Question

You are bullish on Amazon and want to compare 3-month strategies of buying stock to buying call options. Currently Amazon stock is priced S0 = 2900, and 3-month call options with K=3000 cost c0 = 29 (per share). You have $2.9M to invest, so you can buy 1000 shares or go long calls on 100,000 shares.

i] How much does AMZN need to increase over the 3-month period so that the calls are the better investment?

ii] What is the risk of calls versus shares?

Answer 1

(i)

Alternative 1 - Invest in Shares

Buy shares from Cash Market @ $ 2900 each

Number of Shares = 1000, Total Investment = $ 2,900,000

Alternative 2 - Buy Call Options

Buy Call Option Contracts @ $ 29 per share , Strike Price = 3000

Number of Calls = 100,000 , Total Premium Paid = $ 2,900,000

Indifference Price

At Indifference price (IP) for both Alternatives,

Profit from Investment in shares = Profit from Call Options

(IP - Investment Price) x 1000 = (IP - Strike Price - Premium per Unit) x 100,000

(IP - 2900) x 1000 = (IP - 3029) x 100,000

IP x 1000 - 2900,000 = IP x 100,000 - 302,900,000

IP = 3030.31

Hence, Stock should increase $ 130.31 or more to reach $ 3030.31 or more, so that the calls are the better investment.

(ii)

Call options are always much risky that investments in shares. In case of call option, Investor can even lose his entire Invested amount if the Stock price doesn't go beyond strike price i.e., 3000.

Investment in shares is very less risky as compared to call options. Maximum loss is limited to the downward fluctuations in the price of stock.

As per Risk- Reward relationship, the amount of return on an investment and the amount of risk in that investment are always directly related. Hence, the call options give a possibilty of high profits as compared to stock investments.