5138 5607 chapter 7 - single stock futures and stock index futures

Chapter 7

Single Stock Futures and Stock Index
Futures

© 2011 Dorling Kindersley (India) Pvt. Ltd

Objectives of the Chapter
 Understanding what a single stock future is

 What the uses of single stock futures are

 How such futures are priced

 What stock indexes and index futures are

 What the uses of stock index futures are

 How stock index futures are priced

 The concept of index arbitrage and portfolio insurance


Single Stock Futures

 Single stock futures are those with the stock of a
company as the underlying asset

 By taking short or long positions in single stock
futures, the investor agrees to either sell or buy a
specified number of stocks at the prevailing price
in the futures market at the time of agreement, at
the maturity date


Specifications of Single-Stock
Futures

 Listed in the NSE/BSE
 Trading cycle of three months
 Expiry date is the last Thursday of the month
 Contract size is specified by the exchange
 Daily settlement price is the weighted average of
prices in the last half-hour of trading
 Subject to marking-to-market on a daily basis
 Final settlement will be in cash, not delivery


Example to Calculate Margin and
Final Settlement
 ICICI March Futures selling at INR 1230 on Feb 1

 Contract size = 175 shares

 Margin = 5% of contract value

 ICICI share price on March 28, contract maturity is
INR 1260

 Calculate the settlement amount on March 28:

 Settlement amount = (1260 – 1230)*175 = INR 5,250


Hedging with Single Stock Futures I
 Single stock futures can be used to hedge the
price risk of the shares of a company

 If an investor holds stock and expects the price to
drop, he will go for a short hedge by selling
futures

 If an investor plans to buy the shares at a future
tme and expects the price to increase, he will go
for a long hedge by buying futures


Hedging with Single Stock Futures II

The number of contractsto use is based on the hedge ratio, calculated as :
s
h* *
F

* NA
N* h
QA


Example of Short Hedge with Stock
Futures
 On Jan 10, you own 2400 shares of Canara Bank, and are
planning to sell them on February 25. The contract size is 800
shares.

 February futures expiring on February 25 are priced at INR 272
and you take short position in futures.

 On February 25, Canara Bank shares are selling at INR 265.

 What is the net price received per share if you sell them on
February 25?

 Cash settlement received = (272 – 265)*800*3 = INR 16,800
 Sales receipt = 265*800*3 = INR 636,000
 Net receipt per share = 652,800


Example of Long Hedge with Stock
Futures
 On January 10, Biocon Futures are selling at INR
245.00, and you plan to buy 7,200 shares on
February 25 when Feb futures expire.
 Contract size for Biocon = 1800 shares
 On February 25, Biocon sells for INR 270.
 You would go for a long hedge buying 4 Biocon
futures at INR 245
 On February 25, you receive a cash settlement of
4*1800*(270-245) = INR 180,000
 Payment for 7200 shares = 7200 * 270 = 1,944,000
 Net payment = 1,764,000/7200 = INR 245

Risks in Hedging Using Stock
Futures
 Stock futures will protect against downside risk, but all
upside potential will be lost
 If the price moves in favour of the hedger, hedging will
result in a loss compared to not hedging at all
 The hedger should decide whether to hedge or not
based on their expectations of future price movement
 Other risk is basis risk, which arises when
 Futures are not available on the shares you want to
hedge
 The number of shares to be hedged is not an exact
integer multiple of the future contract size
 The time to end-of-exposure is different from contract
maturity


Speculation Using Stock Futures
 Speculators believe that the price will move in a
particular direction over a short period of time

 Stock futures are cheap means of speculating on
share price movement

 If price is expected to move higher or lower, a long or
short position respectively will be taken in futures

 Speculation is risky, as losses can be high if the price
moves in the opposite direction

Example of Speculation Using Stock
Futures
 IOC shares are selling at INR 800 on March 1. April
futures with a contract size of 600 shares are priced
at INR 820.
 You believe that IOC share price will increase to INR
840 by March 5 and want to speculate
 You can take a long position in April futures
 If the IOC share price on March 5 is INR 840, and
April futures are priced at INR 862, then the
speculative gain by closing futures on March 5 =
600*(862 – 820) = INR 25,200
 If the IOC share price falls instead to INR 780 by
March 5, causing the futures price to be at INR
792, the loss would be 600*(820 – 792) = INR 16,800


Pricing of Stock Futures
 Stock futures on stocks that do not pay dividends
during futures are priced based on cost-of-carry
model as:
F0 = S0 * erT
where r = risk-free interest rate and T = maturity
of futures in years

 If the stock pays dividends of D at time t,
F0 = S0 * erT – D * er(T – t)


Pricing of Stock Futures – Example
 ICICI Bank shares are selling at INR 1250 on
January 1
 Feb futures expiring on February 27 are available
 Risk-free rate = 6%/year
 Futures price = 1250 * e(0.06)*(58/365) = INR 1261.98
 If ICICI pays a dividend of INR 10 on Jan 21, then
 Futures price = 1250* e(0.06)*(58/365) – 10 * e(0.06)(58-
21/365) = INR 1251.91


Stock Futures and Arbitrage
 Pricing relationship is theoretical value based on current
share price

 If the actual futures price is different from the theoretical
value, arbitrage opportunity exists

 If futures are overvalued, sell them and buy shares

 If futures are undervalued, buy futures and short-sell
shares

 Futures price may be based on expectations about futures
and arbitrage may not be possible


Arbitrage Example
 IOC shares are selling at INR 800 on March 1
 April IOC futures are priced at INR 820 with maturity on
April 27
 Theoretical futures value: 800 * e(0.06)*(58/365) = INR 810.23
 Futures are overvalued and hence, one would sell futures
and buy shares

 On March 2, IOC shares are selling at INR 810 and futures
are selling at a theoretical value of INR 820.18. One would
close the position in futures and sell shares.
 Gain from shares: INR 10
 Loss from futures: INR 0.18
 Net gain: INR 9.82


Stock Futures and Insurance

 Stock futures can be used to insure a minimum
value for the share price in the future

 This can be accomplished by borrowing money at
risk-free rate, selling futures and buying shares

 This strategy will provide a known value of shares
at futures maturity


Stock Futures and Insurance --
Example
India Cements shares are priced at INR 135 on
January 1. The contract size is 1450. January
futures, with expiry on January 29, are priced at
INR 135.75. The risk-free rate is 7%. You sell the
futures on January 1. Value of portfolio on
January 29:
Share Value of Gain from Interest Value of
price Shares Futures Paid Portfolio

130 188500 8337.50 1091.73 19575.77
135 195750 1087.50 1091.73 195745.77

140 203000 -6162.50 1091.73 195745.77

Stock Futures and Investment
 Using stock futures and risk-free investment, one
can get the same value as the value of investing
in shares directly

 Using this principle, one can create synthetic
positions as follows:
 Long futures  long stock + Risk-Free Borrowing
 Short futures  short stock + risk-free borrowing
 Long stock  long futures + risk-free investment
 Short stock  short futures + risk-free borrowing


Stock Indices
 Index captures the overall behaviour of a group of
stocks

 Index is created by selecting a group of stocks that
are representative of the whole market, or a specified
sector

 Index backs the changes in the value of portfolio of
stocks

 Based on index, index funds, index futures and
options are created


Index Futures
 Index futures use a particular stock index as the
underlying asset

 Index futures are used to hedge equity portfolio
risk

 Index futures are also used for speculative
purposes

 These can also be used for portfolio insurance


Contracts Traded in India
Index Futures Contract Multiplier
BSE 30 Sensex Futures 15
BSE Sensex Mini Futures 5
BSE Teck Futures 124
BSE Bankex Futures 25
BSE Oil and Gas Futures 38
NSE CNX Nifty Futures 50
NSE CNX Nifty Mini Futures 20
NSE CNX IT Futures 100
NSE Bank Nifty Futures 50
NSE Nifty Midcap 50 Futures 300


Example of How Index Futures Work
 CNX Nifty Index is at 5200 on December 1
 CNX Nifty Index futures with expiry on December 28 is at
5232
 If CNX Nifty Index is at 5300 on December 28, the long
hedger will gain, and the short hedger will lose

