Options and Futures Midterm Exam 1 Profit on option a Purchased call long call max spot price strike price 0 b Written call short call max spot price strike price 0 c Purchased put long put max strike price spot price 0 d Written put short put max strike price spot price 0 premium premium premium premium 2 Profit on forwards Futures a Long forward Spot price t Future pricet b Short forward Future pricet S pot price t 3 Long and Short Hedges a Selling Asset Short Hedge i Price asset price short forward long forward ii Price realized final asset price initial futures price final futures price initial futures price basis b Acquiring Asset Long Hedge i Price asset price short forward long forward ii Cost of the asset final asset price final futures price initial futures price initial futures price basis 4 Number of Contracts to Purchase in Order to Hedge a Portfolio a Value of Portfolio Value of Assets Underlying OneContract 5 Optimal Hedge Ratio s F where a b isthe coefficient of correlation between S F c sis the standard deviation of the S the change in the spot price during the hedging period d F is the standard deviation of F the change in the futures price during the hedging period 6 Discrete Compounding a Annual i FV Amount 1 r n b Less than Annual i FV Amount 1 r m nm 1 r interest rate 2 n years 3 m periods per year 7 Continuous Compounding a FV principal ert b PV FV e rt i PV present value ii FV future value iii e exponential iv r interest rate v t time as of year 8 Conversion Formulas Rm m Rc a Rc mln 1 continuously compounded rate b Rm m e m 1 same rate compounding m times per year 9 Forward Rates R 2T 2 R1 T 1 T 2 T 1 forward rate R2 R2 R1 x T1 T2 T1 a 10 Instantaneous Forward Rate a R T R T i Where R is the T year rate 11 Upward vs Downward Sloping Yield Curve a Upward Sloping Yield Curve i Fwd rate Zero Rate Par Yield b Downward Sloping Yield Curve i Par yield Zero Rate Fwd Rate 12 Forward Rate Agreement a Lender b Borrower i L Rk R F T 2 T 1 e R2 T 2 i L RF R K T 2 T 1 e R2 T 2 ii R F is the forward rate for the period and R2 is the zero rate for maturity T 2