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Stock futures: Return of the lenders - Views on News from Equitymaster
 
 
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  • Dec 5, 2001

    Stock futures: Return of the lenders

    In the previous article we had introduced futures on individual stocks. In this article we try to understand the pricing of futures and how they can be used for arbitrage and leveraging.

    If one wants trade in stock futures, understanding how these products are priced is a must. The concept is very simple and is based on the time value of money. One of the very first principles of finance is that ‘cash today is worth more than tomorrow’.

    The future is a derivative contract. Therefore, the price of the future has to be derived from that of the underlying. Future contract is an agreement to buy/sell a stock at a future date. Theoretically, the price of the future contract has to be the current stock price plus the cost of capital required to buy the stock (to keep it for delivery at a future date).

    Thus, if F=Future price of the stock
    S= Current market price of the underlying stock/index
    R= risk free rate of return
    T = time in days

    F= S* e^(r*t)

    This is the fundamental basis (or formula) for pricing future contracts. Irrespective of what the underlying is, an index or an individual stock. A simple definition for futures is that they are an agreement to buy or sell a stock or an index at a particular price on a particular date in the future. And if on the future date if the instrument does not give returns that is equal to the risk free rate there is no point in investing in the instrument. Thus, the future price should always reflect this premium.

    Please note: For simplicity, it is assumed that stocks and the index will not pay any dividends.

    For determining the risk free rate (r), the overnight MIBOR rate or the actual returns, yield, (based on the market price) of a T-bill (Govt. paper) with corresponding duration could be used.

    On the 28th of November, let us take the example of Satyam’s December futures that expire in 29 days from now. The stock closed at Rs 208 in the cash market (on November 28). The 30-day MIBOR rates are 7.89%. Using the data the fair value for the future could be arrived at.

    The price for the future should be Rs 209, theoretically. However, the Satyam futures closed at Rs 215. This indicates that the players are willing to take delivery of the stock at Rs 215, a month from now. This is based on the optimism that the stock price will move higher than Rs 215. Therefore, players are willing to carry the contract at a cost of 40% (or at a premium of 40%). This is on expectations that returns will be higher than cost of carry.

    Stock Price
    (Rs)
    Days to
    expiry
    MIBOR
    rate 1 m
    Theoretical futures price
    (Fair value) (Rs)
    Futures price
    (Rs)
    Implied cost
    of carry
    208 29 7.9% 209 215 39.6%

    In the case of ACC, the players are not willing to pay Rs 167 (the fair value of the current market price in December end) to buy the stock one-month down the line. Infact, they are willing to buy the stock only at Rs 164 (ACC December futures price). Therefore, the stock price could be expected to go down.

    Stock Price
    (Rs)
    Days to
    expiry
    MIBOR
    rate 1 m
    Theoretical futures price
    (Fair value) (Rs)
    Futures price
    (Rs)
    Implied cost
    of carry
    167 29 7.9% 168 164 -15.2%

    Arbitrage opportunities
    The arbitrage opportunities can replace the old badla system. The stock and money can be lent into the markets to make risk less gains. The mispricing in futures contracts gives rise to arbitrage opportunities. Since the future is quoting at such a significant premium or discount to its fair value arbitrage gains could be possible.

    • Futures priced higher than theoretical value

      In a situation where the future contract is highly priced the future could be sold and the stock could be bought in the cash markets. This presents an opportunity to lend money to the markets.

      F> S*e^(r*t)
      F= Futures price
      S*e^r*t = Theoretical futures price

      However, the premium has to be large enough to justify transactions costs. On November 28, the closing prices indicated that Satyam’s November futures were priced at Rs 215, significantly higher that the expected fair value of Rs 209, based on the stock price of Rs 208. Therefore, by shorting Satyam futures at Rs 215 and buying the stocks at Rs 208 arbitrage gains could be made.

      Market lot for Satyam is 1,200
      Buy stocks @ Rs 208 249,600 Sell futures @ Rs 215 257,940
      Brokerage (0.75%) 1,872 Brokerage 284
      Service tax (5%) 94 Required IM @ 20% 51,588
      Cost of borrowing (7.89% annualised) 1,641 Cost of borrowing 339
      Total cost (a) 253,207 Total cost (b) 52,211
       
      At expiry Satyam is Rs 220
      Sell the stocks @ Rs 220 264,000 Buy the futures @ Rs 220 264,000
      Brokerage 1,980 Brokerage 290
      Service tax 99 Gain /(loss) on the contract (6,060)
      Total realisation 261,921 Total cost of transaction 913
      Net gains/(loss) on the stock transaction 8,714 Net gain/(loss) from futures of transaction (6,973)
       
      Net gain/(loss) from both the transactions 1,741    
      Total funds utilised (a+b) 305,418    
      Returns on the transaction 0.6%    
      Annual returns 7.4%    

      Please note: All figures in Rs, except those specified otherwise

      The operation could be used to lend money. In this case there will be not be any need to borrow money and there will be no borrowing costs. Thus, if the cost of borrowing is removed the gains realized will be even higher.

    • Futures priced lower than theoretical value

      If the futures are quoting at a price much lower to the fair value, the future could be bought and the stock could be sold. This presents an opportunity to lend stocks to the markets.

      F F= Futures price
      S*e^r*t = Theoretical futures price

      On November 28, ACC was quoting Rs 167 on close and the December futures were quoting at a discount at Rs 164. The theoretical fair value for the contract was expected to be Rs 168. In such a situation by selling the stock at Rs 167 and buying the futures for Rs 164 one could make arbitrage gains, provided the transaction costs are justified. Therefore, the kindly note the mispricing should be wide enough to lock in the gains. The transaction is equivalent to lending stocks in the Badla market.

      Market lot for ACC is 1,500
      Sell stocks @ Rs 167 250,050 Buy futures @ Rs 164 246,000
      Brokerage (0.75%) 1,875 Brokerage (0.11% incl stamp duty) 271
      Service tax (5%) 94 Required IM @ 20% 49,200
      Total realisation (b) 248,081 Total cost (c) 49,471

      Please note: All figures in Rs, except those specified otherwise

      Here we have assumed that of the total realisations of Rs 248,081 from selling the stocks, Rs 49,200 are utilized to pay for the initial margin requirements for buying the futures.

      At expiry ACC is Rs 175
      Buy the stocks @ Rs 175 262,500 Sell the futures @ Rs 175 262,500
      Brokerage 1,969 Brokerage 289
      Service tax 98 Gain /(loss) on the contract 16,500
      Gains from investing (7.89% annualised) (1,319) Total cost of transaction 559
      Total cost (a) 263,248 Net gain/(loss) from futures of transaction 15,941
      Net gains/(loss) on the stock transaction (15,168)    
       
      Net gain/(loss) from both the transactions 773    
      Total funds utilized (a-b+c) 64,638    
      Returns on the transaction 1.2%    
      Annual returns 15.4%    

      Please note: All figures in Rs, except those specified otherwise

      The transaction is subject to the rules on short selling. However, if there are stocks available for delivery then the operation is possible.

      Please note that the arbitrage opportunity arises in both the cases if the transaction costs are justified.

      Leveraging
      To buy 1,200 stocks of Satyam @ Rs 208 in the cash markets you will have to pay Rs 249,600. But you can take a similar position on the same stock by buying futures. The value of a future contract for Satyam comes to Rs 258,000 at Rs 215. However, to take this position you need to pay only the initial margin, which at 20% works out to be Rs 51,600. If the stock on the expiry day is at Rs 220, the return for selling the stock works out to be 3.4%, while the return on selling the futures works out to be 11.4%.

      Market lot for Satyam is 1,200
      Buy stocks @ Rs 208 249,600 Buy futures @ Rs 215 258,000
      Brokerage 1,872 Brokerage 284
      Service tax 94 Required IM @ 20% 51,600
      Cost of borrowing 1,641 Cost of borrowing 339
      Total cost 253,207 Total cost 52,223
       
      Sell Stocks at @ Rs 220 264,000 Sell futures @ Rs 220 264,000
      Brokerage 1,980 Brokerage 290
      Service tax 99 Total gains from the transaction 6,000
      Total realisation from selling 261,921 Total funds utilised 52,513
      Total gains from the transaction 8,714 Returns 11.4%
      Total funds utilised 253,207 Annualised returns 265.3%
      Returns 3.4%    
      Annualised returns 49.4%    

      Please note: All figures in Rs, except those specified otherwise

      However, there is a flip side. If you take delivery you will have to pay out only once. However, in a futures transaction you will be marked to market daily and but far more critical is to realize that the downside is unlimited. On the expiry day you will have to pay up for whatever losses have been made.

      Therefore, before starting to use derivative instruments please thoroughly understand the mechanics and the risk profile.

       

       

      Equitymaster requests your view! Post a comment on "Stock futures: Return of the lenders". Click here!

      1 Responses to "Stock futures: Return of the lenders"

      YADURAJ

      Feb 23, 2013

      Hi Sirs,

      The concept is very nicely explained. Thanks.

      Like 
        
      Equitymaster requests your view! Post a comment on "Stock futures: Return of the lenders". Click here!
       

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