Question

You have $5,000 to invest in shares of XYZ that currently trade at $50. You choose to invest 25% of your funds in long-term call options with a strike of $60 that currently are quoted at $1.50. The options expire in 12 months. The other funds will be placed into a money market account earning 1.0%, compounded monthly. How much in dollars would the stock price have to increase in order for you to breakeven on this strategy?

Answer 1

Let St be the final stock price

Profit=5000*25%/1.50*(MAX(St-60,0)-1.50)+5000*(1-25%)*(1+1%/12)^12

At breakeven, profit=0
Hence,
5000*25%/1.50*(MAX(St-60,0)-1.50)+5000*(1-25%)*(1+1%/12)^12=0
=>St=-(1-25%)*(1+1%/12)^12*1.50/25%+1.50+60
=>St=56.955

So, if stock price increases by 6.955 dollars