ASSET MANAGEMENT LECTURE VIII Derivatives markets and derivatives in portfolio management Introduction to derivative contracts • Definition of a derivative: an agreement between two parties which has a value determined by the price of something else (underlying). • Derivative securities include 1. Swaps 2. Options and forwards 3. Futures • Different uses: – Risk management – Speculation – Reduce transaction costs – Regulatory arbitrage • End users of derivative products include corporates, investment managers, individual investors. Derivatives may be looked at from different perspectives: – End users – Intermediaries/market makers – Regulators and researchers 2 1. The swap A swap is a contract calling for an exchange of payments, on one or more dates, determined by the difference in two prices. A swap provides a means to hedge a stream of risky payments. Swap contracts are traded OTC. The most common type of swap is the interest rate swap (plain vanilla swaps exchange fixed payments for variable payments semi-annually and the contract is settled for differences). The notional of the swap is the amount on which the interest payments are based and the life of the swap is called swap term or swap tenor. • Let’s make a sample: the company A has a debt with a fixed interest rate of 7% and left maturity of 5 years; the company V has a debt with same maturity but floating interest rate equal to 6 months EURIBOR (same amount). • The company A forecast falling interest rates. The company V forecast rising interest rates. • The interest rate swap (IRS) allows to meet the opposite needs. The company A will pay to the company V the 6 months EURIBOR and will receive from the company rate a 7%. The value of the swap has given from the difference between fixed and floating interest rates (euribor): S=FLR-FXR where 7% Euribor S = swap Euribor Com. A Com. V FLR = floating rate FXR = fixed rate 7% 3 1. The swap and different rating • Let’s consider two companies with different rating: • The company A (with rating A) that can borrow at 8% fixed interest rate or floating rate Euribor (5 year maturity); • The company B (with rating B) that can borrow at 10% fixed interest rate or floating rate Euribor +0,5% (5 year maturity). Is it possible for both to reduce the cost of funding? 8% EURIBOR + 0,5 EURIBOR – 0,75 Com. A Com. B 8% (EURIBOR) (10%) EURIBOR – 0,75 9 + 0,25 4 1. The interest rate swap Introduction to derivative contracts, forward and options • Forward and futures contracts are agreements between two parties: the buyer agrees to purchase an asset from the seller at a specific date at a price agreed to now. Options offer the buyer the right without obligation to buy or sell at a fixed price up to or on a specific date. • Option basics – Option to buy is a call option. Option to sell is a put option. Option premium – sum paid for the option – Option styles: European (at maturity), American, Bermudan – The exercise price is the price the call buyer will pay to-or the put buyer will receive from-the option seller if the option is exercised – Intrinsic value represents the value that the buyer could extract from the option if the holder exercised it immediately – The time premium component is simply the difference between the whole option premium and the intrinsic component • Options trade both in over-the-counter markets and on exchanges. The OTC market is much larger than the exchange traded segment 6 The call option There are 5 different scenarios: A) P < 108, it is not convenient exercise the CALL loosing the premium (OUT OF THE MONEY); B) P = 108, it is indifferent either exercise or not the CALL (AT THE MONEY); C) 108 < P < 110 , exercising the CALL it is possible to reduce the cost of the premium (IN THE MONEY); D) P = 108 + 2, it is convenient exercise the CALL and the P&L isequal to 0 (IN THE MONEY); E) P > 108 + 2, the profit is nominally unlimited (IN THE MONEY). P&L 30 20 10 Underlying price 0 -2 30 40 50 60 70 80 90 100 110 120 130 140 150 -10 7 A summary of payoff graphs for forward and option contracts • A long forward contracts pays the difference between the terminal price of the underlying asset and a certain strike level. The opposite is true for short forward positions. Long and short forward contracts just pay this difference every day, not at maturity • Long calls pay the difference between the terminal price of the underlying asset and a certain strike level, if positive. The opposite is true for short call options • Long puts pay the difference between a certain strike level and the terminal price of the underlying asset, if positive. The opposite is true for short put options References: BROWN & REILLY, Chapter XXI; Mc Donald, Derivatives