Question

Consider the following “portfolio:” buy a call at the premium V_c and buy a Treasury bill having price-per-face of ? and face of E, where E is the exercise price of the option. Now show how you would “short” this portfolio. What is the payoff pattern? Explain.

Answer 1

The answer :

In case of portfolio of buying a call at the premium at Vc is represented by the follwing equation as below:

Initial Outflow =-(Vc +B)

Now however since we are short on this portfolio the initial inflow will be Vc+B

Also if the option is above the exercise price then the call option of this portfolio will be exercised.The bond will give the same return as E-B which leaves an unlimited downside risk potential in the market if the underlying asset falls .

If the underlying portfolio decreases the call option will expire and the return is given by

E(R) =Vc+E -B so the upside risk is limited .

To create a profit and loss diagram, values are plotted along the X and Y axes. The horizontal axis (the x-axis) shows the underlying prices, labeled in order with lower prices on the left and higher prices towards the right. The current underlying price is usually centered along this axis. The vertical axis (the y-axis) represents the potential profit and loss values for the position. The breakeven point (that indicates no profit and no loss) is usually centered on the y-axis, with profits shown above this point (higher along the y-axis) and losses below this point (lower on the axis).

With options, the diagram looks a bit different since our downside risk is limited to the premium we paid for the option. In the example shown a call option has a strike price of $50 and a $200 cost (for the contract). The downside risk is $200 – the premium paid. If the option expires worthless (for example, the stock price was $50 at expiration), the loss would be $200, as shown by the line intersecting the y-axis at a value of negative 200. The breakeven point would be a stock price of $52 at expiration. In this case, the investor would "lose" $200 by paying the premium, which would be offset by the stock's rising price (equal to a $200 gain).