Question

• Evanston Insurance, Inc., has purchased shares of Stock E at $50 per share. It will sell the stock in six months. It considers using a strategy of covered call writing to partially hedge its position in this stock. The exercise price is $53, the expiration date is six months, and the premium on the call option is $2. Complete the following table:

  POSSIBLE PRICE OF STOCK E IN SIX MONTHS	PROFIT OR LOSS PER SHARE IF A COVERED CALL STRATEGY IS USED	PROFIT OR LOSS PER SHARE IF A COVERED CALL STRATEGY IS NOT USED
  $47
  50
  52
  55
  57
  60

• Assume that each of the six stock prices in the table's first column has an equal probability of occurring. Compare the probability distribution of the profits (or losses) per share when using covered call writing versus not using it. Would you recommend covered call writing in this situation? Explain.

Answer 1

Covered call strategy not used

profit per share = price of stock in 6 months - purchase price of stock

Covered call strategy used

Payoff of a short call option = P - Max[0, S-X],

where

S = underlying price at expiry,

X = strike price

P = premium received

Profit per share = (price of stock in 6 months - purchase price of stock) + payoff of short call option

If each of the six stock prices has an equal probability of occurring,

probability of each stock price = 1 / number of possible stock prices

probability of each stock price = 1 / 6

covered call is not used

Expected profit = sum of (probability of each stock price * profit at that stock price)

Expected profit = $3.50

covered call is used

Expected profit = sum of (probability of each stock price * profit at that stock price)

Expected profit = $3.33

I would not recommend covered call writing because the expected profit is lower.