# 17.5 Futures payoff

Hanumant Dhokle

1. Payoff for Long position (Mr Mahesh):

If on the expiry date, the actual price of Reliance Industries is Rs 1300, Mahesh can buy the shares at Rs 1220 and sell them at Rs 1300, thereby gaining Rs 80 per share (Total = 80 x 75 = Rs 6000). If however, the price on expiry is Rs 1150, he will have to bear a loss of Rs 70 (Rs1220 - Rs 1150) per share (Total = 70 * 75 = Rs 5250). The value of a long futures position is marked-to-market daily. Gains are credited and losses are debited from the future trader’s account at the end of each trading day.

The formula for calculating profit is given below:

1. Maximum Profit = Unlimited.
2. Profit Achieved When Market Price of Futures > Purchase
3. Price of Futures.
4. Profit = (Market Price of Futures - Purchase Price of Futures) x Contract Size - Commissions Paid.

Long futures as an investment strategy

The long futures position is an unlimited profit, unlimited risk position that can be entered by the futures speculator to profit from a rise in the price of the underlying.

2. Payoff for Short position (Mr Ramesh):

If on the expiry date, the actual price of Reliance Industries is Rs 1300, then Ramesh has to sell the shares at Rs 1220 but will have to buy the shares at Rs 1300, thereby making a loss of Rs 80 per share. If however, the price on expiry is Rs 1150, he will gain Rs 70 per share.

The formula for calculating loss is given below:

Maximum Loss = Unlimited.

Loss Occurs When Market Price of Futures > Selling Price of Futures.

Loss = (Market Price of Futures - Selling Price of Futures) x Contract Size + commissions Paid.

Pay off of Sensex Futures

Profit - if the futures price goes up.

Loss - if the futures price goes down.

Calculation - The profit or loss would be equal to fifteen times the difference in the two rates.

If June Sensex Futures is sold @ 15500 there would be a profi t of 500 points which is equal to Rs. 7500 (500*15). However if the June Sensex However if the June Sensex Futures is sold @ 14700, there would be a loss of 300 points which is equal to Rs. 4500 (300*15).

Example 2

Position - Short – Sell June Sensex Futures @ 15500

Payoff –

Profit - if the futures price goes down.

Loss - if the futures price goes up.

Calculation - The profit or loss would be equal to fifteen times the difference in the two rates. If June Sensex Futures is bought @ 15900 there would be a loss of 400 points which is equal to Rs. 6000 (400*15). However if the June Sensex Futures is bought @ 15200, there would be a profit of 300 points which is equal to Rs. (300*15).

Short Futures as an investment strategy. There is no maximum profit for the short futures position. The futures trader stands to profit as long as the underlying asset price goes down. Large losses can occur for the long futures position if the underlying futures price falls dramatically.

#### How is the future price arrived at?

Now let us discuss how future price is calculated? Future price is nothing but the current market price plus the interest cost for the tenure of the future. This interest cost of the future is called as cost of carry. If F is the future price, S is the spot price and C is the cost of carry or opportunity cost, then

F=S+C

F = S + Interest cost, since cost of carry for a finance is the interest cost

Thus, F=S (1+r) ^ T

Wherer is the rate of interest (usually the risk free market rate) and T is the tenure of the futures contract.

Example:

The spot price of Reliance is Rs 300. The bank rate prevailing is 10%. What will be the price of one-month future?

Solution:

The price of a future is F= S (1+r)^T. Therefore one-month Reliance future would be the spot price plus the cost of carry. Since the bank rate is 10 %, we can take that as the market rate. This rate is an annualized rate and hence we recalculate it on a monthly basis.

F=300(1+0.10)  ^ (1/12)

F= Rs 302.39

Another Example

The shares of Infosys are trading at 3000 rupees. The 1 month future of Infosys is Rs 3100. The returns expected from the Gsec funds for the same period is 10 %. Is the future of Infosys overpriced or underpriced?

Solution

The 1 month Future of Infosys will be :-

F= 3000(1+.0.10) ^ (1/12)

F= Rs 3023.90

But the price at which Infosys is traded is Rs 3100. Thus it is overpriced by Rs 76.

Note: In case of index futures, the treatment of the futures calculation is the same. The future value is calculated as the spot index value plus the cost of carry.

What happens if dividend is going to be declared?

Dividend is an income to the seller of the future. It reduces his cost of carry to that extent. If dividend is going to be declared, the same has to be deducted from the cost of carry. Thus the price of the future in this case becomes, F= S (1+r-d) ^  T ; where d is the dividend.

Example

The spot price of Reliance is Rs 300. The bank rate prevailing is 10%. What will be the price of one-month future? Reliance will be paying a dividend of 50 paise per share.

Solution: Since Reliance is paying 50 paise per share and the face value of reliance is Rs. 10, the dividend rate is 5%. So while calculating futures, F=300(1+0.10-0.05) ^ (1/12)

F= Rs. 301.22

How do future prices behave compared to spot prices?

Future prices lead the spot prices. (The spot price of a security is the price that is quoted for immediate (spot) settlement (payment and delivery). The spot prices move towards the future prices and the gap between the two is always closing with as the time to settlement decreases. On the last day of the future settlement, the spot price equals the future price.

So when you subtract the futures price from the spot price, the price which you get is called futures basis. Basis can be positive or negative number.

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