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Coec 371 Cheat Sheet (DRAFT) by

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


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
Discount Factor (D) for Coupon Paying Bonds
Price = C*D[1] + (ParVa­lue­+C)D[2]
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[1] + C*D[2] + (ParVa­lue­+C)D[3]

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[0] - 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]*(­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


Constr­ucting an Arbitage
Year 1 => 100x[1] +5x[2] = 7 {x[3]}

Year 2 => 105x[2] = 107 {x[3]}

Solve for x[1] and x[2]
Computing Realized Returns assuming Dividend Reinve­sting
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: 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.