3 finquiz item set answers, study session 15, reading 29

For a call option, the value at expiration is the maximum of zero or the index price less the exercise price: Value = max0, St-x Correct Answer: A The breakeven price of a call option i

Trang 1

FinQuiz.com

CFA Level III Item-set - Solution

Study Session 15

June 2018

Trang 2

Reading 29: Risk Management Applications of Option Strategies

Correct Answer: A

The statement is correct Adding a short call is a covered call strategy, and adding a long put is called

a protective put A covered call limits the upside potential but generates cash up front A protective put retains the upside potential at the expense of requiring the payment of cash up front

Hughes is correct If the price of the bond exceeds the exercise price, the put will expire out of

money The position will be worth only the value of the underlying This is true for all prices of the bond above the exercise price so Reed is incorrect

Correct Answer: B

If Reed adds a long put position to her long bond position, she will be following a protective put strategy The breakeven price for a protective put equals:

S0 + p0

which in this case equals:

104.5 + 11.23 = $115.73

This means the price will have to increase by 10.75% over the life of the option for Reed to

breakeven

In case Reed adds a short call to the long bond position, the strategy would be a covered call The breakeven price will equal:

S0 - c0

In this case it equals: 104.5 – 12.45 = $92.05

Buying the put will result in a protective put A protective put limits the downside but has unlimited

upside potential Even though the option premium reduces the gain, it does not limit the upside

potential Also, a protective put limits the downside risk; the maximum possible loss equals:

S0 + p0-X

= 104.5+11.23-96

=$19.73

Trang 3

Correct Answer: C

In this case, Reed has implemented a protective put The maximum profit for a protective put equals infinity This is because there is no upper limit to price increases, and a protective put strategy gains when the price increases

If the price falls to $93.27, the value of the position will equal:

Value = St + max (0, X- St) = 93.27 + max (0, 96-93.27) = $96

The profit will equal: 96-(104.5+11.23) = -$19.7

In case of a call option held till expiration, for an index value at expiration greater than the exercise

price, both the value and the profit will move up one-for one with the index value (the only difference

is that the profit will be less than the value by the amount of the premium paid)

Statement 2 is correct The point where the profit line crosses the x-axis is the point where the profit

is zero Hence, the index value at that point results in zero profit and is therefore the breakeven price Statement 3 is also correct For a call option, the value at expiration is the maximum of zero or the index price less the exercise price:

Value = max(0, St-x)

The breakeven price of a call option is the exercise price plus the option premium; the value of the underlying at expiration must exceed the exercise price by the amount of the premium to recover the cost of the premium

Breakeven price: 2500+76.05 = 2,576.05

If the price of the underlying is 2650 at expiration, the value will equal:

Value = max (0, St – x) = max (0, 2650 – 2500) = 150

The profit will include the cost of the option:

Profit = value – cost = 150 – 76.05 = 73.95

The maximum profit to the seller of the option equals the premium amount which will be earned by the seller when the option expires out of money The maximum loss for the seller has no upper bound; there are chances of an infinite loss (the price can go up by any amount)

Trang 4

If the price is 2,010, the value and profit equal:

Value = – max(0,2010 – 2500) = 0

Profit = – 0+76.05= 76.05

If the price is 2,550, the value and profit equal:

Value = – max(0,2,550 – 2,500) = – 50

Profit = – 50+76.05 = 26.05

Option spread strategies in which the options differ by time to expiration are called ‘time spread’ strategies There are other strategies in which the two options differ only by exercise price These are known as money spreads

Option spread strategies in which the options differ by time to expiration are usually designed to exploit differences in perceptions of volatility of the underlying (which varies over the length of the

time period)

A bull spread has some similarities to a covered call Both strategies involve positions in a short call, and the short call can be viewed as giving up gains beyond its exercise price Also, in a covered call, the long position in the underlying covers the short position in the call; just as in the bull spread the long position in the call with the lower exercise price covers the short position in the call with the

higher exercise price

If the market is expected to go up (or the price of the underlying is expected to increase), an investor should use bull spreads, which involve selling a call with a high exercise price and buying one with a low exercise price In such strategies, the maximum profit is earned if the price of the underlying increases to at least the exercise price of the written call

Hamilton expects the stock to go down and wants to benefit from this decrease Both a bear call spread and a bear put spread benefit on the downside However, a bear put spread requires a cash outlay at initiation whereas in a bear call spread there is a cash inflow at initiation of the position and

a profit if the calls expire worthless

Trang 5

Statement 1 is incorrect Although a bear put spread and a bear call spread have similar shapes for their graphical depictions, their payoffs and initial investments differ A bear put requires an initial cash outflow whereas a bear call has a cash inflow at initiation of the position Also, the maximum profit for a bear put and a bear call differ as does the maximum loss

