Need help w/Call price & Put price question?

Question

Given the following information, does an arbitrage opportunity exist? If so, how would an arbitrageur take advantage of this opportunity?
Call price---------------$3.60
Put price ----------------$0.40
Market stock price ---$42.00
Exercise price --------$40.00
Expiration---------90 days
T-bill rate----------------6.00%

Answer 1

All the answers seems to be not right. None of the answer show how they reach the $120 profit. If one has to make any profit either the question or the answerers should point out to the direction of the market which is not given either. So the answers seems wrong.
My answer is, since the call price is 3.60 and put is 0.40 probability of the option making a $1.60 move is 3.60/(3.60+0.4)=0.9 and probability of it loosing is 0.1.
So if you buy a call and a put the weighted average winning will be 0.9(3.6) - 0.1(3.6)-3.6-0.4= - 1.12.
So no arbitrage opportunity exists.
Suppose in the strategy given, if you buy stocks along with the calls sold and put bought, you loose on calls sold and put bought and the stock makes 1.60 moves which will be your gain and the losses will be,
3.60 - 0.4 + 1.60 - 3.60=1.20, this happens only if the stock moves in the direction of the probability.
So we can say that it is a strategical opportunity with high probability of sucess not arbitrage opportunity.
Addendum:
The answer seems to be not complete without the following. The strategies prescribed by the above directs one to sell calls when the stocks are going high which is not very sound thing to do for one is bound to loose what he gains.
Better propostion will be to never touch the options market in this scenario but play in the cash market or stock market.
Buy stock by borrowing where your gross income will be $1.60 reducing borrowing costs and transaction costs it will pay something around 50 cents(1.60 - 60 cents borrowing cost - 50 cents brokerage) rather than loosing everything on strategies which will yield you nothing ulitmately. The probability gives you the yield which is possible and if the strategies don't work out it is better to work out alternate cash market strategies. One more thing you should notice is whenever you create a strategy or option move you should follow the 'cheapest to carry' strategy where by you make your outflow the minimal and if there is only such a strategy available for the probability you will get any yield.

Answer 2

I agree with Jelly Roll's answer, but I do not think he completed the explanation.

Your cost for opening the positions is

$42.00 + $0.40 - $3.60 = $38.80 per share.

6% Interest on $38.80 for 90 days is approximately

38.80 x (0.06 / 4) = $0.582

It is the fact that you profit of $1.20 per share is greater than your carrying cost of $0.582 per share that makes this an arbitrage opportunity, assuming your transaction costs are less than $0.618 per share.

Addendum

Mathew C made a good point that there was no explanation of the amount of profit. (The rest of his answer is wrong.)

The $1.20 per share profit is generated by selling the stock for $40.00 per share after you paid $38.80 to open the position. Because it is safe to assume the holder of the call will exercise it if the stock is above $40 per share at expiration, and you are smart enough to execise the put is the stock is below $40 at expiration, you can be sure of selling the stock for $40 per share at expiration.

This combination of positions is called a "conversion" and is sometimes considered risk-free. In reality it is not quite risk-free because of something called "pin risk" which will occur if the stock closes right at $40 per share at expiration. If the stock closes right at $40 per share you do not know if the call holder will exercise his options or not, so you do not know if you should exercise your put options or not.

If both you and the call holder expercise your options, or if neither of you do, you will be left with an unhedged long stock position when trading opens again. If the price of the stock falls before you can sell it, you may lose money.

Even with pin risk, a conversion is considered an arbtrage spread.

Answer 3

It took me a minute to see it, but yes, there is an arbitrage opportunity.
What you would do is create a synthetic long call position by purchasing 100 shares @ $42, and buying one $40 put contract @ $0.40 premium. You would then offset that by selling one $40 call contract @ $3.60 premium - your gross profit from that would be $120, not including transaction or funding costs.