Suppose that apple stock is currently trading at 180 per...

Suppose that Apple stock is currently trading at $180 per share. A call option on the stock with a strike price of $185 and one year to expiration costs $11. Suppose that one year later, there is an 40% probability that the stock price will be less or equal to $180, 30% probability that it will increase to $185, and 30% probability that it will increase to $210. What is the expected return of buying a 1-year call option with a strike price of $185?

Transcript

00:01 Question is in part for part one if the stock price at expires $45 and the call option expire out of money so you have lose the entire investment of call option which is about $5 ,000 you loss you have no return from stock because you didn't buy it so total return total return will be minus 5000 in the second case if the stock expiration price is at $50 in the call option you expire loss of 5000 you have no return so the total return will be minus $5 ,000 now let's move towards the third part if the stock price expiration at $55 in the call option expiring money from expires in the money so you can exercise the option stock at price at $55 per share so with you can buy 5000 divided by 50 which is 90 .91 shares if you sell 90 .91 shares you can get back 55 multiplied by 90 .91 share so it will be 5000 so your total return will be $5 ,000 loss earning minus $5 ,000 loss so it will be zero dollar no loss no profit in the fourth situation if the stock expire at $60 okay so in the case of then the call option expire money so you can purchase the shares again 5000 shares divided by 55 it will be 90 .91 shares and if you sell those shares you got back $60 multiplied by 90 .91 so it will be 54 54 .55 dollars so your total return will be your sale amount minus your loss amount so it will be because call option is lost already so you will get return of 454 .55 dollar now for the fifth part if the stock price expires at $70 call option expire have a loss of 5000 but you can buy shares 5000 divided by 55 same it will be 90 .91 shares if you sell at the 90 .91 shares at the $70 per share you will got 6363 .64 so total return will be 6363 .64 dollar minus $5 ,000 so it will become 1363 .64 dollar your total return so average percentage return we have to calculate average percent return so it will be when do we do sum of individual returns divide by number of scenario so 0 % plus 0 % plus 9 .09 % 9 .09 % plus 27 .27 % divided by 5 so you will got 9 .09 % standard deviation of return return so here it is first we calculated the mean which is average return which is 9 .90 % now then calculate the square difference so you will got for first 82 .64 % we have calculate all the sum of average 80 2 .64 % plus 0 % plus 0 % plus squared it will be 95 .73 % now finally take the square root of 95 .73 % so it will be 9 .78 % our standard deviation so this is the whole answer...

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