Macaulay Duration of an Amortizing Loan

The term “duration” is often used interchangeably by market participants to denote either a volatility measurement, a weighted term to maturity, or a portfolio risk measurement. In practice there is more than one definition of duration. The following describes the most basic duration along with it’s calculations. In a future posts we will discuss Modified Duration, Effective Duration, […]

Valuing Servicing Matrix

On August 26, 2014 I showed  an amortization schedule that could be used for initially valuing servicing. I introduced the use of constant prepayment rates (CPR) in order to get a more realistic pricing than assuming the pool of mortgages or commercial loans would never prepay. Considering the ease of refinancing and the mobility of the labor […]


There is nothing special about this annuity calculator except: All input is with sliders Each line of the results are one cell text and formulas The dollar growth and payout balances are charted You can pick from monthly deposits or lump sum deposit Inputs: Outputs:   Download workbook “Annuity” from:  Downloads Written in Excel […]

Decision Tree for Notice of Defaults

After the housing bubble crash, defaults on mortgage loans became a big problem for financial institutions. A large number of homeowners either could not or would not continue to make payments on homes that were “underwater” (home value less than the amount owed on mortgages and other liens). After 90 days of no payments, a […]

Sum Amounts Sold During Month & Year

You have a table of products, sales dates, and amounts: Objective: Sum all sales amounts , from the same product, during a certain month and year. Input in yellows cells only, any date within the month and year to be summed and a product code: The answer has two formulas that are the same formula except one […]

Simple Mortgage Refi Break-Even

If you do a search, you will find dozens of mortgage refinance calculators on the internet, most on sites of companies that want to sell you a new loan. The big problem with calculating break-even (when the new lower interest rate, will cover the cost to refinance) is: What happens to the difference in monthly payments Where did the money used to […]

Forward Rates Part 3: Spot Rates

A newer version with four bootstrap methods can be found at: A Forth Way To Bootstrap Spot Rates This method of calculating spot rates is referred to as the bootstrapping method. Each spot rate (or zero coupon) along the Treasury yield curve needs the previous spot rates, in order to discount the current securities coupon payments. […]

Forward Rates Part 2: Forward Yield Table

In the last post, Forward Rates Part 1: Gap Analysis, we calculated the forward rate for a two year fixed rate investment, five years from now. Here is a review of the math: Why is everything multiplied by 2? That’s because we are assuming semiannual compounding. First we calculate the value of $1 in 5 years at […]

Forward Rates Part 1: GAP Analysis

  Gap Analysis, sometimes referred to as breakeven analysis, will get us 3/4 of the way to understanding forward rates. There are three different interest rates involved with gap analysis: Term Rate: Security with the longest term to maturity. Head Rate: A shorter maturity alternative to the Term Rate. Tail Rate: A rate that starts at the end of […]