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Derivative Securities (Subject) / Future Contracts (Lesson)

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  • Unregulated market Parties want to keep them private and want little government interference - not illegal or corrupt - prudent level of business secrecy
  • Definition Derivatives A derivative is a financial instrument that o↵ers a return based on the value/return of some underlying asset. 
  • Forward commitments Agreement to engage a transaction at a later date at an established price: Forward contracts Future contracts Swap contracts 
  • Contingent Claims Right (no obligation) to engage a transaction at a later date at an established price Option contracts 
  • Definition Forward Contract Agreement between two parties in which the buyer agrees to exchange an underlying asset at a future date at a price established at the start
  • Characteristics and Types of Forward Contracts Parts of the contract Initial cost is zero Termination of the contract At expiration: Delivery or Cash settlement Before expiration: Default, cancellation or termination by entering an opposite forward contract Types: Equity forward Bond and interest rate forward Currency forward contracts 
  • Equity Forward Contract An equity forward is a contract calling for the purchase of an individual stock, a stock portfolio, or a stock index at a later date. Remark: dividends are not paid  f0(T) = S0 (1+r)T- FV(D,0,T) = S0/ (1+§) * (1+r)T = S0 * (1-§) * (1+r)T §= PV (D,O,T) / S0 =verhältnis Dividendenzahlung zum Initial Value.
  • Forward contracts: Bond and interest rate Individual (portfolios of) bond(s): the long position agrees to buy a t-bill at a later date (but prior to maturity) implicit discount rate can be computed from Pt =1 - r d/360
  • Forward contracts: Forward Rate Agreement (FRA) The long position agrees to buy a interest payment at a specific price. The parties determines: The instrument (type of interest rate) used to compute the value of underlying (interest payment). The termination date The notional value VT= ST - F(0,T) 180 Tage Instruments: Eurodollar and LIBOR deposits Underlying: Interest payment Pay-off: Plong = PVn.p.(ru- rf ) du /360 Where:   Plong : pay-o↵ for the long position PVn.p. : present value of the notional principal ru : underlying rate at expiration rf : forward rate du : days in underlying rate 
  • Pricing and valuation of equity forward contracts: continuous tim Value at the time t: Vt(0,T)=St*e-d(T-t) -  F(0,T)* e-r(T-t) Price of the forward contract: F(0,T) =  S0e(r-d)T 
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  • Arbitrage Strategy: Covered interest arbitrage F (0, T ) > S0/ (1 + r h )T (1+rf )T price of the derivative is too high: 1. sell the forward contract 2. borrow S0/ (1+rf) for a period T 3. buy 1/ (1+rf) and deposit it for a period T  4. cash 1 at T and then convert it to F(0,T) of home currency  5.pay the home bank S0/(1+rf)T *(1+rh)T(smaller than F(0,T)
  • Future vs. Forwards 1. Public and standardized transaction: The parties agree only on the price2.Trading and credit risk: Traded on organized facilities (future exchanges) and guaranteed by the clearinghouse.3.Liquidity: presence of a secondary market.4. Transparency: Transaction are reported to (at least) the exchange and the clearinghouse5. Marking to market Regulation 6. Opening and closing out (offsetting) a position Main differences with forwards: Future price changes through time Every day positions are market to market 
  • Futures Contracts l Delivery and Cash Settlement The exchange specify how the contract will terminate The short position often has the right to make decisions concerning delivery (delivery option) Closeout vs. physical delivery vs. cash settlement  Value is zero at initialization Value is zero after marking to market Arbitrage arguments will be used to find prices 
  • Treasury bill futures: pricing Cash and carry strategy on day 0 buy the h+m T-Bill on day 0 short the futures priced at f0(h) on day h deliver the m days T-Bill and cash f0(h)  if the strategy is risk free: f0(h) = B0(h + m)(1 + r0(h))h/360 or f0(h)/B0(h + m) = 1/B0(h)
  • Implied Repo Rate Repo Rate :The rate of return of the cash and carry strategy Assume that the forward rate prevailing in the market is different than f0(h)  f0(h) = B0 ( h+m)(1+r0(h)) h/360 B0= 1/ (1+r0(h)) h/360
  • Leverage Leverage can be created through options, futures, margin and other financial instruments. For example, say you have $1,000 to invest. This amount could be invested in 10 shares of Microsoft (MSFT) stock, but to increase leverage, you could invest the $1,000 in five options contracts. You would then control 500 shares instead of just 10.
