Question

The current price of a stock is $31.50 per share, and six-month European call options on the stock with a strike price of $32.50 are currently trading at $3.60. An investor, who has $10,000 of capital to invest, believes that the price of the stock will increase by 20% over the next six months. The investor is trying to decide between two strategies - buying shares or buying call options. What return will each strategy produce after six months, if the investor is correct in their assessment of the stock? Assume that either a whole number of shares can be bought OR a whole number of option contracts can be bought (representing the right to buy 100 shares per contract) This information is summarized in the table below: Strategy A: Buy shares Price of security $31.50 Strike price of the call options Strategy B: Buy call options $3.60 $32.50 Hint: The price for the call option is for an option on 1 share; each option contract is for options on 100 shares. Amount available for investment Anticipated change in stock price $10,000 20% For Strategy B: Buy call options 1) How many option contracts can be purchased (rounded)? 2) How much uninvested cash does the investor still have? 3) What is the intrinsic value of the options purchased, assuming they are all exercised at maturity if the anticipated change in stock price is realized? 4) What is the intrinsic value of the options purchased, assuming they are all exercised at maturity if the stock price decreases by 20% (opposite direction of anticipated change in price)?

Answer 1

177 Buying shares (strategy -A) Amount available for investment = $10000 current stuck price = $31.50 No. of Share purchased = $10000/ current stock price = $10000 /$31,50 after 6-months Profit Ishame = 317 shares. = increase in stock price - 209% of$31.50 = $6.3 = Total share a profit Ishare - 317 * $ 6.3 - $1997.10. .. Net profit Buying call options (strategy - B o ne UNIONUMPARA PARTY 1) No. of shares in 1 contract = 100 Amount avaible - $10000 price of option contract = $3.60 eff. price per share - $31.50 + $3.60/00 - $ 31-536 price of 1 contract (too shares) = 100 x $31.536 - $3153.60 No. of option contract purchased - Investment amount price per contract = $10000/43153.60 = 3.17 2) Amount of uninvested cash with investor = Investment amount - 3x(price of contract) = $10000 -$41460.80 - $ 539.20