I understand the calculations they have made to arrive at the conclusion that the portfolio would be worth $7.50 in both scenarios.
But since we’ve sold the call option, when the price of the stock decreases, the value of the portfolio should be worth 0.5*$15 as well as some value for selling the call option no?
Am i missing something?
The question only asks about value. We don’t have all the numbers (we needa risk free rate) to calculate everything but.
I assumed rf rate of 10% and worked out fair value of call to be 5.6818 (U = 62.5% D = 37.5%)
But at the start we would buy 0.5 of a share cost $12.5 we would write a call receiving prm $5.68182
Total cost of position =$ 6.8182
In either scenario the value of the share and call = $7.5
Return = $7.5 / $6.8182 - 1 = 10% = risk free rate.
This is the assumption when pricing bonds using this model.
We would get equivalent of risk free return on investment no matter which scenario plays out.
Hey thanks for replying!
I am still somewhat confused. If we purchase 0.5 shares we have $12.50 right. If the price of the stock increases to $35 we have $17.5 which is then offset by the short call by $10. Hence we end up with $7.50
Now in the scenario that the stock goes down to $15, we have 0.5 shares worth $7.50 but we would more than this since we shorted the call. The investor would have made some premium from selling the call option on top of the 0.5 shares which are worth $7.50 no?
The investor WRITES the call. They are paying out on the call.
Initiall BUy 0.5 share = 12.5 RECEIVE premium.
Stock goes up to 35.
Own 35 x 0.5 = 17.5 have to pay out of call 10 = position = 7.5
Stock goes up 15
Own share 15 x 0.5 = 7.5 call expires worthless. No payout needed.
We received the premium as the start (say 5.68 using numbers above) but we also bought a 0.5 share = 12.5
Net cash OUTFLOW = share - prem, i.e. 6.82
We wrote the call, received premium, we don’t own anything of value, we have a contigent claim on us. Also once the option has expired it has no value to anyone.
I understand that they are paying out on the call and that the call has no value to the buyer in the situation that the stock goes down.
So using your numbers the investor sold the call option and received $5.68, the investor simultaneously bought 0.5 shares at $25. Now when the stock goes down, the call has no value and they don’t have to payout but they still have that premium from initially selling the call option. So they have 0.5 shares of a stock worth $15 which is $7.50 PLUS they still received a $5.60 premium for selling the call. So wouldn’t this leave the investor with $13.10 as opposed to $7.50?
Shares
25 x 0.5 = 12.5 This cost them money. Cash had to leave their bank account or they borrowed money (lets assume they borrow)
The get money in from premium 5.68, but this offsets some of the money they had to borrow to buy the share.
At start they have
share worth 12.5
debt of 12.5 - 5.68 = 6.82
At end
The debt will cost interest at risk free rate 10% In 1 years time, at expiry of option, they will need to repay 6.82 x 1.1 = 7.5 (I have simplief rounding)
If share goes up or down the combination of the share and payoff on option is worth 7.5
The same as amount due on loan.
Ahh ok this explains it!! Thank you so much for your help
