I can’t understand the way how it could earn risk-free rate. Could anyone help me to figure this out. So we would have a bull call(Buy lower exercise price call and sell higher exercise price call) Then have a bear put(Buy higher exercise price put and sell lower exercise price put) This strategy has four options and no underlying security(correct me if I am wrong) Bull call spread costs money Bear put spread costs money Why they could generate a positive risk-free rate?

For a box strategy, you are guaranteed to exercise your options. Example: Stock at 70 on call side: buy 70 call sell 75 call on put side: buy 75 put sell 70 put In this way you will exercise your options no matter where the stock goes. Therefore you are guaranteed to get your initial investment back. If markets are efficient, you would get just a risk free rate back, otherwise you could get more back and earn a risk free profit

Since it is net premium discounted is PV, that is not why you earn risk free rate?

deep2002 Wrote: ------------------------------------------------------- > For a box strategy, you are guaranteed to exercise > your options. Example: > > Stock at 70 > > on call side: > buy 70 call > sell 75 call > > on put side: > buy 75 put > sell 70 put > > In this way you will exercise your options no > matter where the stock goes. Therefore you are > guaranteed to get your initial investment back. If > markets are efficient, you would get just a risk > free rate back, otherwise you could get more back > and earn a risk free profit Hi, Deep2002, thank you for your explanation. I think I get it, when it puts in price there, it is much easier to understand. This is my interpretation on this now So we did spend money on the options we payed but we are guaranteed with the profit from the combination of those opinions wherever the direction we go. That’s why we should earn a risk-free rate if market is efficient…

Well, what happens if the price is $72.50 on the expiration date. You make $2.50 on your call and there will be no profit on your put ($2.50 profit on put buy - $2.50 loss on your put sell). Now, it is theorized that the net profit you will make is (if the market is efficient) $2.50 minus the net cost of all the buy/sell of calls and puts; which is risk-free rate.

Ashwin Wrote: ------------------------------------------------------- > Well, what happens if the price is $72.50 on the > expiration date. You make $2.50 on your call and > there will be no profit on your put ($2.50 profit > on put buy - $2.50 loss on your put sell). Now, it > is theorized that the net profit you will make is > (if the market is efficient) $2.50 minus the net > cost of all the buy/sell of calls and puts; which > is risk-free rate. if the stock is at 72.50, you would make $5 net: +2.50 from your call +2.50 from you put now you have remember that options are priced on black sholes and you would not be paying $5 in premiums to initiate this box. In an efficient market, you would be paying 5/(1+risk free rate). There are other variables but this is the simplified version. As a result, you would earn a risk free rate if it is priced correctly or you would earn a risk free profit.