DefinitionA forward contract is anagreement between two parties inwhich one party, the buyer, agrees tobuy from the other party, the seller,an underlying asset at a future date ata price established today. The contractis customised and each party issubject to the possibility that theother party will default.
Forwards FuturesOver the counter Futures exchangePrivate PublicCustomized StandardizedDefault risk Default freeNot marked to market Marked to marketHeld until expiration Offset possibleNot liquid LiquidUnregulated Regulated
Differentiate between the positions held by thelong and short parties to a forward contractLF LALong party SA Short party SF• Party that agrees to buy the asset has a long forwardposition• Party that agrees to sell the asset has a short forwardposition
Pricing and valuation of forward contractsAre pricing and valuation not the same thing?• The price is agreed on the initiationdate (Forward price or forward rate)i.e. pricing means to determining theforward price or forward rate.• Valuation, however, means todetermine the amount of money thatone would need to pay or wouldexpect to receive to engage in thetransaction
Pricing and valuation of forward contracts cont…F(0,T)- The forward contract price initiated attime 0 and expiring at time TVo(0,T) – the value of a forward contractinitiated at time 0 and expiring at time TVt(0,T) – the value of a forward contractat the point in time during the life of acontract such as tToday(0)TimebetweenToday andExpiration(t)Expiration(T)VT(0,T)- Value at expiration
F(0,T) =S0(1+r)^TThe transaction is risk-free and shouldequivalent to investing S0 Rands inrisk free assetPricing and valuation of forward contracts cont…Buy asset atSoSell forwardcontract atF(0,T)Outlay: S0Hold assetand loseinterest onout layDeliverassetReceiveF(0,T)
Vo(0,T) = S0 –F(0,T)/(1+r)^TFor forward contract Vo(0,T) shouldbe ZERO (0)If Vo(0,T) ≠ 0 arbitrage would theprevailPricing and valuation of forward contracts cont…The forward price that eliminates arbitrage:F(0,T) =S0(1+r)^T
By definition an asset’svalue is the present valueof future value thus,Vt(0,T) = St –F(0,T)/(1+r)^(T-t)Pricing and valuation of forward contracts cont…(T-t) is the remaining timeto maturity
F(0,T) =(S0-PV(D,0,T))*(1+r)^TWhen dividends are paid continuouslyF(0,T) =So℮^(-∂c*t) . ℮^(rc*t)To convert discrete risk-free interest(r)to continuosly compoundedequivalent(rc):rc = Ln(1+r)Pricing and valuation of forward contracts cont…PV (D,0,T) =∑(Di/(1+r)^(T-ti)
Pricing and valuation of forward contracts cont…A portfolio manager expects to purchase a portfolioof stocks in 60 days. In order to hedge against apotential price increase over the next 60 days, shedecides to take a long position on a 60-day forwardcontract on the S&P 500 stock index. The index iscurrently at 1150. The continuously compoundeddividend yield is 1.85 percent. The discrete risk-freerate is 4.35 percent.Calculate the no-arbitrage forward price on thiscontract, the value of the forward contract 28 daysinto the contract (index value 1225), and the valueof the contract at expiration (index value 1235).
0.0185 60 365 LN 1.0435 60 365F 0,T 1,150e e $1,154.56Decrease the spot index value by thedividend yield and thereafter calculate thefuture value (first convert the discrete rateto a continuously compounded rate).
The value of a contract is the difference between the discountedcurrent spot price (at the dividend yield) and the discountedforward price (at the converted risk-free rate) for the remainingperiod.0.0185 32 365 LN 1.0435 32 365tV 0,T 1,225e 1,154.56e1,223.00 1,150.26$72.76
At expiration, the value is simply thedifference between the end-period spotindex and the forward contract price, ascalculated.TV 0,T 1,235 1,154.56 $80.44
Identify the characteristics offorward rate agreements• Forward contract to borrow/lend money at acertain rate at some future dateLong position Borrows money (pays interest) Benefit when forward rate < market rateShort position– Lends money (receives interest)– Benefit when forward rate > market rateFixed-Income and interest rate forwardcontracts
Calculate and interpret the payment atexpiration of a FRA and identify each ofthe component terms
• ESKOM P/L is expecting to receive a cash inflow ofR20, 000,000.00 in 90 days. Short term interestrates are expected to fall during the next 90 days. Inorder to hedge against this risk, the company decidesto use an FRA that expires in 90 days and is basedon 90day LIBOR. The FRA is quoted at 6%. Atexpiration LIBOR is 5%. Indicate whether thecompany should take a long or short position tohedge interest rate risk. Using the appropriateterminology, identify the type of FRA used here.Calculate the gain or loss to ESKOM P/L as aconsequence of entering the FRA.