Question

The table below gives today’s prices of one-year European call options written on a share of stock XYZ at different strike prices. Strike Price ($) Call Price ($) 50 11 60 5 70 1 In each of the following strategies, derive a table showing the relationship between profit and stock price at maturity as well as the range of stock prices at maturity for which the strategy is profitable. Explain your calculations.
a) A bear spread with strike prices of $50 and $60. b) A portfolio where you buy one $50 call and sell two $60 calls. c) A portfolio where you buy one share of stock for $60 and sell one $70 call.

Answer 1

Strike Price	Call Price
$               50	$          11
$               60	$             5
$               70	$             1

B) A PORTFOLIO WHERE YOU BUY ONE $50 CALL AND SELL TWO $60 CALLS

	Strike Price	Price
Purchase of Call Option	$               50	$          11
Sale of Two Call Option	$               60	$        (10)
Net Investment in Portfolio		$             1

Maximum Loss that can be incurred on Purchase of Call Option is $11.

Maximum Profit that can be earned on Sale of Call Option is $10.

Stock price at which the Position of Trader remains unchanged:

Situation 1: Stock Price Rises

Profit on Purchase of Call Option	Stock Price at Maturity (x) - $50 - $11
Loss on Sale of Call Option	(Stock Price at Maturity (x) - $60 - $5) X2
Stock Price on Maturity	$                                                                              69

Situation 2: Stock Price Falls

Loss on Purchase of Call Option	($50 - Stock Price at Maturity (x) + $11
Profit on Sale of Call Option	$                                                                              10
Stock Price on Maturity	$                                                                              51

THEREFORE BETWEEN THE PRICE RANGE OF $ 52 - $ 68 THE TRADER WILL EARN A PROFIT.

(c) A PORTFOLIO WHERE YOU BUY ONE SHARE OF STOCK FOR $60 AND SELL ONE $70 CALL.

Purchase of Stock	$          60
Sale of Call Option	$          (1)
Net Investment in Portfolio	$          59

For Call Option:

This shows that call option will not incur a loss upto the Stock price level of $71 because the Payoff of difference in Stock Price rise above Strike Price Level will be compensated by Premium Received on Sale of Call Option.

The Maximum Profit that can be earned on Call Option is $1 whereas the maximum loss on call option can be (St - $70 - $1)

For Stock:

The maximum loss that can be incurred on stock will be ($60 - St )
The maximum profit that be earned on stock will be (St - $60)

Situation 1: Stock Price Falls on Maturity

Let's suppose stock price at maturity to be x.

Loss on Stock	$60 - Stock Price at Maturity (x)
Profit on Call Option	$1
Stock Price at Maturity (x)	$59

With every $1 fall in Price of Stock, loss rises by $1 below Price of $59.

Stock Price at Maturity	Profit on Stock	Profit on Call Option	Total profit
$                                                 59	$                                                                 (1)	$                                        1	$                   -
$                                                 58	$                                                                 (2)	$                                        1	$                  (1)
$                                                 57	$                                                                 (3)	$                                        1	$                  (2)
$                                                 56	$                                                                 (4)	$                                        1	$                  (3)
$                                                 55	$                                                                 (5)	$                                        1	$                  (4)

Situation 2: Stock Price Rises on Maturity:

If stock price rises on Maturity the maximum profit that can be earned by this strategy can be only $11.

Stock Price at Maturity	Profit on Stock	Profit on Call Option	Total profit
$                                                 60	$                                                                  -	$                                        1	$                 1
$                                                 61	$                                                                   1	$                                        1	$                 2
$                                                 62	$                                                                   2	$                                        1	$                 3
$                                                 63	$                                                                   3	$                                        1	$                 4
$                                                 64	$                                                                   4	$                                        1	$                 5
$                                                 65	$                                                                   5	$                                        1	$                 6
$                                                 66	$                                                                   6	$                                        1	$                 7
$                                                 67	$                                                                   7	$                                        1	$                 8
$                                                 68	$                                                                   8	$                                        1	$                 9
$                                                 69	$                                                                   9	$                                        1	$              10
$                                                 70	$                                                                 10	$                                        1	$              11
$                                                 71	$                                                                 11	$                                      -	$              11

Beyond price of $ 72, with every $1 increase in Price of stock, the loss on Call option will also increase by $1, therefore the overall profit wil always remain at level of $11.

THEREFORE THE RANGE OF STOCK PRICES IS $59 - $71.