Category: Money tips Release Date: 2006-05-11
1, stock index futures and stock index arbitrage principle
Refers to investment in stock index futures contracts and the corresponding package of stock trading strategies, to seek from the futures and spot markets exist in the same set of stock price difference in profit.
First, the actual price when the futures price is greater than the theory, to sell stock index futures contracts, buying index constituent stocks in the portfolio so as to obtain risk-free arbitrage returns.
Second, when the futures price is lower than the actual theory of price, to buy stock index futures contracts, sold index constituent stocks in the portfolio so as to obtain risk-free arbitrage returns.
2, stock index futures and stock index arbitrage between the risk-free
For example: buyers and sellers to sign a package of 3 months after delivery of the portfolio of forward contracts, the package of the Hang Seng Index in Hong Kong equity portfolio constitutes a complete counterpart, and now the market value of 75 million Hong Kong dollars, which corresponds to 15200 points, the Hang Seng Index (HSI Futures the contract multiplier of 50 Hong Kong dollars), higher than the theoretical index of 15124 points, 76 points. Assume that the market interest rate was 6%, and is expected to receive 5,000 yuan a month in cash dividends.
Step 1: Ask a Hang Seng Index futures contracts, traded price of 15200 points to 6% annual interest rate loans to 750,000 Hong Kong dollars, buy the appropriate package of equity portfolio;
Step 2: One month later, received 5,000 Hong Kong dollars, according to a 6% annual interest rate loan;
Step 3: In a few months, to the delivery period. At this juncture, the two cities at the same time period of the current open positions. (Period is consistent with the current delivery price)
Different when the index delivery, the results are different. As illustrated below:
Can be seen, regardless of the level of the final delivery price, the traders from the number of recoverable resources are the same 760,000 Hong Kong dollars, coupled with recovery of principal and interest loan of HK 5000 and HK 5050, a total of 765.05 thousand Hong Kong dollars to recover the funds;
Step 4: repayment, 750000 Hong Kong dollar 3-month Hong Kong dollar interest rate 11250, for a total principal and interest is also required to 761.25 thousand Hong Kong dollars, while Hong Kong dollar 765050-761250 = 3800 net profit for the traders to obtain. Exactly equal to the actual period of year with the theoretical value of the price difference (15200-15124) × 50 = 3800 HK dollar.
Description:
The use of futures prices of the actual price is inconsistent with the theory, while the current period of two cities in the opposite direction in order to cash in profits trading transactions is called Arbitrage. Current price of overvalued when buying stock at the same time period selling price, usually called the positive arbitrage; current price of undervalued and selling stock, buying futures, called reverse arbitrage.
Because arbitrage is present between the two cities at the same time period, profits lock, regardless of price change, will not be any risk, Gu Chang will be referred to as risk-free arbitrage Arbitrage, and the corresponding profit is called risk-free profits. In theory, this carry trade without capital, because the funds are borrowing, and the required interest payments have considered, then the arbitrage profit in fact is already a net profit after deducting opportunity cost and is not this the Lee.
If the actual forward price is neither over-nor underestimated, the spot price exactly equal to theoretical futures price, arbitrageurs will obviously be unable to obtain arbitrage profits. The above example does not take into account transaction costs, Securities Lending issues, interest rates and so on, the actual operation, will exist no arbitrage interval. In the no-arbitrage interval, the carry trade, instead of getting profit, but will lead to a loss.
Assume that TC is the total number of all transaction costs, then:
Arbitrage-free interval should be the upper bound of F (t î–?T) + TC = S î—?t î—?î™?1 + î—?r-d î—?î–?î—?T-t î—?/ 365 î™?+ TC;
Arbitrage-free interval should be the lower bound of F (t î–?T)-TC = S î—?t î—?î™?1 + î—?r-d î—?î–?î—?T-t î—?/ 365 î™?TC
Borrowing costs and interest rates related to the length of the holding period, with the decrease of the holding period decreases, when the holding period is zero (ie, delivery days), borrowing costs are zero difference in interest rates; while transaction costs and market impact cost is and independent of the length of the holding period. Therefore, the no-arbitrage interval width of the upper and lower bounds mainly by the cost of transaction costs and market impact cost of these two decisions.
