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  • 1. Arbitrage Page 1 of 5 Arbitrage - Safety with Smartness Arbitrage by definition is a financial transaction that makes an immediate profit without involving any risk. Technically it consists of purchasing a commodity or security in one market for immediate sale in another market (deterministic arbitrage). However popular usage has expanded the meaning of the term to include any activity which attempts to buy a relatively underpriced item and sell a similar, relatively overpriced item, expecting to profit when the prices resume a more appropriate theoretical or historical relationship (statistical arbitrage). The recently introduced futures index by the BSE and NSE is an instrument which can be used for arbitrage. Arbitrage opportunities are said to exist whenever the futures price moves away from the fair value. Fair value is the summation of spot price and the holding cost . Holding costs could be Cost of financing plus Storage costs plus Insurance purchased, etc.(In case of commodities) and holding cost = Cost of financing minus Dividend returns, which could be in the form of dividends in case of equities futures. For example, suppose a futures contract is traded on two different exchanges. If, Futures price = Spot price + Holding F=S+C However if If F> (S + C) or F< (S + C), then arbitrage opportunity exists. The futures price is calculated as follows:- Example Futures price of 100 gms of silver one-month down the line i.e. a contract expiring 30th November is computed as follows: What is the spot price of silver? The spot price of silver, S= Rs. 7000/kg What is the cost of financing for a month? rT, cost of financing for a month, 15% annualized = ln (1.15)*30/365 What are the holding costs? Assume storage cost, C = 0 The fair value of futures price, F=S*exp(rT) + C = 700 * exp(ln(1.15)*30/365) = Rs. 708 If the contract was for a three-month period i.e. expiring on 30th January, the cost of financing would increase the futures price. Therefore, the futures price would be F = 700 * exp(ln (1.15)*90/365) = Rs. 725 In case of calculation of the price of future contracts on equities there is no cost of storage considered in holding paper, however equity paper comes with a dividend stream, which is a negative cost if you are long on the stock, and a positive cost if you are short the stock. 1/12/2009
  • 2. Arbitrage Page 2 of 5 C = financing cost - dividends Thus, a crucial aspect of dealing with equity futures as opposed to commodity futures is an accurate forecasting of dividends. The better the forecast of dividend offered by a security, the better is the estimate of the futures price. For example What is the fair value of a two-month S&P CNX Nifty futures contract expiring on April 25? What is the annual dividend yield on S&P CNX Nifty index? The dividend yield on S&P CNX Nifty, 2% annualized = ln(1.02)*60/365 What is the spot value of S&P CNX Nifty? Current value of S&P CNX Nifty is 910 What is the cost of financing for two months? RT, cost of financing for a month, 15% annualized = ln(1.15)*60/365 What are the holdings costs? Assume storage cost, C=0 The fair value of futures price, F=S*exp(ln(1+r-q))*T + C = 910 * exp(ln(1.13)*60/365) = Rs. 928.47 Arbitrage helps investors to lend funds into the stock market, without suffering the slightest risk. In the traditional methods of loaning money into the stock market there is a price risk or credit risk involved. But through the index futures market an investor can hedge both the price and credit risk. The basic idea is simple. The lender buys all 50 stocks of S&P CNX Nifty on the cash market, and simultaneously sells them at a future date on the futures market. There is no price risk since the position is perfectly hedged. There is no credit risk since the counter party on both legs is the National Securities Clearing Corporation (NSCC) which supplies clearing services on NSE. It is an ideal lending vehicle for entities which are shy of price risk and credit risk, such as traditional banks and the most conservative corporate treasuries. Hedging the Price Risk One buys a portfolio in which all the 50 stocks in S&P CNX Nifty are in correct proportion, (i.e. where the money invested in each stock is proportional to its market capitalization.) on the cash market. Simultaneously sell S&P CNX Nifty futures of equal value. Now you are completely hedged, so fluctuations in S&P CNX Nifty do not affect you.A few days later, you will have to take delivery of the 50 stocks and pay for them. This is the point at which you are "loaning money to the market".Some sell your portfolio and reverse your future position. A few days later, you will have to make delivery of the 50 stocks and receive money for them. This is the point at which "your money is repaid to you".The interest rate that you will receive is the difference between the futures price and the cash S&P CNX Nifty plus any dividends earned minus the transactions costs (impact cost, brokerage) in doing these trades. 1/12/2009
