Delivery Standardisation: When a particular bond is delivered, a parameter known as its "Conversion Factor" (to be explained later) defines the price received by the party with the short position (the seller). Thus the cash received for each PKR 100 face value of the delivered bond is amended to include the conversion factor thus: (Quoted Futures price x Conversion factor) + Accrued interest. In the foregoing example, assume the conversion factor is 1.38. Then the cash price would be:(95.50 x 1.38) + 1.64 = 133.43 (PKR 133,430). Since bonds issued at various times in the past have varying coupons, for convenience of trading, these are standardised using a hypothetical fixed coupon rate...determined by regulators...say 6%. Also, by convention, bond maturities and the times to the coupon payment dates are rounded down to the nearest three months for purposes of calculation.
This practice allows a Futures Exchange to produce comprehensive tables of Conversion factors. If, after rounding, the bond lasts for an exact number of six-month periods, the first coupon is assumed to be paid after six months. If, after rounding, the bond does not last for an exact number of six-month periods (ie there is an extra three months), the first coupon is assumed to be paid after three months and accrued interest is subtracted.
Calculating Conversion Factors: Consider a 10% coupon bond with 10 years and two months to maturity. For the purposes of calculating the conversion factor, assume the bond has exactly 10 years to maturity. The first coupon payment is assumed to be made after six months. With the hypothetical discount rate approved by SECP being 6%, the value of such a bond is:
Si=120 5 / (1.03)I + 100 / (1.03)20 = PKR 129.75 Dividing by the face value, this gives a conversion factor of 1.2975 for such a bond. Thus all that a conversion factor does is to translate any coupon rate bond into a standard 6% coupon bond.
As another, slightly more complicated, example of the rules of standardisation, consider an 8% coupon bond with 8 years and four months to maturity. For purposes of calculating the conversion factor, the bond is assumed to have exactly 8 years and three months to maturity. Hence, discounting all the payments back to a point in time three months from today at 6% per annum (compounded semi-annually) gives a value of:
Si=116 4 / (1.03)I + 100 / (1.03)16 = PKR 112.56, But this value is what the bond will be worth three months from today. It needs to be discounted by the interest rate factor for three months (ie by v 1.03 - 1 = 1.4889%). Thus, the foregoing value discounted to the present becomes:
112.56 / 1.14889 = 97.97 And, since this value contains one quarter (3 months) accrued interest that rightfully belongs to the holder to date, we must subtract PKR 2 (one quarter's coupon payment), yielding the correct value of the bond as PKR 95.97. The corresponding conversion factor for this bond is therefore 0.9597.
Cheapest to deliver Bond: In the bond futures market, the party that has a short bond position may deliver any one of several bonds during the delivery month on a date of its choosing. Obviously, it will choose the "cheapest to deliver" bond. Because the party with the short position receives cash equal to:
(Quoted futures price x Conversion factor) + Accrued interest... (1)
And its cost of purchasing a bond is Quoted Spot Price + accrued interest... (2) Therefore, the cheapest to deliver bond is one for which (2) - (1) is minimum, or (Quoted futures price x Conversion factor) - Quoted Spot price is minimum.
Once the party with the short position has decided to deliver it can determine the cheapest-to-deliver bond by examining each of the bonds available in turn. As an example, let's assume that the current futures price is quoted as 93.25, and the following three bonds are being considered.
The relevant calculations to determine the cheapest to deliver bond are then:
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Bond 1. 99.50 - (93.25 x 1.0382) = PKR 2.69
Bond 2 143.50 - (93.25 x 1.5188) = PKR 1.87
Bond 3 119.75 - (93.25 x 1.2615) = PKR 2.12
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Clearly, Bond 2 is the cheapest to deliver and will be chosen by the short party. A number of factors determine the cheapest-to-deliver bond. When bond yields are in excess of 6% (or whatever benchmark rate is chosen by regulators), the conversion factor system tends to favour delivery of low-coupon, long-maturity bonds.
When yields are less than 6%, the system tends to favour delivery of high-coupon, short-maturity bonds. Also, when the yield curve is upward sloping, there is tendency for bonds with a long time to maturity to be favoured, whereas when it is downward sloping, bonds with a short time to maturity will be delivered.
Determining the Quoted Futures Price: In all of the foregoing, we have still not discussed how the bond's Futures price is determined. Theoretically, a bond's Futures price is related to its Spot price by the relationship:
F = (S - I) x e r.T Where F = Futures price, S = Spot price, I = present value of all coupon payments during the life of the Futures contract, r = risk-free interest rate, and T = length of time period.
EXAMPLE: Suppose that, in a Treasury bond futures contract, it is known that the cheapest to deliver bond will be a 12% coupon bond with a conversion factor of 1.4000. Suppose also that we know delivery will take place in 270 days. Coupons on the bond are paid semi-annually as shown in the following diagram. Suppose spot price of bond is quoted as PKR 120.
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Bond Quoted Price (PKR) Conversion Factor
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1. 99.50 1.0382
2. 143.50 1.5188
3. 119.75 1.2615
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Coupon Current Coupon Maturity of Coupon
Payment time Payment futures Contract payment
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60 122 148 35
days days days days
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According to the diagram, the last coupon payment date was 60 days ago, and the next coupon payment date is in 122 days. Thereafter, the next coupon payment date is 305 days from today (122+148+35). Let's also assume that the term structure of interest rate is flat, and the rate of interest (with continuous compounding) is 10% per annum.
