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Options and Futures Midterm Exam1. Profit on option a. Purchased call/ long call= max (spot price – strike price, 0) -premiumb. Written call/ short call= -max (spot price – strike price, 0) + premiumc. Purchased put/ long put= max (strike price – spot price, 0) -premiumd. Written put/ short put= -max (strike price – spot price, 0) + premium2. Profit on forwards/ Futures a. Long forward= Spot pricet- Future pricetb. Short forward= Future pricet – S pot pricet3. Long and Short Hedges a. Selling Asset/ Short Hedgei. Price= asset price + (short forward – long forward)ii. Price realized= final asset price+ (initial futures price-final futures price) = initial futures price + basisb. Acquiring Asset/ Long Hedgei. Price= asset price – (short forward + long forward)ii. Cost of the asset= final asset price- (final futures price- initial futures price) = initial futures price + basis4. Number of Contracts to Purchase in Order to Hedge a Portfolioa.βValue of PortfolioValue of Assets Underlying OneContract5. Optimal Hedge Ratio a.ρσsσF where:b.ρ isthe coefficient of correlationbetween ΔS∧ΔFc.σsis the standard deviation of the Δ S, the change in the spot price during the hedging periodd.σF is the standard deviation of Δ F, the change in the futures price during the hedging period6. Discrete Compounding a. Annuali. FV= Amount * (1+r )nb. Less than Annuali. FV= Amount * (1+rm)nm1. r= interest rate2. n= years3. m= periods per year7. Continuous Compounding a. FV= principal * ertb. PV= FV * e−rti. PV= present valueii. FV= future valueiii. e= exponentialiv. r= interest ratev. t= time as % of year8. Conversion Formulas a.Rc=mln (1+Rmm¿)¿ continuously compounded rateb.Rm=m(eRcm−1) = same rate compounding m times per year9. Forward Rates a.R2T2−R1T1T2−T1 = forward rate = R2 +(R2-R1)x(T1/(T2-T1))10. Instantaneous Forward Ratea.R+T∂ R∂Ti. Where R is the T year rate11. Upward vs. Downward Sloping Yield Curvea. Upward Sloping Yield Curvei. Fwd rate> Zero Rate > Par Yieldb. Downward Sloping Yield Curvei. Par yield > Zero Rate > Fwd Rate12. Forward Rate Agreementa. Lenderi.L(Rk−RF) (T2−T1)e−R2T2b. Borroweri.L(RF−RK) (T2−T1)e−R2T2ii.RF is the forward rate for the period and R2 is the zero rate for maturity


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KSU FIN 46055 - Midterm Exam

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