Sako MwakaloboINTERNATIONAL BOND MARKETThe international bond market encompasses two basic market segment Foreign bonds EurobondsA foreign bond issue is one offered by foreign borrower to the investor in a national capital market and denominated in that nations currency. e.g. a Germany MNC issuing dollar denominated bonds to US investor.

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Sako MwakaloboEUROBONDEurobond issue is one denominated in a particular currency but sold to investors in national capital markets other than the country that issued the denominating currency. e.g. a Dutch borrower issuing a dollar denominated bonds to investors in the U.K, Switzerland, and the Netherlands.The market for foreign bonds and Eurobonds operate in parallel with the domestic national bond markets, and all three market groups compete with one another

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Sako MwakaloboEUROBONDEurobonds are known by the currency ibn which they are denominated, for example, U.S. dollar Eurobonds, yen Eurobonds and Swiss franc Eurobonds or correspondingly, Eurodollar bonds, Euroyen bonds, and EuroSF bondsThe Foreign bonds frequently have colorful names that designate the country in which they are issued. e.g. Yankee bonds are dollar denominated foreign bonds originally sold to US investor, Samurai bonds are yen denominated foreign bonds, sold in Japan, and Bulldogs are pound sterling denominated foreign bonds sold in the UK

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Sako MwakaloboBEARER BONDS AND REGISTERED BONDSEurobond, Bearer bond, possession is evidence of ownership. The issue does not keep any records indicating who is the current owner of a bond. Registered bonds, the owners name is on the bond and it is also recorded by the issuer, or else the owners name is assigned toe the bond serial number recorded by the issuer. When a registered bond is sold, a new bond certificate is issued with the new owners name, or the new owners name is assigned to the bond serial number.Which one would you like and why?

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Sako MwakaloboFOREIGN BONDSThe foreign bonds must meet the security regulations of the country in which they are issued. These may includeProspectus disclosing the financial information about the issuer and should be available to the would be investorsThey may be required to meet all conditions as local bonds.They may not be sold to the residents of the country concerned.

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Sako MwakaloboGLOBAL BONDSIt is a very larger international bond offering by a single borrower that is simultaneously sold in North America, Europe and AsiaThey follow the bond registration requirements of domestic bonds, but have the fee structure of Eurobonds. They enlarge the borrowers opportunities for financing at reduced costs. Purchasers mainly institutional investors to date, desire the increased liquidity of the issue and have been willing to accept lower yields.

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Sako MwakaloboGLOBAL BONDThe largest corporate bond issue is the $14.6 billion Deutsch Telecom multicurrency offering. The issue includes three US dollar tranches with 5, 10 and 30 year maturities totaling $9.5 billion, two euro tranches with 5,10 year maturities totalling 3 billion, two British pound sterling tranches with 5 and 30 year maturities totaling 950 million and one 5 year Japanese yen tranche of 90 billion.

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Sako MwakaloboPARTICIPANTS IN EUROBOND MARKETPrivate enterprises, for example in France, one of them is RenaultPublic enterprisesFinancial institutionsGovernments and Central BanksInternational organizations, such as World Bank, European Bank of investmentThe industrialized countries seems to have greater recourse to the market; Western Europe is on the top, followed by Japan and USA

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Sako MwakaloboInvestors and financial institutionsThe investors in the Euromarkets are mostly institutional investors, such as insurance companies, mutual funds, pension funds.The principal financial institituions and banks that participate in these issues are of international reputation, namely Dutsche Bank, Paribas, Merril Lynch, Goldman Sachs, Credit Lyonnais.

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Sako MwakaloboORGANISATION OF EUROBOND MARKETThe market can be bifurcated into two segments, namely, Primary market in which securities are issued and the Secondary market in which securities are traded.The figure below indicates the steps involved in a primary issue.

