application of futures

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Application of Futures

Chitra Potdar



The Future Payoffs The payoff for a person who buys a futures contract

is similar to the payoff for a person who holds anasset

He has a potentially unlimited upside as well as apotentially unlimited downside

For e.g. a speculator who buys a two-month Niftyindex futures contract when the Nifty stands at 2220

The underlying asset in this case is the Niftyportfolio. When the index moves up, the long futuresposition starts making profits, and when the indexmoves down it starts making losses



The Future Payoffs for the

Seller



Valuation of Stock Index A stock index traces the changes in the value

of hypothetical stocks

The value of a futures contract on a stockindex may be obtained by using the cost of carry model

The asset price today would simply be the

future price less the cost of storage andinterest



Valuation of Futures Futures price = Spot price + Cost of Carry

Spot price is the price of the asset today (in

the cash market)

Cost of carry is the sum of all costs incurred if a similar position is taken in cash and carried

to expiry of the futures contract LESS anyrevenue that may arise out of holding theasset. The cost is typically interest cost andrevenue is in the form of dividend



Valuation of Futures Future price = Spot price + Cost of

carry - Inflows

Cost of carry = Financing cost, storagecost and insurance cost

Inflows = Dividend or interest income

The difference between the Future price andthe Stock price is Basis



Valuation of Futures Mathematical terms

Compounding F = S(1+r/m)mt

Continuous Compounding F = Sert

r = Cost of financing (using continuously

compounded interest rate) T Time till expiration in epsilon 2.71828



Valuation of Futures Securities Providing no income

F = Sert

Securities Providing an expected cash Income/ Dividend

F = (S - I)ert , wherein I = de-rt

Securities Providing a known yield F = Se (r-y)t



Security XYZ Ltd trades in the spot market at Rs. 1150. Money can be invested at 11%

p.a. What is the fair value of a one-monthfutures contract on XYZ?

Illustration 1

Securities providing no income



Illustration 1 - Answer



Illustration 2

An equity share of IPCL quoting at Rs.270/-on 1.1.2007 in the cash market & the future

price with March 2007 expiration date,quoting at Rs.275/- The borrowing rate is10% & the expected dividend payable before31.03.2007 is Rs.2.50. What is the 3 monthfutures price of IPCL as on 1.1.2007?

Pricing index futures given

expected dividend



Illustration 3

A two-month futures contract trades on theNSE. The cost of financing is 10% and the

dividend yield on Nifty is 2% annualized. Thespot value of Nifty 4000. What is the fairvalue of the futures contract?

Pricing index futures given

expected dividend yield



Pricing of Futures Consider a 3 month expiry futures contract

on a stock. The underlying stock is available

for Rs.70 (Face value Rs.10). Withcontinuously compounded risk free rate of 8% p.a. find out the price of a Future undervarious circumstances

Illustration 3



Pricing of Futures When the stock does not pay dividend Ans : 71.414

When the stock pays a dividend of 5% Ans : 70.53 When the stock pays a dividend of Rs.1.50/- Ans : 69.91

When the stock Pays a dividend of 1.50 in amonths time Ans : 69.89



Pricing of Futures 4. When the stock pays a dividend of Rs.

2/- today

Ans : 69.37

5. When the stock pays a dividend of 10%today

Ans : 70.39



Pricing of Index Futures A futures contract on the stock market index

gives its owner the right and obligation to

buy or sell the portfolio of stockscharacterized by the index

Stock index futures are cash settled; there isno delivery of the underlying stocks



Pricing of Index Futures The main differences between commodity

and equity index futures are that

There are no costs of storage involved inholding equity

Equity comes with a dividend stream,which is a negative cost if you are long thestock and a positive cost if you are short the stock



Pricing of Index Futures Cost of carry = Financing cost Dividends

A crucial aspect of dealing with equity futures

as opposed to commodity futures is anaccurate forecasting of dividends

The better the forecast of dividend offered bythe better is the estimate of the futures price



Pricing of Index Futures The pricing of stock futures is also based on

the cost-of-carry model, where the carrying

cost is the cost of financing the purchase of the stock, minus the present value of dividends obtained from the stock

If no dividends are expected during the life of

the contract, pricing futures on that stock isvery simple. It simply involves multiplying thespot price by the cost of carry



Pricing of Index Futures Ft = St [1+(rt) (T/365) (dt) (T/365)]

where St = Spot price of Index

T = the no of days until expiration

Ft = Fair value of futures contract that expires in T days

rt = risk free rate of return for T days

dt = dividend yield for the T days



Illustration - 1 If NSE spot index is 4000, the cost of

borrowing is 10.50% and the expected

dividend yield is 2%p.a. What is the fair valueof the Nifty futures contract with one monthexpiration?

= 4000 [1+0.1050*30/365 0.02*(30/365)]

= 4027.95



Illustration -2 Consider a 3 month expiry futures contract on

an index. The underlying index is available for

4000. With continuously compounded Riskfree rate (CCRI) of 8% p.a. For each of thescenario the price of the index is



Illustration -2 When the dividend yield is 5% and only 50%

of the stocks in the index distribute dividends

Ans : 4055 [4000* e(0.08-0.5*0.05)*0.25]

When the dividend yield is 5% and only 25%of the stocks in the index distribute dividends

Ans : 4068



Effect of Corporate announcementson stock future prices Role of

Exchange If announcements like dividends, bonus, stock split,

rights etc. are made by the company the exchangeadjusts the future position on cum-benefit and on ex-

benefit day is the same As per the policy and the stock exchanges if the

dividend is more than 10% of the market price of thestock on the day of the announcement, the futureprice is adjusted

The exchanges rollover the positions from the last-cum-dividend day to the ex-dividend day by reducingthe settlement price by dividend



Future Price Indicators1. Volume and Open Interest

2. Market wide Open Interest

3. Cost of Carry and Basis



Volume and Open Interest Is the total no of shares or contracts that

have changed hands in one day trading

session in the market Open interest is the no of contracts that are

bought but not yet settled

Volume and open interest can be a barometer

of future activity and direction



Future Price Indicators A price change on a low volume is a

correction against the direction of the major

price trend A price change on a high volume is a signal

in the direction of the major price trend

Futures is the zero sum game i.e. losersprovide the funds to the winners (those whopredicted the correct trend)



Future Price Indicators The trend could be up or down If the winners are bulls i.e. market is going

up, increasing open interest means upwardprice move would continue If the winners are bears i.e. market is going

down, increasing open interest meansdownward price move would continue

Increasing open interest means the playersare betting on the prevailing price trend andthe trend is expected to continue and viceversa



Future Price Indicators

Price Volume

Open

Interest Change in market

Rising Up Up New money enetring market

Rising Down Down Money Leaving Market

Declining Up Up Aggressive New Short Selling

Declining Down Down

Liquidation by discouraged

traders, market bottoms out,

a bullish signal



Cost of carry in the rising and

falling market Incremental cost of carry + incremental long position

= Fresh Long position

Reducing cost of carry + Reducing open interest =Long squaring

Reducing cost of carry + Increasing open interest =Fresh Short position

Increasing cost of carry + Decreasing open interest =

Short covering

application of futures

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