  • 3. Arbitrage Page 3 of 5 Suppose the S&P CNX Nifty spot is at 1000 and the two-month futures are at 1040. Suppose the transactions costs involved are 0.4% per month and dividends over the two months are nil. Then the rate of return in loaning money to the market is 1.5% (1040/1000 over two months is near 1.9% per month. Subtract out 0.4% as transaction costs to get 1.5% per month. On 1 August, S&P CNX Nifty is at 1200. A futures contract is trading with 27 August expiration for 1230. Ashish wants to earn this return (30/1200 for 27 days). He buys Rs. 3 million of S&P CNX Nifty on the spot market. In doing this, he places 50 market orders and ends up paying slightly more. His average cost of purchase is 0.3% higher, i.e. he has obtained the S&P CNX Nifty spot for 1204. He sells Rs. 3 million of the futures at 1230. The futures market is extremely liquid so the market order for Rs. 3 million goes through at near-zero impact cost. He takes delivery of the shares and waits. While waiting; a few dividends come into his hands. The dividends work out to Rs. 7,000. On 27 August, at 3:15, Ashish puts in market orders to sell off his S&P CNX Nifty portfolio, putting 50 market orders to sell off all the shares. S&P CNX Nifty happens to have closed at 1210 and his sell orders (which suffer impact cost) goes through at 1207. The futures position spontaneously expires on 27 August at 1210 (the value of the futures on the last day is always equal to the S&P CNX Nifty spot). Ashish has gained Rs. 3 (0.255) on the spot S&P CNX Nifty and Rs. 20 (1.63%) on the futures for a return of near 1.88%. In addition, he has gained Rs. 7,000 or 0.23% owing to the dividends for a total return of 2.11% for 27 days, risk free. Arbitrage also offers an investor the opportunity to lend securities to the market and earn revenues. The mechanism is simple -you sell off your certificates and contract to buy them back in the future at a fixed price. The basic idea is quite simple. You would sell all 50 stocks in S&P CNX Nifty and buy them back at a future date using the index futures. You would soon receive money for the shares you have sold. You can deploy this money as you like until futures expiration. On this date, you would buy back your shares, and pay for them. Suppose you have Rs. 5 million of the S&P CNX Nifty portfolio (in their correct proportion, with each share being present in the portfolio with a weight that is proportional to its market capitalization). Sell off all 50 shares on the cash market. This can be done using a single keystroke (offline order entry) using the NEAT software. Buy index futures of an equal value. 1/12/2009
  • 4. Arbitrage Page 4 of 5 A few days later, you will receive money and have to make delivery of the 50 shares. Deploy this money at the riskless interest rate. On the date that the futures expire, at 3:15 PM, put in 50 orders (using NEAT again) to buy the entire S&P CNX Nifty portfolio. A few days later, you will need to pay in the money and get back your shares. This is possible when the spot-futures basis (the difference between spot S&P CNX Nifty and the futures S&P CNX Nifty) is smaller than the riskless interest rate that you can find in the economy. If the spot-futures basis is 2.5% per month and you are loaning out the money at 1.5% per month, it is not profitable. Conversely, if the spot-futures basis is 1% per month and you are loaning out money at 1.2% per month, this stocklending could be profitable.The stock lending rate is calculated as follows:- we assume that transactions cost account for 0.4%. Suppose the spot-futures basis is x% and suppose the rate at which funds can be invested is y%. Then the total return is y - x - 0.4%, over the time that the position is held. Example Suppose Akash has Rs. 4 million of the S&P CNX Nifty portfolio which he would like to lend to the market. Akash puts in sell orders for Rs. 4 million of S&P CNX Nifty using the feature in NEAT to rapidly place 50 market orders, in quick succession. The seller always suffers impact cost; suppose he contains an actual execution at 1098. A moment later, Akash puts in a market order to buy Rs. 4 million of the S&P CNX Nifty futures. The order executes at 1110. At this point, he is completely hedged. A few days later, Akash makes delivery of shares and receives Rs. 3.99 million (assuming an impact cost of 2/1100) Suppose Akash lends this out at 1% per month for two months. At the end of two months, the money comes back to him as Rs. 4,072,981. Translated in terms of S&P CNX Nifty, this is1098 * 1.012 or 1120. On the expiration date of the futures, he puts in 50 orders, using NEAT, placing market orders to buy back his S&P CNX Nifty portfolio. Suppose S&P CNX Nifty has moved up to 1150 by this time. This makes shares costlier in buying back, but the difference is exactly offset by profits on the futures contract. When the market order is placed, suppose he ends up paying 1153 and not 1150, owing to impact 1/12/2009
  • 5. Arbitrage Page 5 of 5 cost. He has funds in hands of 1120, and the futures contract pays 40 (1150-1110) so he ends up with a clean profit, on the entire transaction, of 1120+40-1153 = 7. On a base of Rs. 4 million, this is Rs. 25,400. Aru Srivastava 1/12/2009