The cash price is therefore the spot price plus interest accrued and payable to existing bondholder for the elapsed 60 days of the accrual period consisting of the sum of 60 and 122 days shown on the left side of the diagram:
120 + [60 / (60 +122)] x 6 = 121.978 Going forward from current time, coupon of PKR 6 will be received in 122 days (=0.3342 years). The present value of this is:
6 x e-0.1 x 0.3342 = 5.803 The futures contract lasts for 270 days (0.7397). The cash futures price if the contract were written on the 12% bond would therefore be:
(121.978 - 5.803) x e0.1 x 0.7397 = 125.094 But wait, from this we still have to deduct accrued interest for 148 days to maturity of the futures contract thus:
125.094 - 6 x [148 / (305-122)] = 120.242 Finally, to get the quoted futures price, we divide by the conversion factor of 1.4000 to get:
120.242 / 1.4000 = 85.887 The foregoing should suffice to drive home the point that a bond futures market is not for the uninitiated and the unlettered like the vast majority of traders abounding in our premier stock market, the KSE. Moreover, NCEL, if it does become operational, will first itself have to train its own senior management and staff before it can launch bond futures. The same goes for its regulator, the SECP.
EQUITY INDEX FUTURES: In contrast to fixed-interest securities, a share has no certain income stream, since dividends may be cut, passed or increased, and there is no pre-arranged date for their payment. Dividend income has therefore to be estimated in the case of an equity index futures contract. The historical dividend yield is usually used as an approximation of the expected income flow.
It is usually assumed that the dividends provide a known yield rather than a known cash income. If q is the dividend yield, then the futures price is given by:
F = S x e(r-q)T Let's assume that either KSE or NCEL (or both) have begun trading KSE-100 Index futures, and we are considering three months Index futures. Suppose that the stocks underlying the Index provide a dividend yield of 2% p.a. (remember yield is not the same thing as annual dividend rate. When PSO, with its share price at PKR 375, declares a 75% annual dividend, its yield is only 7.5/375 = 2.00%), the KSE-100 Index stands at 7,220, and the continuously compounded risk-free interest rate is 6% p.a.
In this case, r = 0.06, S = 7,220, q = 0.02, and T = 0.25. Hence, futures price, F, is given by F = 7,220 x ee(0.06-0.02) x 0.25 = 7,292.5. Now, that is a lot easier to calculate than bond futures, isn't it?
CURRENCY FUTURES: The fair value of a currency futures contract is largely determined by the interest rate differential between deposits in different currencies (interest rate parity). The easy part is that currency futures are calculated just like equity index futures, and all one has to do is to replace dividend yield by the risk-free interest rate of the foreign currency in the formula described above.
THEORETICAL, BID AND OFFER PRICES: The calculation of the fair value of a futures contract is a theoretical exercise and need not be the actual price quoted in the futures market. The fair value (or theoretical price) is a value only in the eye of the beholder, while the actual futures price quoted is a function of supply and demand factors for a particular contract.
However, arbitrage operations will ensure that the actual futures prices quoted do not differ too much from their theoretical values. It is mainly differences in impact costs that lead to differences between the theoretical prices and actual futures prices quoted.
The actual futures prices quoted are split into bid (buying) and offer (selling) prices. Investors always buy at the higher price and sell at the lower price to dealers, while futures dealers buy at their bid price, which is always lower than their offer price. The difference between the bid and offer price is the profit margin for the dealer.
FUTURES MARKETS: Futures markets generally display the following major characteristics:
-- Contracts are traded either by open outcry on a centralised exchange or on electronic exchanges (ie exchanges without a centralised floor, using automated trading systems, through which transactions take place by means of a computer network);
-- Contracts are highly standardised, with trading in specific months for specific quantities of products;
-- Underlying commodities or financial securities are delivered through a clearing system, and the clearing house guarantees the fulfilment of contracts entered into by clearing members;
-- Actual delivery against futures contracts tends to be rare;
-- Liquidity has to be high for a futures contract or such a contract tends to "die";
-- Trading costs tend to be relatively low;
-- All futures contract prices are publicly disclosed; and
-- Profits and losses on futures contracts have to be settled daily (mark-to-market).
The aim of all these regulations is to reduce the transaction and information costs for standard types of contracts.
FUTURES MARKET PARTICIPANTS: The participants in the futures market can be divided into four main groups, viz. hedgers, speculators, and arbitrageurs.
HEDGERS: A hedger can be defined as anyone who has a significant price or interest rate exposure in the cash market, and who wishes to reduce this risk by taking an opposite position in the futures market. The most important hedgers are financial institutions (such as banks, insurance companies, and mutual funds), commodity producers (gold, wheat, sugar, etc), and corporate treasurers with interest rate, currency or investment risk exposures.
For this group, regulators allow futures exchanges to set low margin requirements for trading positions, often in the range of 0-15%.
SPECULATORS: A speculator can be defined as anyone who uses the futures market for capital gain only. Speculators provide the liquidity necessary to ensure that, whenever a hedger requires a hedge position, the market is able to absorb his or her trade without undue disturbance to the current price.
A speculator accepts the risks of adverse price changes, thereby allowing the hedger to reduce his or her risks at the cost of forsaking any potential profits to be gained from favourable price movements. Speculators are confined mainly to brokers and professional traders.
Since most speculative activity is based on naked or one-sided positions, exchanges usually levy heavy margins on this group...often ranging to as high as 50%.
ARBITRAGEURS: Arbitrage means the simultaneous purchase and sale of the same asset in different markets (eg the cash market versus the futures market) to profit from differences that may exist between these markets. Arbitrageurs seek risk-free profits, thereby ensuring that futures prices converge with cash prices on close out, and that futures prices will not exceed cash prices by more than the net carry costs plus transaction costs.
Usually arbitrage operations account for about half of all trade in the futures markets. Because arbitrage by definition is a covered trade, exchange margins are set at zero.
(Concluded)
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