HOW?

To illustrate this relationship, we will take the case of two investors, each having Rs.5,00,000 to invest.

Investor 1 buys INFY CE1000, which gives him the right to buy 500 shares of Infosys at the strike price of 1000. He pays only a small premium and retains the cash with him.

Investor 2 buys 500 shares of Infosys at Rs.1000 each. Now he has exhausted all his funds. So, he purchases a put option of Infosys at a strike rate of Rs.1000

Which investor had a better strategy?

Let us look at the two strategies.

The first Investor No.1 idea was to wait and watch how the price would move before investing and so, in the meanwhile, invest his money in a risk-free investment. If the stock price were to close higher than Rs.1000 at the time of expiry, he would exercise his option to buy at Rs.1000 and sell the stock at the market price to make a profit. He would have allowed the call option to lapse if the price were to close less than Rs.1000. Whatever way one looks at it, he has protected his Rs.5 lakhs.

The other investor wanted to protect his investment of Rs.5 lakhs in Infosys shares from a fall in price. So, he bought a put option of Infosys at a strike price of Rs.1000. If the stock price were to close lower than Rs.1000 at the time of expiry, he would exercise his option to sell at Rs.1000 to make a profit. He would have allowed the put option to lapse if the price were to close higher than Rs.1000. Whatever way one looks at it, he has protected his Rs.5 lakhs.

Whatever strategy they employed, the investors played a risk-free game and protected their assets. A call + cash by investor No.1 was equal to the put + underlying stock. In theory, both INFY CE1000 + cash and INFY PE 1000 + underlying stock has the same value on the expiry date. If this were true, then the present value of both portfolios would be the same.

This call – cash and put – underlying stock relationship is known as Call – Put parity. This Put-Call parity value will always be zero for all practical purposes.

In the strategies of two investors we mentioned above, one was, buying a call and investing an amount equal to the strike price value in risk-free assets. The other was buying a put and also the stock at spot price. The pay-off in both strategies was identical. Now that we have seen the relationship let us illustrate it as a formula.

• CE + PV = S + PE

Where,

• CE = Buy European Call option

• PV = Cash at present value invested in risk-free investments.

• S = Spot buy price of the share

• PE = Buy European put option

As these formulas are mathematically related, it can be re-written to derive the missing variable.

How to read and construct a formula?

When we interchange the letters on one side to the other side of the formula, the mathematical relationship between them also changes. When you move the positive figure to the other side of the equal sign, it becomes a negative figure.

Let us say that we would like to create an equivalent transaction of PE (buying a put). The formula would be PE = CE + PV – S. Here, S, which was the buy spot price, becomes a sell spot price.

When you buy a call and invest the money in risk-free stocks, and later sell them in the spot market, you have created a transaction that is complex and as good as buying a put option.

Why do we need such combinations?

These combinations are needed when the option for a particular stock is not available, and we have created one for our use.

Here is an example.

XYZ three months call option with a strike price of Rs.400 is sold for Rs 36. The spot price of the stock is Rs.380 right. The risk-free return is 8% per annum. What would be the theoretical value of an XYZ put, having the same maturity and strike price?

Here we have to find ‘PE’. So the formula is modified as:

· PE = C + PV –S

· CE= Call option price = Rs.36

· PV = Present value of Rs.400 invested at 8% for 3 months.

· S = Current market price of the stock = Rs.380

How do we find the present value?

· PV=FV / (1+r) N

· PV denotes the present value,

· FV denotes the future value

· ‘r’ is the rate of interest

· N is the number of years. ( here, it is three months or 0.25 years)

Applying this formula, the present value will be:

· PV = 400 / ( 1+ 0.08 ) 0.25

· PV = 400 / 1.019427

· PV = 392.38

Now with all available values, let us calculate the value of the put.

· PE = CE + PV –S

· PE = 36 + Rs.392.38 – 380

· PE = 48.38 the equivalent theoretical value of the call sold at Rs.36

· In other words, when we buy a call and invest the value of strike value in 8% risk-free investments and later selling the stock, we are creating an equivalent of put.

· 48.38 is theoretical. The put is under-valued if the value of the put is below 48.38. If the put is over-valued if it is above 48.38. One must buy undervalued put and sell overvalued put.