Statement 2 is correct

Statement 1 is incorrect It is not necessary for the exercise prices of both puts to be lower than the current price of the underlying for implementing a bear put spread Sometimes one put can be in-the-money and one can be out-of-in-the-money

Statement 2 is incorrect It is rare for both calls to be in the money in a bull call spread Usually both are out of money, but sometimes one can be in the money

If the price of the underlying is $62, the profit equals:

max(0,ST-X1) – max(0,ST-X2) –C1 +C2

max (0,62 – 55) – max(0,62 – 65) – 15+7 = 7 – 0 – 15+7 = – $1

Maximum profit equals:

X2 – X1 – C1 + C2

65 – 55 – 15+7 = $2

Maximum loss equals:

C1 – C2

15 – 7 = $8

The breakeven price equals:

X1 + C1 – C2

= 55+15 – 7 = $63

The maximum profit for a bear put spread occurs when both the puts (the long put and the short put) are in the money The breakeven price falls between the exercise prices of the two puts, so that one is

in the money and the other is out of money

Trang 6

A bear call spread is the exact opposite (inverted image) of a bull call spread The other two options are incorrect The worst outcome for a bear put spread occurs when the underlying’s price is greater than the exercise price of the long put (and the options expire out of money) The maximum a bull

call spread can gain is the difference between the exercise price of the short call and the long call less

the initial cash outlay

If the price of the underlying is $92 at expiration, the value and profit equal:

Value= max (XH-ST) – max (0, XL-ST) = max (0, 105-92) – max (0,95-92) = 13-3 = $10

Profit = VT – V0 = 10 – 17 + 12 = $5

Option A is correct For all prices above $105 (the exercise price of the long put) and below $95(the exercise price of the short put) the profit remains the same (negative in the former case and positive in the latter case) Between the exercise prices, the profit will vary

Breakeven price for a bear put spread equals:

XH – pH+pL

In this case the breakeven price equals:

105 – 17 +12 = $100

The maximum profit will equal:

XH – XL – (pH – pL) = 105 – 95 – 17+12 = $5

pH-pL = 17 – 12 = $5

Statement 1 is correct The maximum profit for both a bull call spread and bear put spread equals the difference between the exercise prices of the options less the initial outlay

Statement 2 is incorrect The breakeven prices for a bull call spread and bear put spread differ In case

of a bull call, the breakeven price is the lower exercise price plus the initial outlay In case of a bear put, the breakeven price is the higher exercise price less the initial outlay

Trang 7

The profit if the bond’s price is $95 will equal:

Max (0,105 – 95) – max(0,95 – 95) – 17+12 = 10 – 0 – 5 = $5

The profit if the bond’s price is $105 will equal:

Max(0,105 –105) – max(0,95 – 105) –17+12 = 0 – 0 – 5= – $5

The breakeven price equals:

XL+cL-cH = 1350 + 18 – 13 = 1355

The market is currently at 1400 This means that the market must go down by:

1355/1400 – 1 = 0.9678 – 1 = – 3.21%

The maximum loss to a bear call spread will equal:

1600 – 1350 - (18 - 13) = 1600 - 1350 - 18 + 13 = $245

Palmer is correct A butterfly spread is a combination of a bull and bear spread Also, in virtually all cases in practice, the exercise prices of the options used to construct a butterfly spread are equally spaced such that:

2X2 – X1 – X3 = 0

Where X2= the exercise price of the sold call options

X1 and X3 = the exercise prices of the long call options

Payne is incorrect with respect to the initial value of a butterfly spread The initial value of the

position is almost always positive This is because the bull spread bought is more expensive than the bull spread sold (because the lower exercise price on the long bull spread is lower than the lower exercise price on the short bull spread) Therefore, there is almost always a cash outflow at initiation Payne is incorrect with respect to the maximum profit The maximum profit occurs when the price of

the underlying is at the exercise price of the sold options (the middle exercise price)

Trang 8

If the price of the underlying is $22, the value will equal:

If X2 ≤ ST < X3

Value = max(0, ST – X1) – 2max(0, ST – X2) + max(0, ST – X3)

Profit = max(0, ST – X1) – 2max(0, ST – X2) + max(0, ST – X3) – c1 + 2c2 – c3

Max(0, 22 – 20) – 2max(0, 22 – 25) + max(0, 22 – 30) = 2 – 0 + 0 = $2

Profit equals:

