# Please help in answering this investment problem?

The common shares of the Corporation? No call has been trading in a narrow band around 50 d? Dollars per share? N for months, and you think you are going to stay in that range for pr? Ximos three months. The price of an extraordinary choice of selling three months with an exercise price of $ 50 is $ 4, and a call with the same expiration date and strike price is sold at $ 7.? a. ? Cu? L be? To a simple option strategy with an extraordinary choice of sale and a call to exploit their convictions? N on the future price movement of shares? b. ? Cu? L is the largest amount of money you can do in this position? N? ? To d? Nde the stock price movement in any direction? N before losing money? c. “C” mo you can create a position? N which involves extraordinary choice of selling a call, and the pr? Stamo risk-free with the same structure as the payment of maturity value? The action? N not pay? dividends in the pr? ximos three months. ? Cu? L is the net cost of establishing such a position? N now?

This isn’t the completed answer, but maybe these pointers will help.

You are seeking an options strategy which is appropriate for an expectation of a stagnant (neutral) stock price – so ones that require a sudden move up or down are out.

There are only two things you can do with an option – either sell it (write) or buy it, so the strategy must involve presumably one of these:

buy call + buy put – at same strike price ($50) is called a straddle, but only makes money if

buy call + sell put explosive move.

sell call + buy put – you receive income from call-selling so $7 in, and $4 out for put, so $3 up.

sell call + sell put – receive income from both so get $7 + $4 = $11, but if stock explodes up or down

your losses could be massive – called a “short straddle” – see:

http://www.poweropt.com/shortstraddlehelp.asp

The following webpage has all the possible option strategies, so you could go through each one and throw out all those that are not concerned with a put and a call at the same strike price, and see which strategies remain. My guess is its the “short straddle” that fits all the requirements in this question, but its pretty risky if the stock moves up or down a lot.

http://www.poweropt.com/strategymenu.asp

Usually traders put on “iron condors” to make money out of stocks that don’t move much, but that requires buying and selling options at more than the one strike price (here $50) so its too sophisticated to be “the answer” here, but is probably a better way to trade a stagnant (neutral) market.

There’s a clever little options calculator at:

http://www.cboe.com/LearnCenter/OptionCalculator.aspx

You have to wait a short time before the “I accept” button appears on the screen, which you have to click to get to the calculator.

Click the tab at the top which says “Equity Options”, and put in 50 twice for the “Equity price” and the “Strike price”.

Now enter any date that’s more than 3 months away (I used the American date style for 30th January next year, and typed “01/30/2011” in the box marked “First dividend date”)

and on the right it will show what it expects the put price and call price to be.

Yep – the example prices in this question are miles out – they’re nowhere near $7 and $4 !

Just for fun, click on the button marked “Volatility” and a little data entry window will pop out.

Click the circle in top left next to the word “Call”, put 7 in the top box, and click on the “Calculate” button.

It now shows you that the volatility of the share must be 68% to have a price of 7.

Now click the circle next to the word Put, type 4 in the top box, and click the “Calculate” button.

It shows the volatility of the share would have to be 43% to give a put price of 4.

But a share can’t have two different volatilities (68% and 43%) ! ๐

“How far can it move to show a loss?” To any share price where the combined total of the two options prices exceeds $11 – in other words, because you’ve sold both options, the only way you can get out is to buy them back.

So if when you add the 2 option’s prices together you get a value greater than the $11 you received at the start, then you’re in a loss position. Its costing you more to buy them back, than you received at the start, to close down this position.

The last part sounds like “how do you create a synthetic stock using options and lending?” You create a synthetic stock by buying the call and selling the put. See:

http://www.option-info.com/optionssynlongstock.htm

So you buy the call (cost $7) and sell the put (receive $4) so cost is $3.

Dunno where riskless lending fits in.

I’d love to be in class, or watching with a webcam, when the teacher explains the answers to this question.

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Short a put and short a call

The most you’ll make is $11 per share. $110 for one call and one put contract. You’ll only make money if the stock price remains between $39 and $61 so you would want the sqrt( number of trading days in three months,60) * geometric standard deviation of percentage daily price change (volatility) to be less than $5.50/$50 or 11% for a 95% assurance that you will make money then you should buy out of money puts and calls at strikes of $39 and $61 to remove risk of loss. If it’s less than 22% then you have a 62% chance of making money.

The involvement of the term riskless lending seems to indicate the use of the Black Scholes equation which requires the risk free interest rate usually estimated by the treasury bond rate over the same period. The equation effectively estimates the most probable extrinsic value of the option which decays away as the option approaches expiration. Not sure why anyone would want to structure a derivative hedge to have the same payout structure as the underlying stock, technically an in the money call would suffice. Would really need to know the context of the course lessons to be able to guess at that one.

If you buy a call and short a put then you have the same price movements as the sock but at a cost of $3 instead of $50 but I would hardly call this the say payout structure since a $1 price move would represent 2% of the stock’s value but 33% of the value of the long call/short put plus you haven’t reduced any risk at all, just holding the call without shorting the put costs you $7 hence a $1 price movement is 14% but it limits your loss, that $4 isn’t worth the downside risk. This is the closest you’ll get to the stock price behaviour with a put and a call but the only advantage is leveraging just like the people playing with penny stocks are trying for.

If you write a covered call (short a call while holding stock to cover) with a strike of $50 for $7 and buy a put with a strike of $50 for $4, then you lock in a profit from the extrinsic value of $3 regardless of price change but you’re basically trading any potential profit from the stock appreciation for that $3 profit during the 3 months but how else are you going to guarantee a 24% per annum rate. Note writing a covered call requires that you own shares to cover the call that you are shorting. The advantage here is that you’re guaranteed making that $3 a share over the three months. Although you would need the $47 for the play ($50 for the share, $4 for the put minus $7 from the short of the call), the play only costs you the $4 for the put and the opportunity cost of the $50 which using the 10 yr Treasury bond rate of 2.5% as the riskfree rate (assuming you can borrow at that rate which very few can), the opportunity costs is only $0.31 (you still have the $50 after the play), giving you a return of $7/($4+$0.31) or 62% which equates to a 696% per annum compounded interest rate at no risk. Maybe this is what they meant by involving riskfree lending but it’s hardly the same payoff structure as the stock and this involve a put, a call and stock. This is the play I would make cause there’s no risk.