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Sako MwakaloboIssuerSelection of the lead managerSelection of co-lead managers by the lead managerGuarantee syndicate:Lead managerCo-lead managersMajor GuarantorMinor GuarantorSub-major and subMinor guarantorsPlacement syndicate:BanksPlacementsEstablishmentDifferent phases of Euro-issue

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Sako MwakaloboTypes of instruments ( characteristics of Eurobonds

The international bond market has been much more innovative than the domestic bond market in the types of instruments offered to investors. Straight fixed rate issue- these are the most current and represent about three-for the of total volume. The issues have been designated maturity date at which the principal of the bond issue is promised to be repaid. During the life of the bond , fixed coupon payments, which are percentage of face value are paid as interest to the bondholders. In contrast to many domestic bonds, which make semiannual coupon payments, coupon interest on Eurobonds is typically paid annually.

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Sako MwakaloboTypes of InstrumentsFloating rate bonds( FRN)- the interest rate of the bonds is revised every three or six months. Common reference rates are either three or six months US dollar LIBOR.Equity related bonds- there are two types of bonds. Convertible bonds issue allows the investor to exchange the bond for a predetermined number of equity shares of the issuer. The floor value of convertible bond is its straight rate bond values. Bonds with warrants these are straight fixed-rate bonds with the addition of a call option ( or warrant) feature. The warrant entitles the bondholder to purchase a certain number of equity shares in the issuer at the pre-stated price over a predetermined period of time

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Sako MwakaloboTypes of instrumentsZero-coupon bonds are sold at a discount from face value and do not pay any coupon interest over their life. At maturity the investor receives the full face value.Stripped bond is a zero coupon bond that results from stripping the coupons and principal from a coupon bond. The results is the series of zero-coupon bonds represented by the individual coupon and principal payments.

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Sako MwakaloboTypes of instrumentsReverse floating rate bonds- the bonds pay a higher interest rate when the rate of reference decreases. The coupon is fixed at a rate minus- LIBOR so that when LIBOR decreases, the interest rate increases. e.g. suppose Euro-bank offers a rate of 16- LIBOR %; therefore, a LIBOR of 7.5 per cent, the effective rate is 16 8.2%, i.e 7.8%.

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See handout 6 for continuation of stock markets, stock exchange procedures and assessment of shares performance

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Sako MwakaloboThe Nature of DerivativesA derivative is an instrument whose value depends on the values of other more basic underlying variables

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Sako MwakaloboExamples of DerivativesFutures ContractsForward ContractsSwapsOptions

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Sako MwakaloboDerivatives MarketsExchange tradedTraditionally exchanges have used the open-outcry system, but increasingly they are switching to electronic tradingContracts are standard there is virtually no credit riskOver-the-counter (OTC)A computer- and telephone-linked network of dealers at financial institutions, corporations, and fund managersContracts can be non-standard and there is some small amount of credit risk

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Sako MwakaloboSize of OTC and Exchange Markets

Source: Bank for International Settlements. Chart shows total principal amounts for OTC market and value of underlying assets for exchange market

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Sheet:

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

East

West

North

Sako MwakaloboWays Derivatives are UsedTo hedge risksTo speculate (take a view on the future direction of the market)To lock in an arbitrage profitTo change the nature of a liabilityTo change the nature of an investment without incurring the costs of selling one portfolio and buying another

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Sako MwakaloboForward ContractsForward contracts are similar to futures except that they trade in the over-the-counter marketForward contracts are particularly popular on currencies and interest rates

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Sako MwakaloboForeign Exchange Quotes for JPY Jan 22, 2007 (16:23 EST)

BidOfferSpot121.62121.631-month forward121.08121.093-month forward120.17120.186-month forward118.75118.77

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Sako MwakaloboForward PriceThe forward price for a contract is the delivery price that would be applicable to the contract if were negotiated today (i.e., it is the delivery price that would make the contract worth exactly zero)The forward price may be different for contracts of different maturities

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Sako MwakaloboTerminologyThe party that has agreed to buy has what is termed a long positionThe party that has agreed to sell has what is termed a short position

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Sako MwakaloboExampleOn June 3, 2003 the treasurer of a corporation enters into a long forward contract to buy 1 million in six months at an exchange rate of 1.6100This obligates the corporation to pay $1,610,000 for 1 million on December 3, 2003What are the possible outcomes?

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Sako MwakaloboProfit from aLong Forward PositionK

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Sako MwakaloboProfit from a Short Forward PositionK

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Sako MwakaloboFutures ContractsAgreement to buy or sell an asset for a certain price at a certain timeSimilar to forward contractWhereas a forward contract is traded OTC, a futures contract is traded on an exchange

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Sako MwakaloboExchanges Trading FuturesChicago Board of TradeChicago Mercantile ExchangeLIFFE (London)Eurex (Europe)BM&F (Sao Paulo, Brazil)TIFFE (Tokyo)and many more (see list at end of book)

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Sako MwakaloboExamples of Futures ContractsAgreement to:buy 100 oz. of gold @ US$400/oz. in December (NYMEX) sell 62,500 @ 1.5000 US$/ in March (CME)sell 1,000 bbl. of oil @ US$20/bbl. in April (NYMEX)

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Sako Mwakalobo1. Gold: An Arbitrage Opportunity?

Suppose that:The spot price of gold is US$300The 1-year forward price of gold is US$340The 1-year US$ interest rate is 5% per annumIs there an arbitrage opportunity?

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Sako Mwakalobo2. Gold: Another Arbitrage Opportunity?

Suppose that:The spot price of gold is US$300The 1-year forward price of gold is US$300The 1-year US$ interest rate is 5% per annumIs there an arbitrage opportunity?

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Sako MwakaloboThe Forward Price of Gold If the spot price of gold is S and the forward price for a contract deliverable in T years is F, then F = S (1+r )Twhere r is the 1-year (domestic currency) risk-free rate of interest.In our examples, S = 300, T = 1, and r =0.05 so thatF = 300(1+0.05) = 315

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Sako Mwakalobo1. Oil: An Arbitrage Opportunity?Suppose that:The spot price of oil is US$19The quoted 1-year futures price of oil is US$25The 1-year US$ interest rate is 5% per annumThe storage costs of oil are 2% per annumIs there an arbitrage opportunity?

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Sako Mwakalobo2. Oil: Another Arbitrage Opportunity?Suppose that:The spot price of oil is US$19The quoted 1-year futures price of oil is US$16The 1-year US$ interest rate is 5% per annumThe storage costs of oil are 2% per annumIs there an arbitrage opportunity?

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Sako MwakaloboOptionsA call option is an option to buy a certain asset by a certain date for a certain price (the strike price)A put option is an option to sell a certain asset by a certain date for a certain price (the strike price)

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Sako MwakaloboAmerican vs European OptionsAn American option can be exercised at any time during its lifeA European option can be exercised only at maturity

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Sako MwakaloboIntel Option Prices (Jan 22, 2007; Stock Price=86.79)

Strike PriceFeb CallMar CallApr CallFeb PutMar PutApr Put85.004.105.707.702.053.304.9090.001.853.305.304.705.907.50

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Sako MwakaloboExchanges Trading OptionsChicago Board Options ExchangeAmerican Stock ExchangePhiladelphia Stock ExchangePacific ExchangeLIFFE (London)Eurex (Europe)and many more

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Sako MwakaloboOptions vs Futures/ForwardsA futures/forward contract gives the holder the obligation to buy or sell at a certain priceAn option gives the holder the right to buy or sell at a certain price

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Sako MwakaloboTypes of Traders Hedgers Speculators ArbitrageursSome of the largest trading losses in derivatives have occurred because individuals who had a mandate to be hedgers or arbitrageurs switched to being speculators

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Sako MwakaloboHedging ExamplesA US company will pay 10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contractAn investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1. The investor decides to hedge by buying 10 contracts

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Sako MwakaloboValue of Microsoft Shares with and without Hedging

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Sako MwakaloboSpeculation Example

An investor with $4,000 to invest feels that Amazon.coms stock price will increase over the next 2 months. The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2What are the alternative strategies?

