# Tag Archives: Math

## Fast Formulas #6: Finding the Time

The Fast Formulas on this blog provide shortcut calculations for financial instruments such as mortgages and bonds. Most formulas involve the symbol n to represent the number of periods (e.g. years or months) until the end of the instrument. Usually … Continue reading

Posted in Bonds, Fast Formulas, Math | | 2 Comments

## Fast Formulas #4: Geometric Series (One of the Tricks)

In Fast Formulas #3: Pool Average Life with CPR Prepayments, I presented Formula 3.1, a shortcut calculation for the average life of a loan pool under a constant prepayment assumption.  I mentioned that Formula 3.1 was derived by using “a … Continue reading

Posted in Fast Formulas, Math | | 5 Comments

## Fast Formulas #3: Pool Average Life with CPR Prepayments

Fast Formulas #2: Average Life of Mortgage (Amortizing with Balloon) presented a compact formula for calculating the average life of a mortgage that pays as scheduled until it is paid off with a “balloon” payment before the scheduled end of its term.  It occurred to … Continue reading

## Fast Formulas #2: Average Life of Mortgage (Amortizing with Balloon)

Fast Formulas #1: Average Life of Mortgage (as Scheduled) showed a quick way to calculate the weighted average life (“WAL”) of a fixed-rate mortgage that pays as originally scheduled.  I found this formula (which is probably not original) by substituting the standard  level … Continue reading

Posted in Fast Formulas, Math | | 12 Comments

## Fast Formulas #1: Average Life of Mortgage (as Scheduled)

The weighted average life (“WAL”) of a mortgage is the average time until principal is repaid.  It is also the average amount of time that the principal is outstanding.  Recall that for a standard fixed-rate mortgage with level payments, the principal … Continue reading

Posted in Fast Formulas, Math | | 9 Comments

## Puzzle #4: Bond Pricing

Here’s another puzzle I’ve used to teach bond math. It’s not hard, but it requires some understanding of bond concepts that I will explain as we go (I beg the patience of bond mavens). Suppose you are the financial advisor … Continue reading

Posted in Bonds, Fun, Math, Puzzles | | 12 Comments

## Puzzle #3: A Better Answer

Puzzle #3 asked for the weighted average life (“WAL”) of the principal payments for a 30-year mortgage that is cut short by a balloon payment at 15 years. The following information was provided: \$100,000 Principal; 5% Interest Rate; \$536.82 Level … Continue reading

Posted in Fun, Math, Puzzles | | 5 Comments

## Derivative of the Quotient

Given a function F = G/H, the first derivative is usually expressed as (HG’ – H’G)/(H^2) But this is equivalent to: (G’ – F H’)/H The second form seems to be easier to implement in some cases and requires less … Continue reading

Posted in Math | Tagged , , , | 2 Comments

## Last Week’s Bond Refunding Optimization Talk

I enjoyed giving a talk last week at the UC Denver Operations Research Seminar.  There were many excellent questions from those attending, who included representatives from investment banking and the public sector.  Many thanks to Alex Engau for the opportunity … Continue reading

Posted in Bonds, Math, Optimization | Tagged , , ,

## Puzzle #3: Mortgage with Balloon

Puzzle #1 posed the question: given a \$100,000 mortgage at 5% with monthly payments of \$536.82 for 30 years, what is the average life of the principal payments? The puzzle was to be solved with just a few simple calculations. … Continue reading

Posted in Fun, Math, Puzzles | | 22 Comments