Last tutor sucked and answered it in one line. gave him negative rating. 6. A ce
ID: 2710574 • Letter: L
Question
Last tutor sucked and answered it in one line. gave him negative rating.
6. A certain common stock currently sells for $50. A call option on that stock with X = $50 and an expiration in one year costs $6.41. A put option on that stock, also with X = $50 and a one-year expiration costs $5.42. Explain how the payoff of buying 1 share of stock is very similar to the payoff of simultaneously buying one call and selling one put. Buying one share of stock requires $50, but buying one call and selling one put requires just $0.99. If the payoffs of these two investment strategies are very similar, but their costs are very different, is it always better to use the “buy a call, sell a put” strategy rather than just buying the stock? Why or why not?
Explanation / Answer
Current Price of common stock = $ 50
Cost of Call Option with strike price $50 = $ 6.41
Cost of Put Option with strike price $50 = $ 5.42
Call option provide the buyer an option to buy the stock one year from now at $ 50. The option will be exercised only if the stock price in the market will be more than $50. If the market price is say $ 60 on the date of expiry, then the option holder will exercise the option and sell the share in the market.
Profit = $60-$50 - $6.41 = $ 3.59
In case the market price is $50 on the date of expiry then the option holder allows the option to expire and incurs a cost of $6.41 paid for the purchase of the option.
So the pay-offs for a call option of $50 with a price of $6.41 would be -$6.41 at the spot price less than $ 50 and turns positive after $56.41 onwards.
Similarly a Put option gives the buyer an option to sell the stock one year from now at $50 and costs $5.42. That is the option holder will exercise the option only if the spot price of the stock one year from now is less than $50-$5.42 (price of the option) = $44.58.
Profit from put option if spot price is $ 44.58 = $50 - $ 44.58 - $5.42 = 0
That is the option holder can buy the stock in the market at current spot price of $ 44.58 and sell to the option seller at $50.
In case the price is above this he will allow the option to expire.
So the pay-offs of a put option are -$5.42 and will turn positive after the stock price is less than $ 44.58.
If one buys a call option and sells put option at a strike price $ 50, the investor is turning both a buyer and a seller at the same time. He receives an amount of $5.42 from the buyer of put option and pays $6.41 to seller of call option.
Net cost = +5.42 – 6.41 = -$ 0.99
If the investor does not the stock and involves in the above strategy, then the pay offs if the spot price on expiry is is $ 60 is as follows
Call option - Buys the security from the call option seller and sells the security in the stock market
Put Option - Option buyer would allow the option to expire
Profit from the operation would be = $ 60 - $ 50 + $5.42 - $ 6.41 = $ 9.01
If the investor does not own the stock involves in the above strategy, the pay off if spot price on expiry is $40
Call Option – Allows the option to expire
Put Option – Buy at $ 50 from Put Option Buyer and sells in the market at spot rate of $40
Loss from the operation = $40 - $50+ $ 5.42 - $ 6.41 = $ 10.99
The operation will have a break-even point when
X - $50 + 5.42 – 6.41 = 0 or X = $ 50.99
At this price the buy call sell put option strategy will result in a no profit no loss situation. Any price above or below this will result in positive or negative pay-offs
The strategy of buying a stock will have a similar pay-off like a buy a call and sell a put strategy provided the transaction costs on buy and sell together equals the net pay off of commissions in case of buy a call and sell a put on the same stock at the same strike price.
However this strategy may not always work. The reason is when there is a high demand for the stock in the market which generally happens near the option expiry dates, there will be severe fluctuations in the stock prices and often it may not be possible to get the stock or sell the stock.
Also holding the options does not give the holders any rights to the corporate actions like dividends, stock splits, bonus shares etc., like holding a stock. These corporate actions will provide an additional benefit to the holders which are not available to the option holders.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.