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Sako MwakaloboArbitrage ExampleA stock price is quoted as 100 in London and $172 in New YorkThe current exchange rate is 1.7500What is the arbitrage opportunity?

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Sako MwakaloboHedge FundsHedge funds are not subject to the same rules as mutual funds and cannot offer their securities publicly. Mutual funds must disclose investment policies, makes shares redeemable at any time,limit use of leveragetake no short positions. Hedge funds are not subject to these constraints.Hedge funds use complex trading strategies are big users of derivatives for hedging, speculation and arbitrage

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Sako MwakaloboReal World Situation - CashJapanese Bank: Borrow USD in Interbank Euromarket for 3 month term, TCould perform the same transaction as a Synthetic in the FX and domestic yen mktBorrow yen in local mkt for term T, at L(t0,Y)Sell yen and buy USD in spot FX mkt at e(t0,Y)Finally, the bank buys yen in the forward FX mkt for delivery at t0+T

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Sako MwakaloboReal World Situation - CashCash Flows are Additive++=t0t0+TYYx(1+L(t0,Y)xT)USDYYx(1+L(t0,Y)xT)USDUSDx(1+L(t0,$)xT)Borrow Y for T at L(t0,Y) Pay back: Yx(1+L(to,Y)xT)

Buy USD sell Y at e(t0,Y)

Y=e(t0,Y)xUSD

Buy Y forward, t0+T delivery in amount so

Yx(1+L(t0,Y)xT)= f(t0,T;Y)xUSD1 USD1=USDx(1+L(t0,$)xT)USDx(1+L(t0,$)xT)

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Sako MwakaloboReal World Situation CashAt t0 Borrowing rates in USD & Yen are knownExchange rate USD & Yen are knownForward market for Yen must preclude riskless arbitrage so,

e(t0,Y)xUSD x (1+L(t0,Y)xT) = f(t0,T;Y) x USDx(1+L(t0,$)xT)or,f(t0,T;Y) = e(t0,Y) x [(1+L(t0,Y)xT) / (1+L(t0,$)xT)]

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Sako MwakaloboMoney Rates Close Friday, 1/26/07 / YEN / 1WK .345 1MO .35 2MO .435 3MO .47 4MO .505 5MO .515 6MO .545 9MO .585 1YR .655 / US DOLLAR / 1WK 5.265 1MO 5.275 2MO 5.285 3MO 5.295 4MO 5.295 5MO 5.355 6MO 5.365 9MO 5.385 1YR 5.39

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Sako MwakaloboSpot/Forwards USD-JPYU S D -J P Y S P O T / F O R W A R D S Source CMPN Composite (NY)

Close Time of Bid Ask Bid Rate Ask Rate Time of PRDFri 1/26 Offset Offset Offset Rate 2 Spot 16:59 121.54 121.54 121.54 121.54 16:59 1 Week 16:59 -11.59 -11.59 121.42 121.42 16:59 1 Month 16:59 -47.80 -47.80 121.06 121.06 16:59 2 Month 16:59 -96.20 -96.20 120.58 120.58 16:59 3 Month 16:59 -140.80 -140.80 120.13 120.13 16:59 4 Month 16:59 -192.90 -192.90 119.61 119.61 16:59 5 Month 16:59 -239.41 -239.41 119.15 119.15 16:59 6 Month 16:59 -287.14 -287.14 118.67 118.67 16:59 9 Month 16:59 -424.05 -424.05 117.30 117.30 16:59 1 Year 16:59 -554.20 -554.20 116.00 116.00 16:59 2 Year 16:59 -1022.37 -1022.37 111.32 111.32 16:59 3 Year 16:59 -1422.50 -1422.50 107.32 107.32 16:59 4 Year 16:59 -1789.00 -1789.00 103.65 103.65 16:59 5 Year 16:59 -2146.00 -2146.00 100.08 100.08 16:59

* All forward offset rates on this screen are direct quotes from banks; see FRD for rates calculated through USD

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Sako Mwakalobo1. Gold: An Arbitrage Opportunity?

