## How to Price an EFP (Exchange Futures for Physical) using Single Stock Futures

**Pricing of the EFP **

An Exchange Futures for Physical (EFP) trade allows for the substitution of a long or short stock position for a long or short SSF position. EFPs allow one to decrease finance charges for long stock positions or increase the interest received on short stock positions. That is because the interest rate built into the price of an SSF and hence its EFP is competitively determined by numerous market participants rather than by a single broker who can set less advantageous margin loan and stock borrow rates. Accordingly, through the EFP, funds can offer their long stock out in return for a SSF that will expire back into long stock at expiration but with returns that are greater than those currently being received for lending the stock to an intermediary.

An EFP is a combination order to sell (buy) an amount of stock and simultaneously buy (sell) a proportionate number of SSFs. Taking a long position in the EFP involves buying the SSF and selling the underlying stock. The stock position becomes flat due to the sale of the existing long stock position and the position now holds a SSF with the same economic exposure. The EFP is priced in interest rates as there is no underlying price risk since the stock and the SSF are equivalents but does involve interest rate risks as the two parties are simply engaging in a loan as they switch positions. Selling the EFP has the opposite positioning as the SSF is sold and the underlying is purchased. Hedge funds and other short sellers who are currently short and paying for the privilege would be able to lower their costs of financing this position by executing an EFP at a much more favorable rate without changing their economic position vis-à-vis the stock moves. Both parties will have the added benefit of removing their current positions from their balance sheets without changing their market position, as SSF are off-balance sheet items.

**Cost of buying an EFP**

The cost of buying an EFP in basis points is determined by solving the following equation for the interest rate (r) that reproduces the EFP ask price from the stock trade price given certain dates and dividend amounts.

F | Price at which the SSF is bought. This price is determined by the price at which the stock is sold plus the EFP Ask Price. |

S | Price at which the stock is sold. |

r | The average bank year, exponential interest rate that reconstructs the EFP and stock trade prices. |

N_{exp} |
Number of calendar days to expiration of SSF. |

D_{i} |
The i^{th} stock dividend payment that goes ex-dividend between now andthe expiration of the SSF. |

N_{i} |
Number of calendar days to the ex-dividend date for the i^{th} stockdividend payment. |

and exp{x} = e

^{x}

Note that F = S + EFP Ask Price.

Once the Interest Rate is known the Basis points Paid is calculated as follows-

An approximation formula for Basis Points Paid is as follows.

This formula is valid when (r N_{exp}) is small compared to 360.

**Amount Received Selling an EFP **

The amount received on selling an EFP also takes into account the estimated dividends in the period and is shown on an annualized basis. The cost of selling an EFP in basis points is calculated by solving the equation below for the Interest Rate that gives us the implied SSF Bid price from a known stock ask price and estimated dividends in the period.

Where,

SSFiBid = Implied SSF Bid Price, which is the sum of the EFP Bid Price and Stock Ask Price

Stock Ask = Stock Ask Price

r = Interest Rate

N_{exp} = Number of days from the day of trade to the expiry of the futures contract

N_{div} = Estimated number of Dividends from the time an EFP is entered into till expiry

D_{i} = Estimated Dividend in the current period

N_{i} = Number of days from the day on which the dividend is received till expiry

Once the Interest Rate is know the Basis points Received is calculated as follows:

An approximate calculation for Basis Points Received can be obtained by using the formula: