STOCK PORTFOLIO HEDGING WITH DERIVATIVES Madalina Cojocaru Petrila Darius Cipariu Mentor: Professor Thomas Krueger July 15 th, 2005

STOCK PORTFOLIO HEDGINGWITH DERIVATIVES

STOCK PORTFOLIO HEDGINGWITH DERIVATIVES

Madalina Cojocaru PetrilaDarius Cipariu

Mentor: Professor Thomas KruegerJuly 15th , 2005

United States stock marketUnited States stock market

New York Stock Exchange (NYSE) - founded in 1792 and was named New York Stock & Exchange Board until 1863

National Association of Securities Dealers Automated Quotation System (NASDAQ) – an electronic stock exchange founded by the National Association of Securities Dealers (NASD)

United States Exchange IndexesUnited States Exchange Indexes

The Dow Jones Industrial Average - is the oldest and most watched index The NASDAQ Stock Market composite (IXIC) - is composed of all the stocks on the NASDAQ exchange – more than 5,000 firms

The Standard & Poor’s 500 Index (S&P500) – is a market weighted index - tracks 500 of the most representative companies based in the US selected upon size, liquidity and sector

Romanian stock marketRomanian stock market

Bucharest Stock Exchange was re-opened in 1995 and launched the first official index in September 1997: BET – Bucharest Exchange Trading index

Rasdaq Electronic Exchange was designed for filling the trading needs as a result of mass-privatization program and launched the first official index in July 1998: RAQ-C – Rasdaq Composite index

Stock PortfolioStock Portfolio

Steps in order to build a portfolio:

Setting the objective Setting the time horizon Choosing the stocks

Stock PortfolioStock Portfolio

Strategies for choosing the stocks: Buy and hold Market timing Growth Value GARP Income

Stock SelectionStock Selection

Fundamental analysis: Earnings per share Dividend Payout Ratio Return on EquityTechnical analysis: Chart patterns analysis

Stock portfolio protection with derivatives


Risk of stock portfolio: price DECLINE in the stock market

Hedging: “Taking a position in a futures or option market opposite to a position held in the cash market to minimize the risk of financial loss from an adverse price change.”

Position cash market: LONG Position in futures market: SHORT

¹ www.liffeweather.com/glossary.aspx



By using derivatives instruments a portfolio manager can preserve or improve the value of a stock portfolio.

Hedging: “Taking a position in a futures or option market opposite to a position held in the cash market to minimize the risk of financial loss from an adverse price change.”

Risk: DOWNTREND in stock market Cash market position: LONG on stocksFutures market position: SHORT on stocks or indexOption market position: LONG PUT OPTIONS on stock or index

¹ www.liffeweather.com/glossary.aspx



Derivatives instruments used to protect a stock portfolio

Single stock futures - One Chicago, SMFCE

Equity Index futures - CME, CBOT

Single stock options - CBOE

Equity options - CBOE

Options on futures - CME, CBOT, SMFCE

Stock portfolio hedging with single stock futures


Single stock futures contract : an agreement to deliver a certain amount of shares of a specific stock at the expiration date.

In the USA, over 200 stocks are traded at One Chicago.In Romania 19 stocks are traded at SMFCE.

Position cash market: LONG Position in futures market: SHORT



Example – Best Buy Co (BBY)

gain

loss

LONG BBY

(NYSE)

SHORT BBY

(One Chi)

BBY cash price

55 68

NYSE

LONG 1,000

BBY shares at $55 One Chicago

SHORT 10 BBY

contracts at $68

(1 futures = 100 shares)

Value of BBY shares ensured:

1,000 x $68 = $68,000



1 2 3 4

BBY price

at futures expiration date

Stock market

(NYSE)

Futures

(One Chicago)

Net result

(2+3)

BBY (NYSE)<$68

Assume BBY = $60

1,000*60

= $60,000 (68-60)*10*100

= $8,000

$60,000 + $8,000 =

$68,000

BBY (NYSE) = $68

1,000*68

= $68,000

(68-68)*10*100

= 0 $68,000 + 0=

$68,000

BBY(NYSE)>$68

Assume BBY = $75

1,000*75

= $75,000

(68-75)*10*100

= - $7,000

$75,000 – $7,000=

$68,000

Stock portfolio hedging withequity index futures


The stock index futures contract has the same specifications as the single stock futures contract, the only difference arising from the underlying assets which is not a specific number of stocks, but a specific number of index units.

At the expiration date, all settlements are in cash because of the nature of the indexes (they are just abstract numbers and not physical items like agricultural commodities for example).



The principle of using stock index futures for hedging purpose is the same like in the single stock futures situation: a long position in the stock market will be offset by a short position taken in the stock index futures market.

Most traded indexes on the US futures markets:

S&P 500, DJIA, NASDAQ



The number of futures contracts that must be sold in order to hedge a stock portfolio is called hedge ratio and is computed by using the following formula:

Dollar value of portfolio

HR = * beta of portfolio

Dollar value of S&P 500

index futures contract



Number of SPX Sep 05 futures contracts needed to be sold in order to protect the $10,000,000 portfolio:

10,000,000

HR = * 1.1 = 36.72 (37 rounded).

250 x 1,198



1 2 3 4

S&P 500 value price at futures expiration

date

Stock market Futures Market Net result

(2+3)

S&P 500 < $ 1194

Assume

S&P 500 = 1,100

(decrease of 7,87%)

10m –

(10m * 7,87%) * 1.1

= $9,134,300

37 * 250 *

(1,198 – 1,100)

= $906,500

9,134,300

+ 906,500

= $10,040,800

S&P 500 = 1,194 $10,000,000 37 * 250 *

(1,198 – 1,194)

= $37,000

10,000,000

+ 37,000

= $10,037,000 S&P 500 > $ 1194

Assume

S&P 500 = 1,230

(increase of 3.015%)

10m* +

(10m * 3.015% * 1.1)

= $10,331,650

37 * 250 *

(1,198 – 1,230)

= - $296,000

10,331,650

- 296,000

= $10,035,650

Stock portfolio hedging withoptions

Stock portfolio hedging withoptions

Options give the buyer the right, but not the obligation to buy or sell the underlying asset at the strike price until the expiration date of the contract. The buyer must pay a premium to the seller of the option.

In this situation, the underlying asset means a stock, an equity index or a futures contract.

The best hedging strategy with options means to buy PUT options on single stock or equity index.

Stock portfolio hedging withPUT options

Stock portfolio hedging withPUT options

Number of Puts needed to be sold in order to protect the stocks purchased on the cash market is given by the

formula of hedge ratio:

Dollar value of portfolio 1

HR = * Contract value Delta

Delta is a specific element of options and shows how an option price changes for a given change in the underlying asset.

Thank youThank you

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STOCK PORTFOLIO HEDGING WITH DERIVATIVES Madalina Cojocaru Petrila Darius Cipariu Mentor: Professor Thomas Krueger July 15 th, 2005