Value of futures on December 1 = 5232 * 50 = INR 261,600
Value of futures on December 28 = 5300 * 50 = INR265,000
Gain for long hedger = (265000 – 261600) = INR 3400
Loss for short hedger = (261600 – 265000) = INR 3400

The long hedger will bet that the index will increase, and the
short hedger will bet that the index will decrease


Pricing of Index Futures
 Index futures are priced using the cost of a carry
model, as
Ft St D* e rT

Ft St e ( r d )T
Or,

 Where D* = present value of dividends from all
stocks, and d = dividend yield on the index


Example of Pricing on Index Futures
On December 1, CNX Nifty Index is at 5200. CNX
Nifty futures with maturity on December 28 and
January 25 are available.
The risk-free rate is 8%
The dividend yield on the index is 2%

December futures price = 5200*exp [(8%–%)28/365 ]
= 5224
January Futures Price = 5200*exp [(8%–2%)56/365]
= 5248

Speculation Using Index Futures
 Speculators who believe that the market as a
whole will perform better in the future will buy
index futures, and will gain if the index value
increases beyond the contracted futures price

 Speculators who believe that the market as a
whole will perform poorly in the future will sell
index futures, and will gain if the index value
decreases


Portfolio Insurance Using Index
Futures

 Index futures can be used to provide a minimum
futures value

 Portfolio insurance strategy calls for going short in
futures so that gain in futures will exactly offset
the loss, and vice versa such that the loss in
futures will exactly offset the gain


Index Arbitrage
Theoretical price = Ft = St e–(r – d)(T – t)

 If the market value of futures is different from the
theoretical value, arbitrage opportunity arises
 If market value exceeds theoretical value, one
should sell futures and buy underlying shares of
the index using risk-free borrowing
 On the other hand if the market value is less than
the theoretical value, one should buy futures,
short-sell underlying shares of the index, and
invest in risk-free securities


Program Trading

 Program trading refers to automatic trading
triggered by computers whenever there is an
index arbitrage opportunity


Hedging Portfolio Value Using Index
Futures

 One would hedge portfolio value by selling index
futures
 This strategy provides gains from futures if the
market index goes down

S
 Optimal number of futures =
F

 Where = beat of the portfolio, S = portfolio
value, and F = value of futures contract = futures
price x multiplier


Example of Hedging Portfolio Value
On January 1, portfolio value = INR 500,000,000
Nifty Index = 5250
Risk-free rate = 8%; dividend yield = 2%
March futures at 5325.62, expiry on March 28
Value of futures = 5325.62 * 50 = INR 266281
Beta of portfolio = 1.2
Number of contracts to sell = (1.2 * 500,000,000)
/266281 = 2253
On Feb 28, Nifty is at 5100
Futures price would be 5107.83


Example of Hedging Portfolio Value:
Value of Portfolio
Change in index = (5250 – 5100)/5250 = -2.857%
Dividend yield = 2% per year = 2 (59/365) = 0.32%
Return on index = -2.857% + 0.32% = -2.527%
Expected return on portfolio = 8% (59/365) + 1.2 [-2.527 –
(8% (59/365) ) = -3.3%

Portfolio value = 500,000,00 (1 – 3.3%) = 483,503,718
Gain from futures = 2253*50 (5325.62 – 5107.83) =
24,534,044
Hedged portfolio value = 483,503,718 + 24,534,044
Hedged portfolio value = 508,031,762


Adjusting Equity Beta
 Beta measures the sensitivity of a portfolio return
to market return
 If the market is likely to do well, the appropriate
strategy is to increase the beta of the portfolio
 If the market is likely to fall, one should decrease
the portfolio beta
 Adjusting beta by buying or selling shares is
costly
 Can be accomplished using futures


Adjusting Equity Beta Using Futures
T S S
Optimal number of contracts NF
F F

If the beta is to be increased, NF will be
positive, and futures must be bought

If the beta is to be decreased, NF will be
negative, and futures must be sold


Issues in Index Futures
 Index underlying futures may not match with a
portfolio

 Futures may not be valued correctly

 The number of contracts will be rounded

 Beta may be inaccurate

 Hedge may have to be lifted before maturity

 Borrowing and lending rates might differ


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