Profit = 2 – 8 + 2 (5) – 3 = $1

Maximum profit = X2 – X1 – c1 + 2c2 – c3

Maximum profit equals:

25 – 20 – 8 + 2 (5) – 3 = $4

Maximum loss = c1 – 2c2 + c3

8 – 2 (5) + 3 = $1

Ford is correct The strategy is a straddle that benefits from high volatility The short butterfly spread can also be used in such cases but its gains are limited A straddle, however, can be costly to

implement

Value = max (0, ST – X) + max (0, X – ST)

Profit = max (0, ST – X) + max (0, X – ST) – c0 – p0

If the price of the stock is $98, the value and profit will equal:

Value = max(0,98 – 76) + max (0,76 – 98) = 22 + 0 = $22

Profit = 22 – 7.5 – 5.8 = $8.7

Ford is correct regarding the long butterfly spread The long butterfly spread earns its maximum profit if the price of the underlying is precisely at the exercise price of the sold options (the middle

exercise price) However, in case of the strategy mentioned (straddle), the maximum loss occurs if the

underlying ends up at the exercise price of the options

Trang 9

Breakeven = ST* = X ± (c0 + p0)

The breakeven prices equal:

76 ± (7.5+5.8) = 76 ± (13.3) = $89.3, $62.7

Options A and B are incorrect A straddle would be profitable around major events such as earnings announcements (because of a higher chance of the price increasing/decreasing significantly)

However, if the announcement is expected then the uncertainty surrounding it may have already been reflected in options’ prices Also, a straddle is beneficial if the volatility is expected to increase (not decrease)

The maximum profit and maximum loss equal:

Max Profit = ∞ (because of the long call)

Max Loss = 7.5+5.8 = $13.3 (if the options expire out of money the premiums will be lost)

Statement 1 is incorrect Long butterfly spreads (whether they are executed using puts or calls) are used when the expectation is that the market will be less volatile than what everyone else expects Statement 2 is correct When a butterfly spread is executed using puts, the investor is in effect buying

a bear put spread and simultaneously selling a bear put spread

Value = max (0, X1 – ST) – 2max (0, X2 – ST) + max (0, X3 – ST)

Profit = Value – (p1 – 2p2 + p3)

If the price is $67, the value and profit will equal:

Value = max(0,60 – 67) – 2max(0,70 – 67)+max(0,80 – 67)

= 0 – 6+13 = $7

Profit = $7 – 4.75 + 2(5.89) – 7.89 = $6.14

The breakeven prices for the butterfly spread equal:

BP = 60 + 4.75 – 2 (5.89) + 7.89 = $60.86

BP = 2 (70) – 60 – 4.75 + 2 (5.89) – 7.89 = $79.14

From the starting value of $70, this represents a range of ± 13% from the starting value of the stock

Trang 10

If the stock price is $71, the profit will equal:

max (0,60 – 71) – 2max (0,70 – 71) + max (0,80 – 71) – 4.75 + 2 (5.89) – 7.89 = 0 – 0 + 9 – 0.86 =

$8.14

The initial investment is 4.75-2(5.89)+7.89= $0.86

Therefore the return equals 8.14/0.86 = 946.5%

Gibson is correct Both a butterfly spread using puts and butterfly spread using calls are used if the expectation is that the market (or any underlying for that matter) will remain relatively low over the specific time horizon Both would earn their maximum profit if the price of the underlying is at the exercise price of the sold options Also, if the options are priced correctly, it does not really matter whether one uses puts or calls However, if puts were underpriced, it would be better to buy the butterfly spread using puts (and vice versa)

A short butterfly spread (whether executed using calls or puts) is sometimes called a “sandwich spread”

A collar is a combination of a short call and protective put position An investor buys a put to protect the underlying and then sells a call to cover the premium of the long put If the call and put premiums exactly offset each other, the position is referred to as a ‘zero cost collar’ However, there are still costs to the position even though there may be no cash paid up-front The cost takes the form of forgoing upside gains (due to the sale of the call)

Statement 1 is incorrect There is cost associated with a collar in terms of the forgone profit by

capping both losses and gains

Statement 2 is correct The profit is strictly determined by the underlying and moves directly with

the value of the underlying

Statement 3 is also incorrect For a zero cost collar, the breakeven price is simply the original

underlying price, which in this case is $45.5

Định dạng
Số trang	13
Dung lượng	67,1 KB