Markets, Pearson 8 Asset Management, lecture VI Option strategies: bull spreads and collars • An option spread is a position consisting of only calls or only puts, in which some options are purchased and some written. A bull spread is a position, in which you buy a call and sell an otherwise identical call with a higher strike price: it is a bet that the price of the underlying asset will increase • A collar is the purchase of a put option and the sale of a call option with a higher strike price, with both options having the same underlying asset and having the same expiration date. Example: purchased zero- cost collar 9 Other option spreads and non-directional strategies • A bear spread is a position in which one sells a call and buys an otherwise identical call with a higher strike price. Clearly, it is a bearish position, profiting when asset prices fall • A box spread is accomplished by using options to create a synthetic long forward at one price and a synthetic short forward at a different price. A box spread is a means of borrowing or lending money: It has no stock price risk • A ratio spread is constructed by buying m calls at one strike and selling n calls at a different strike, with all options having the same time to maturity and same underlying asset • Options can be used to create positions that a non-directional with respect to the underlying asset. Examples are straddles, strangles and butterflies • Who would use non-directional positions? Investors who do not care whether the stock goes up or down, but only how much it moves, i.e., who speculate on volatility (or diversify, using volatility as an additional asset class ) 10 A summary of payoff graphs for forward and option contracts • A straddle is obtained by buying a call and a put with the same strike price and time to expiration. A straddle is a bet that volatility will be high relative to the market’s assessment • A strangle is created by buying an out-of-the-money call and put with the same time to expiration. A strangle can be used to reduce the high premium cost, associated with a straddle. Write a straddle + add a strangle = butterfly 11 A summary of payoff graphs for various option strategies • Bull spreads and purchased collars are synthetic long and short positions in the underlying asset obtained by using options. The collar can cost nothing if the option strikes are chosen correctly • Long straddles and long strangles profit when the movement in the underlying securities is large. The opposite is true for written strangles and written straddles • Long butterfly spreads profit when the market moves sideways, i.e. when the price moves are moderate. Long ratio spreads profit for small downside moves. Short positions in these strategies yield the opposite result 12 Options parity: the put call parity 1. Buy a share = Asset 1 2. Buy a put at an exercise price X and expiration T = Asset 2 3. Sell a call at an exercise price X and expiration T = Asset 3 Assumptions: put and call are european and no dividends for the underlying Portfolio: Asset 1 = Si = 110 Asset 2 = Pi = 2 Asset 3 = - Ci = 4 Net investment is: Si + Pi + Ci Scenarios: A) T+1, S = 90 B) T+1, S = 120 • Asset 1 = 90 • Asset 1 = 120 • Asset 2 = 100 – 90 • Asset 2 = 0 • Asset 3 = 0 • Asset 3 = - (120 -100) 100 100 13 Options parity: the put call parity In either case the investor will sell the stock at time T for the fixed price X... It means that in To the Portfolio is equal to a T-Bill, wich is the face value X discounted using the risk free rate: So + Po - Co = X/(1 +RFR)^T 1) LONG STOCK + LONG PUT + SHORT CALL = LONG T-BILL After 6 months 108 = 110/(1 +RFR)0,5 RFR =(110/108)^2 – 1 = 1,037 – 1 = 3,7% 2) Short stock + short put + long call = Short T-Bill ... In efficient markets there are links among stocks, bonds, put and call options 14 Options parity relationships • Using the payoff graphs we just introduced you find that (long call) + (short put) = (long forward) and that (long underlying) + (long put) + (short call) = (long risk free security) • Instead of buying a stock, take a long position in a forward contract to buy a stock. Supplement this transaction by purchasing a put option and selling a call option, each with the same exercise price and expiration date. This reduces the net initial investment compared to purchasing the stock in the spot market • The difference between put and call prices must equal the discounted difference between the common exercise price and the contract price of the forward agreement, otherwise arbitrage opportunities would exist • A risk-free portfolio could be created using three risky securities: a stock (for example), a put option on the stock and a call option on the stock.