Suppose that:The spot price of gold is US$300The 1-year forward price of gold is US$340The 1-year US$ interest rate is 5% per annumIs there an arbitrage opportunity?

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Sako Mwakalobo2. Gold: Another Arbitrage Opportunity?

Suppose that:The spot price of gold is US$300The 1-year forward price of gold is US$300The 1-year US$ interest rate is 5% per annumIs there an arbitrage opportunity?

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Sako MwakaloboThe Forward Price of Gold The Principal of Cash and CarryIf the spot price of gold is S(t0) and the forward price for a contract deliverable in T years is F(t0,T), thenCan borrow money, buy gold, and sell the commodity forward - where there should be no arbitrage: F(t0,T) - S(t0) x (1+r )T = 0where r is the 1-year money rate of interest to finance the gold carry trade.In our examples, S = 300, T = 1, and r =0.05 so thatF(t0,T) = 300(1+0.05) = 315The no arbitrage 1 year forward price of gold is $315

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Sako MwakaloboThe Forward Price of Gold The Principal of Cash and CarryHow does this come about?S(t0)t0receivepayS(t0)x(1+r)GoldS(t0)F(t0)GoldOwnDeliverGoldGoldBorrow S(t0)Buy Gold at S(t0)Sell Gold Forward at F(t0)No Arbitrage condition says:

F(t0) S(t0)x(1+r) = 0++=

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Sako MwakaloboGold Arbitrage?The no arbitrage gold, 1-year forward condition is F(t0,T) - S(t0) x (1+r )T = 0If 1-year forward is $340, then F(t0,T) - S(t0) x (1+r )T > 0so our strategy is to borrow money, buy gold, sell it forward, deliver gold, and pay off loan for a riskless profit of $25If 1-year forward is $300, thenF(t0,T) - S(t0) x (1+r )T < 0and if I own gold, I can sell it, deposit proceeds, buy forward, pay with the proceeds of the deposit and collect a riskless profit of $15 over the 1-year period

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Sako MwakaloboHedging ExampleA US company will pay 10 million for imports from Britain in 3 months and decides to hedge using a long position in a forward contractPossible strategies:Buy now, deposit in bank, withdraw 10 million in 3 months, pay for importsBuy 10 million forward in 3 months, deposit USD, use deposit proceeds to settle and pay for importsDo nothing now and buy 10 million in the spot FX market in 3 monthsFirst 2 are riskless, third has currency risk.Which makes most sense?

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Sako MwakaloboFutures ContractsAvailable on a wide range of underlyingsExchange tradedSpecifications need to be defined:What can be delivered,Where it can be delivered, & When it can be deliveredSettled daily

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Sako MwakaloboForward Contracts vs Futures ContractsPrivate contract between 2 partiesExchange tradedNon-standard contractStandard contractUsually 1 specified delivery dateRange of delivery datesSettled at end of contractSettled dailyDelivery or final cashsettlement usually occursContract usually closed outprior to maturityFORWARDSFUTURESSome credit riskVirtually no credit risk

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Sako MwakaloboMarginsA margin is cash or marketable securities deposited by an investor with his or her brokerThe balance in the margin account is adjusted to reflect daily settlementMargins minimize the possibility of a loss through a default on a contract

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Sako MwakaloboExample of a Futures TradeAn investor takes a long position in 2 December gold futures contracts on June 5contract size is 100 oz.futures price is US$400margin requirement is US$2,000/contract (US$4,000 in total)maintenance margin is US$1,500/contract (US$3,000 in total)

