Principles of Futures

Cost of carry includes: The opportunity cost, that is, the cost of

financing the asset, Any storage-related costs, Maintenance, Insurance, Tax

Convenience yield

Convenience yield accrues to the owner of the physical assets which includes:

-Rent,

-Royalties,

- Utility of consumption,

-profiting from temporary shortages,

- Collateral

Stock Index Futures

The underlying instruments in stock index futures are stocks in the composite indices such as:

- Standard & Poor’s 500 (S&P 500),

- Nasdaq 100,

- and other stock indices. The cost of carry is equal to the opportunity cost of

financing the stock (r) less the dividend income (convenience yield) that are assumed to be proportional to the spot price.

Index Arbitrage

Example: It is August 2, 2002. The S&P 500 index is at 864.24, and September futures is priced at the close of the business at 864.90. The three-month T-bill is priced to yield 1.61 percent. The implied dividend yield on the S&P 500 index is estimated to be 1.29 percent.

What is the fair value of the S&P futures Is there an arbitrage profit? Had the futures price been 870, what would you do to

profit. Had the futures price been 860, what would you do to

profit.

Example: It is July 17. A portfolio manager at NPR is concerned over the increased volatility of the market and plans to hedge his $430 million growth portfolio over the next three months. The beta of his portfolio is 1.65. The December futures contract for the S&P 500 index is currently quoted at 874.5. The value of each futures contract is 250 times the value of the index.

What actions you would take to protect the value of the portfolio over the next three months?

What is the hedge ratio? Show what happens if the market drops by 8 % over the

next three months. Show what happens if the market advances by 5 % over

the next three months.

Hedging with futures/options

What is the downside for hedging with futures? What is the basis risk? What is the downside hedging with options? How would you reconcile differences in hedging

with options and futures?

Option Quote

It is August 12, and a portfolio manager of a growth fund with a portfolio worth $200 million in stocks with a beta of 1.65 is concerned about falling stock prices in October and is planning to buy S&P 500 index futures options at a strike price of 900.

- How much premium he pays to buy October option?

- What action portfolio manager can take to pay for the cost of option?

- Is zero collar possible in the above case?

Example

Pricing T/Bond Futures

The price of T-bond futures is related to: Spot price Less PV of any income Less value of any options (delivery options)

Duration based hedging

Δ F = - Df F. Δ Y

Δ S = - Ds .S. Δ Y

Where F is the contract price of the futures Df is the duration of the futures

Ds is the duration of the spot

S is the market value of the spot Rf is the yield on the futures (the forward rate)

Rs is the yield on the spot portfolio

Hedge ratio

Hedge ratio in interest rate futures Market

h = [Ds .S. (1+Rf )] / [Df .F. (1+Rs)]

Hedge ratio in the Stock index futures

h=B* S/F Where B is the beta of the portfolio, and S

and F are market value of spot and futures

Price of 2-year spot, 2.25 % coupon = 100 1/32 Price of 2-year Sept futures = 106.4844 CF for this contract according to CBOT as of

September 02 was .9358 The party with short position receives:Futures price X CF= 106.4844*.9358=$99.648 The party with short position pays at settlement

the spot price for the CTD

Delivery Process

Day 1. The short serves notice of intention for deliver to the clearinghouse,known as positions day.

Day 2. The clearinghouse notifies both long and short and matches the oldest long to the short that is expected to deliver and invoice the long, known as notice of intention day.

Day 3. The short delivers the cheapest-to-deliver issue to long; in return, the long makes payment to the short and assumes title to the instrument.

Delivery Options

Delivery Options: Identification of the deliverable instrument that satisfies the exchange requirements as well as the requirement of the party with the short position which should be the cheapest instrument to be delivered, known as quality option.

Timing Option: The option that is afforded to the party with short position the timing in delivery month to deliver.

Wild Card Option: The option to deliver after the closing bell at 2 PM CST, until 8 pm if prices in the T-bond spot drops and the party with short position proceeds to purchase the cheapest issue for delivery.