  • Hedging Hedging involves taking an offsetting position in a derivative in order to balance any gains and losses to the underlying asset. Hedging attempts to eliminate the volatility associated with the price of an asset by taking offsetting positions contrary to what the investor currently has. Hedgers reduce their risk by taking an opposite position in the market to what they are trying to hedge.
  • Speculation GO LONG on Call-Option The main purpose of speculation, on the other hand, is to profit from betting on the direction in which an asset will be moving. Speculators make bets or guesses on where they believe the market is headed. For example, if a speculator believes that a stock is overpriced, he or she may short sell the stock and wait for the price of the stock to decline, at which point he or she will buy back the stock and receive a profit. Speculators are vulnerable to both the downside and upside of the market; therefore, speculation can be extremely risky.
  • Conversion Factor To avois unfair bonds choice so the long position will not loose when different bonds have the same maturity but come from different issue periods
  • Treasury Bill Futures Characteristics Underlying:  - 1000000$ 90-day Bond - Cash settles, annualized  1$ Pa Price = 1-i * d/360 Quoted price international IMM = 100(1-i) i=100-IMM/ 100 *t/360 Change of 1% leads to change of 2500 in the price  each basis point changes by 25$
  • Treasury Bond Futures Maturity > 15 years face vaule of 100.000 - delivery option by SHORT Conversion Factor 
  • Actual price of a Treasury Bond IMM 1000000* (1- 100-IMM/100 * 90/360 ) 1 basis point = 25 Dollar increase
  • How to offset a position l close out early Peson can short his position and offset his position 1. He reenters the market offering a June futures contract now he holds the SHORT + LONG position in the market 2. For the clearing house, he no longer holds a position in the market
  • Maintenance Calls Fall in Price = LOSS for the LONG = LONG receives a maintenance Call Rise in Price = LOSS for the SHORT = SHORT receives a maintenance CALL
  • LIBOR and IMM LIBOR annualized = 100 - IMM Index = LIBOR-Rate
  • To exploit an expected increase in interest rates, an investor would most likely Sell Treasury Bond Futures
  • A futures contract definition is an agreement to buy or sell a specified amount of an asset at a predetermined price on the expiration date of the contract.
  • To hedge a long position in Treasury bonds, an investor most likely would sell interest rate futures.
  • Strategy Arbitrage Currency l Importer of Goods and you have to pay When you have to pay You expect the Value of the Foreign Currency to increase l Go LONG l HEDGE When you receive money You expect the Value of the Foreing Currency to increase l Go SHORT l HEDGE
  • T-Bills, Treasury-Bills kurzfristige amerikanische Staatsanleihen mit einer Laufzeit von 1 Monat 3 Monaten, 6 Monaten 1 Jahr 
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  • Treasury-Bonds Amerikanische Staatsanleihen mit einer Laufzeit zwischen 10 und 30 Jahren werden als „T-Bonds“ bezeichnet 1000000* (1- 100-IMM/100 * 90/360 ) 1 basis point = 25 Dollar increase
  • Find the cash flow from the mark-to-market proceeds on the contract. The initial futures price is F0 = 1,240 × (1 + 0.005 – 0.003)12 = 1,270.09In one month, the futures price will be: F0 = 1,275 × (1 + 0.005 – 0.003)11 = 1,303.33The increase in the futures price is 33.24, so the cash flow will be: 33.24 × $250 = $8,310.66
  • What if the T-bill rate is less than the dividend yield, for example, 1%? If the T-bill rate is less than the dividend yield, then the futures price should be less than the spot price
  • To exploit an expected increase in interest rates, an investor would most likely expected decrease in bond prices = bearish = speculate As bond prices decrease the short position gains. Thus, if you are bearish about bond prices, you might speculate by selling T-bond futures contracts.

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