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Sako MwakaloboA Possible Outcome

DailyCumulativeMarginFuturesGainGainAccountMarginPrice(Loss)(Loss)BalanceCallDay(US$)(US$)(US$)(US$)(US$)400.004,0005-Jun397.00(600) (600) 3,4000..................13-Jun393.30(420) (1,340) 2,6601,340 .................19-Jun387.00(1,140) (2,600) 2,7401,260 ..................26-Jun392.30260 (1,540) 5,0600+=4,0003,000+=4,000

Sako MwakaloboOther Key Points About FuturesThey are settled dailyClosing out a futures position involves entering into an offsetting tradeMost contracts are closed out before maturity

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Sako MwakaloboCollateralization in OTC MarketsIt is becoming increasingly common for contracts to be collateralized in OTC marketsThey are then similar to futures contracts in that they are settled regularly (e.g. every day or every week)

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Sako MwakaloboAnother Detail for Cash and Carry ArbitrageContract price changes with longer termHigher or LowerTo this point we have neglected storage costLets re-visit no-arbitrage equationF(t0,T) - S(t0) x [(1+r )T ] = - Storage (T) Storage costs ignored in earlier gold exampleNo storage costs for FXLets look at consequence of storage

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Sako MwakaloboFutures Prices for Gold on Feb 4, 2004: Prices Increase with MaturityStorage Costs < Financing

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Sako MwakaloboFutures Prices for Oil on February 4, 2004: Prices Decrease with MaturityStorage Cost > Financing

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Sako MwakaloboDeliveryIf a futures contract is not closed out before maturity, it is usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses. A few contracts (for example, those on stock indices and Eurodollars) are settled in cash

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Sako MwakaloboSome TerminologyOpen interest: the total number of contracts outstanding equal to number of long positions or number of short positionsSettlement price: the price just before the final bell each day used for the daily settlement processVolume of trading: the number of trades in 1 day

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Sako MwakaloboConvergence of Futures to Spot TimeTime(a)(b)FuturesPriceFuturesPriceSpot PriceSpot Price

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Sako MwakaloboQuestionsWhen a new trade is completed what are the possible effects on the open interest?Can the volume of trading in a day be greater than the open interest?

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Sako MwakaloboRegulation of FuturesRegulation is designed to protect the public interestRegulators try to prevent questionable trading practices by either individuals on the floor of the exchange or outside groups

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Sako MwakaloboAccounting & TaxIdeally hedging profits (losses) should be recognized at the same time as the losses (profits) on the item being hedgedIdeally profits and losses from speculation should be recognized on a mark-to-market basisRoughly speaking, this is what the accounting and tax treatment of futures in the U.S.and many other countries attempts to achieve

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Sako MwakaloboForward Contracts vs Futures ContractsPrivate contract between 2 partiesExchange tradedNon-standard contractStandard contractUsually 1 specified delivery dateRange of delivery datesSettled at end of contractSettled dailyDelivery or final cashsettlement usually occursContract usually closed outprior to maturityFORWARDSFUTURESSome credit riskVirtually no credit risk

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Sako MwakaloboForeign Exchange QuotesFutures exchange rates are quoted as the number of Tshs per unit of the foreign currencyForward exchange rates are quoted in the same way as spot exchange rates. This means that GBP, EUR, AUD, and NZD are quoted as Tshs per unit of foreign currency. Other currencies (e.g., CAD and JPY) are quoted as units of the foreign currency per Tshs.

