Unformatted text preview: Session 13: Payoff & Profit/Loss Diagrams A.
i) No. of
units NAB share
NAB Jul $29.00 call bought (1)/ Bid/Ask
Exercise
Type of
sold (1)
price
price
option
1
1
30.03
1
1
0.12
31 C Initial
payoff
30.03
0.12 Total initial payoff 29.91 ii) S*
Payoff of share
Payoff of option
Final payoff of covered call
P/L of covered call
P/L in share
P/L in option 29
29
0 29.5
29.5
0 30
30
0 30.5
30.5
0 29 29.5
30
0.91 0.41 0.09
1.03 0.53 0.03
0.12 0.12 0.12 30.5
0.59
0.47
0.12 31
31
0 31.5
31.5
0.5 32
32
1 32.5
32.5
1.5 33
33
2 31
31
31
31
31
1.09 1.09 1.09 1.09 1.09
0.97 1.47 1.97 2.47 2.97
0.12 0.38 0.88 1.38 1.88 iii) The payoff diagram
The Payoff Diagram for a Covered Call
35 30 25
Payoff of share Payoff $ 20 Payoff of option
Final payoff of covered call 15 10 5 0
29 29.5 30 30.5 31 31.5 32 32.5 33 5
range of stock prices on expiration date iv) The P/L diagram 1 The Profit/Loss Diagram for a Covered Call
P/L in share
P/L in option
4 P/L of covered call 3 profit/loss $ 2
1
0
29 29.5 30 30.5 31 31.5 32 32.5 33 1
2
3
range of stock price S* v) The call option is currently out of the money since the current stock price of $30.03 is less
than the option exercise price of $31.
vi) final payoff = S* – max{0, S*  X} = 30.03 – max(0, 30.0331) = $30.03
P/L = S* – max{0, S*  X} – (S0 – C0) = 30.03 – 29.91 = $0.12.
vii) When investors anticipate that there is little change in the price of the stock, they may
form a covered call to earn the premium (the time value to be exact) and result in an
overall positive return despite a zero return on the stock.
viii) To solve for S* when P/L = S* – max{0, S*  X} – (S0 – C0) = 0, S* must be less than X
so that
S* –0 – (S0 – C0) = 0
⇒ S* = (S0 – C0) = 30.03 – 0.12 = $29.91.
Otherwise, S* cancel out in the equation.
ix) If the call I wrote is exercised, I must deliver the share in exchange for the exercise price.
When S* >> X, the call is in the money:
final payoff = S* – max{0, S*  X} = X = $31, and
P/L = S* – max{0, S*  X} – (S0 – C0) = X – (S0 – C0) = 31 – (30.03 – 0.12) = $1.09
B.
i) Initial payoff = PL + 2×PM  PH = 0.105 + 2×0.23  0.37 = $0.015
ii) Final payoff = max{0, XL – S*} + 2× max{0, XM – S*}  max{0, XH – S*}
= max{0, 29 – 24} + 2× max{0, 29.5 – 24}  max{0, 30 – 24}
= 5 + 11  6 = $0
P/L
= final payoff – initial payoff
= 0 – 0.015 = $0.015
2 iii) Final payoff = max{0, XL – S*} + 2× max{0, XM – S*}  max{0, XH – S*}
= max{0, 29 – 35} + 2× max{0, 29.5 – 35}  max{0, 30 – 35}
= 0 + 0  0 = $0
P/L
= final payoff – initial payoff
= 0 – 0.015 = $0.015
iv) To solve for S* when
P/L = max{0, XL – S*} + 2× max{0, XM – S*}  max{0, XH – S*} – 0.015 = 0
Note that S* cannot be less than XL nor greater than XH, otherwise, S* cancel out in the
equation.
The first breakeven point occurs when XL < S* < XM so that
P/L = 0 + 2× max{0, XM – S*}  max{0, XH – S*} + 0.015 = 0
⇒ S* = 2XM – XH + 0.015 = 29.015
The second breakeven point occurs when XM < S* < XH so that
P/L = 0 + 2×0  max{0, XH – S*} + 0.015 = 0
⇒ S* = XH – 0.015 = 29.985
C. If traders believe that (i) the stock price is to fall or (ii) the quoted price of the call
is above its model price, they may write naked calls hoping that the call will fall in
value at which time they will buy the same call to close off the position and earn a
profit. Obviously, they have to take into account of transaction costs and the
possibility that their belief may turn out to be wrong.
D.
i) Payoff & P/L table on expiry date
S* 25 26 27 28 29 30 31 32 33 34 35 Payoff of share 25 26 27 28 29 30 31 32 33 34 35 4 3 2 1 0 0 0 0 0 0 0 Payoff of put
Payoff of call
Final payoff of collar
P/L of collar 0 0 0 0 0 0 0 1 2 3 4 29 29 29 29 29 30 31 31 31 31 31 1.045 1.045 1.045 1.045 1.045 0.045 0.955 0.955 0.955 0.955 0.955 P/L in share 5.03 P/L in put 3.865 2.865 1.865 0.865 0.135 0.135 0.135 0.135 0.135 0.135 0.135 P/L in call 0.12 4.03
0.12 3.03
0.12 2.03
0.12 1.03
0.12 0.03
0.12 0.97
0.12 1.97
0.88 2.97
1.88 3.97
2.88 4.97
3.88 ii) Payoff & P/L diagram on expiry date 3 The Payoff and P/L Diagram for a Collar
35 30 25 Payoff / P/L 20
Payoff
P/L 15 10 5 0
25 26 27 28 29 30 31 32 33 34 35 5
range of stock prices on expiration date iii) There is little chance of seeing stock prices rising above $31 as a call is sold to
give up the profit potential beyond that price. On the other hand, the user
believes that there is room for the price to fall below $29 as a put is purchased
to floor the potential loss (see the P/L) or the value (see the payoff) of his stock
investment.
iv) The put option protects the downside risk of the stock investment. As soon as
S* falls below $29, the put becomes in the money and offsets the loss in the
stock.
v) The call reduces the cost of insurance (or downside risk protection) associated
with the purchase of the put. As long as S* does not rise beyond $31, the user
keeps the premium of the call. 4 ...
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This note was uploaded on 10/29/2010 for the course FINS 2624 taught by Professor Hneryyip during the Three '10 term at University of New South Wales.
 Three '10
 HneryYip

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