Cheatography

# Coec 371 Cheat Sheet (DRAFT) by Spazztaco

This is a draft cheat sheet. It is a work in progress and is not finished yet.

### Formula

 Price of Longer Maturity Coupon Paying Bond P = c/r*(1 - 1/(1+r)t ) + ParVal­ue/­(1+r)t Price of Zero Coupon Bond P = ParVal­ue/­(1+r)t Price of Short Maturity Coupon Paying Bond P = Coupon­/(1+r)t + (ParVa­lue­+Co­upo­n)/­(1+r)t Nominal Growth rate of Cash Flows i = (1+Gro­wth­Rat­e)*­(1+­Inf­lat­ion­Rate) - 1 Real Return Adjusted for Inflation r = (1+i)/­(1+­Inf­lation) Present Value of Cash Flows PV = Cash * ((1+i)t-1/(1+Di­sco­unt­Rate)t-1+(1+i)t/(1+Di­sco­unt­Rate)t +...) Computing YTM Rates = Flat; Rates = YTM. Rates =/= Flat; Solve for Price, Swap Rates for Y and solve for Y Discount Factors (D) for Zero Coupon Bonds Price/100 Discount Factor (D) for Coupon Paying Bonds Price = C*D + (ParVa­lue­+C)D Calcul­ation for Spot Rates Using Discount Factor r = (1/D)/T -1 For semiannual multiply answer by 2 Calcul­ating Price with Discount Rates P = C*D + C*D + (ParVa­lue­+C)D For semiannual C/2 Macaulay Definition D = (1+r)/r - {[(1+r) + T(C-R)] / (C[(1+r)T - 1] +r)} Where R = Flat Rate Or YTM. When Semiannual r/2 and c/2, divide final answer by 2 Modified Duration D*= D/1+r Present Value of Liabil­ities Liabil­ities * 1/(1+r)T Compute Realized Returns ( P - P[-1] )/ P[-1] Computing Expected Returns E(R) = (Proba­bility * Return + ...) Computing Standard Deviation Sd(R) = Sqrt(P­rob­abi­lit­y*(­Return - E(R)2 +...) Effective Annual Rate (EAR) P*(­1+EAR)T = P[T] Converting Monthly APR to Semiannual (1+APR/12)6 -1 Calcul­ating for Spot Rates using Price Formula Price = ParVal­ue/­(1+r) then solve for r

### Descri­ptive

 Constr­ucting an Arbitage e.g: Year 1 => 100x +5x = 7 {x} Year 2 => 105x = 107 {x} Solve for x and x Computing Realized Returns assuming Dividend Reinve­sting e.g: Invest \$1000, 1000/Share Price = # of Shares # of Shares + [# of Shares­*Di­vid­end­Pay­out­]/N­ext­Sha­rePrice Repeat til end of Periods, compute the realized returns Monthly Payment Questions Owed Amount = c/r*[1­-1/­(1+r)T] Solve for C, Make sure T is in the right format (Monthly Payments, Yearly, Daily) What is your return if term structure remains flat and you hold for X years? TSR = Term Structure Rate (1+r)T = R/100 R = C*(1+TSR)T-1 + C*(1+TSR)T-2 +... ...+ C*(1+TSR)1 + (ParValue + C) Plug in R to first equation then solve for small r

### Simple Trading Model

 Expected Value of Stock E(V) = P[h]*V[h] + P[l}*V[l] Ask price so Market Maker breaks even A = ( P[u]*P­[l]­*V[l] + P[h]*V[h] ) / ( P[u]*P[l]+ P[h} ) Bid price so Market Maker breaks even B = ( P[l]*V[l] + P[u]*P­[h]­*V[h] ) / ( P[l] + P[u]*P[h] Bid-Ask Spread s = A - B

### Note

 Note: Spot Rates = Flat Term Rate. And Equal to YTM if the rates are flat. If not, YTM is found using the formula to your left.