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Sako MwakaloboLong & Short HedgesA long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the priceA short futures hedge is appropriate when you know you will sell an asset in the future & want to lock in the price

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Sako MwakaloboArguments in Favor of HedgingCompanies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables

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Sako MwakaloboArguments against HedgingShareholders are usually well diversified and can make their own hedging decisionsIt may increase risk to hedge when competitors do notExplaining a situation where there is a loss on the hedge and a gain on the underlying can be difficult

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Sako MwakaloboConvergence of Futures to Spot(Hedge initiated at time t1 and closed out at time t2) TimeSpot PriceFuturesPricet1t2

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Sako MwakaloboBasis RiskBasis is the difference between spot & futuresBasis risk arises because of the uncertainty about the basis when the hedge is closed out

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Sako MwakaloboShort HedgeSuppose thatF1 : Initial Futures PriceF2 : Final Futures PriceS1 : Initial Asset PriceS2 : Final Asset PriceYou hedge the future sale of an asset (one which you might be long) by entering into a short futures contractP/L = (S1 F1) (S2 F2) = S1 [S2+ (F1 F2)] = S1 [F1+ (S2 F2)] Price Realized = S2+ (F1 F2) = F1 + Basis

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Sako MwakaloboLong Hedge Suppose thatF1 : Initial Futures PriceF2 : Final Futures PriceS1 : Initial Asset PriceS2 : Final Asset PriceYou hedge the future purchase of an asset (one you might be short) by entering into a long futures contractP/L = (S1 F1) + (S2 F2) = S1 + [S2 (F2 F1)] = S1 + [F1+ (S2 F2)] Cost of Asset = S2 (F2 F1) = F1 + Basis

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Sako MwakaloboChoice of ContractChoose a delivery month that is as close as possible to, but later than, the end of the life of the hedgeWhen there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging.

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Sako MwakaloboOptimal Hedge RatioProportion of the exposure that should optimally be hedged iswhere sS is the standard deviation of DS, the change in the spot price during the hedging period, sF is the standard deviation of DF, the change in the futures price during the hedging periodr is the coefficient of correlation between DS and DF.

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Sako MwakaloboOptimal Hedge Ratio Minimum Variance ResultThe number of futures, NF, in ratio h (the hedge ratio), required to hedge NA units of an asset follows from P/LP/L = (NAS1 NFF1) (NAS2 NFF2)= NF DF - NA DS = NA x (DFh DS) where NF = h x NAmin [DFh DS] when the variance of the linear combination of DF & DS , v = Var [DFh DS] = sS2 h2 sF2 2 h r sS sF minimize v when h is such that dv/dh = 0 if d2h/dh2 > 0 or 2 h sF2 2 r sS sF = 0 impliesh =

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Sako MwakaloboHedging Using Index FuturesTo hedge the risk in a portfolio the number of contracts that should be shorted is

where P is the value of the portfolio, b is its beta, and A is the value of the assets underlying one futures contract

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Sako MwakaloboReasons for Hedging an Equity PortfolioDesire to be out of the market for a short period of time. (Hedging may be cheaper than selling the portfolio and buying it back.)Desire to hedge systematic risk (Appropriate when you feel that you have picked stocks that will outpeform the market.)

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Sako MwakaloboExampleValue of S&P 500 is 1,000Value of Portfolio is $5 millionBeta of portfolio is 1.5

What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?

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Sako MwakaloboChanging BetaWhat position is necessary to reduce the beta of the portfolio to 0.75?What position is necessary to increase the beta of the portfolio to 2.0?

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Sako MwakaloboHedging Price of an Individual StockSimilar to hedging a portfolioDoes not work as well because only the systematic risk is hedgedThe unsystematic risk that is unique to the stock is not hedged

Sako Mwakalobo

Sako MwakaloboWhy Hedge Equity ReturnsMay want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolioSuppose stocks in your portfolio have an average beta of 1.0, but you feel they have been chosen well and will outperform the market in both good and bad times. Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market.

Sako Mwakalobo

Sako MwakaloboRolling The Hedge ForwardWe can use a series of futures contracts to increase the life of a hedgeEach time we switch from 1 futures contract to another we incur a type of basis risk

Sako Mwakalobo

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