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[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 |