The Cheapest to Deliver

The party with a short position receives:

(Quoted futures price x conversion factor) + accrued interest

The cheapest to deliver (TCD) the T-bond is estimated by the party with the short position as the issue from among the acceptable issues having the highest implied repo rate and makes delivery at settlement date. The party with the short position pays to purchase the T-bond:

Quoted price + Accrued Interest

Cheapest to deliver (CTD) issue

T/bond Futures

Anticipatory Hedge

It is July 20 and the portfolio manager is expecting to borrow $27 million in three months over a six-month period.

Hedging Strategy  

July 20, 2002: Spot Market The six-month commercial paper is rated to yield

1.78 percent Proceeds per $100: 100- .5(1.78%) (100) =99.110 Effective yield (100/99.11)365/180 –1= .0183

Anticipatory Hedge Continued October 20, 2002: Spot Market: Issue $27

million commercial paper at 2.35 percent Proceeds per $1 million: is $1,000,000-.5

(2.35%) (1,000,000) = $988,250 Effective yield (100/98.825)365/180 –1= .0243 Futures Market: December Eurodollar futures

IMM index is 97.60 Close out the December futures at interest

rate of 2.4 percent The Eurodollar delivery is in cash as

opposed to T/bill.

Futures Market: December Eurodollar futures IMM index is 98.32

Price per $1million is 1,000,000-.25(1.68%) (1,000,000) = $995,800

Implied yield (100/99.58)365/90 –1= .0172 Sell 54 Eurodollar futures Contract

Anticipatory Hedge Continued

The final marking to market on the second London business day before the third

Wednesday of the month will set the Price per $1,000,000:

10,000 (100-.25 (2.4)) = $994,000 Buy 54 Eurodollar futures contract

Anticipatory Hedge Continued

Result  Unhedged position: the effective cost of financing six-

month commercial paper will be 2.43 percent on October 20.

Hedged position: profit on the futures per one contract is $995,800-$994,000 =$1,800

Total profit 54x $1,800 =$97,200 The proceeds from the issue of the commercial paper

on October 20, $26.682750 M The effective proceeds, the cash proceeds plus the

profit in the futures: $26,779,950 Implied yield: (100/99.185)365/180 –1= .0167

Hedging with T-Bond Futures

It is May 9 and a life insurance company who has a portfolio of Treasury bonds currently valued at $35 million with yield of 5.6 percent priced at par and 16 years to maturity. The bonds have to be liquidated in three months to meet obligations.

May 9 Bond market value is $35,000,000 Price of the T/bond futures is 105-23 Price per contract is $105,718.8 Sell 310 contracts

August 9 Proceeds of the bonds at the spot

market$33,159,978.8 The cheapest to deliver bond in the T/bond futures

contract is a 7.25 percent priced at $114.35 per $100 face value with 6 percent conversion factor of 1.1445 and 19 years and 9 months at the maturity. The short invoices the long and receives (quoted futures) x Conversion factor, $105,718.8 x 1.1445 and pays $114,351.6 per one Cheapest to deliver contract.

Buy 310 Cheapest to deliver bond

Results Loss of $1,840,021.2 in the spot market Profit in the T/bond futures: $6,643.56 x 310

= $2,059,503.17 Net profit =$219,481.97

Example: The quoted futures price is 105-23. The following three bonds with their price and respective conversion factors are provided in the following table. Which bond is the cheapest to deliver?

Bond Price Conversion Factor A 127.625 1.308 B 120.25 1.2264 C 110 1.1317

Example

Example: Consider a quoted futures price is equal to 95 –08, the conversion factor for this bond is 1.425 and the bond has $2.5 accrued interest per $100 face value at delivery. The cash paid by the party with the long position and the cash received by the party with short position is therefore equal to:

Cash received by the short seller = 95.25 x 1.425 +2.5

= $138.231