Checking Conditions for (Lack of) Redington Immunization in a Spreadsheet
Spreadsheets are extremely useful tools for many business, academic, and personal applications.
Examples of situations where spreadsheets are useful include: budgeting (totals, averages, piecharts), descriptive statistics (means, standard deviations, correlations, graphs), inferential statistics (t-statistics, p-values, ANOVA regression tables), finance (monthly payments, internal rates of return), simulation (random number generation, discrete probability distributions), and much, much, more.
In fact, in my personal experience, I have found that if you can become familiar with even the most basic aspects of spreadsheet use, people will be impressed. Of course, it’s also easy to mis-use mathematical and statistical tools, so you should make sure you have co-workers who can check your work and confirm your assumptions. Learning to work with others and have humility is important both on the job and in life (Proverbs 11:2).
Computationally, the key idea that makes spreadsheets so useful is the idea of a spreadsheet formula. In any given cell of a spreadsheet, a formula starts by typing an equal sign “=”. The equal sign is a signifier to the spreadsheet that you want it to do a computation.
The computation could be to just do some basic arithmetic, e.g. you could enter =4+3*5 to get an output of 19 (not 35 — the spreadsheet is programmed to know about order of operations — in this case, the fact that the multiplication must be done before addition).
If the number “4” happens to be in cell A1 (a “cell reference“) the number “3” in cell A2, and the number “5” in cell A3, then entering =A1 + A2*A3 into cell A4 will produce the same answer of “19” in cell A4. This has the advantage of allowing you to make changes and having the answer get updated. For example, if you change the number in cell A1 to be “6”, then the answer in cell A4 will get updated to “21”.
Another advantage of using formulas involving cell references is that they are “copy-and-paste-able” in a useful way. For example, if you have a bunch of numbers in cells A1 through A10 (the first ten cells down the first column of the spreadsheet), and you would like to multiply each of these numbers by 5, you can just enter =5*A1 into cell B1 and then copy-and-paste this formula into cells B2 through B10. When you do this, the spreadsheet is programmed to automatically use =5*A2 in cell B2, =5*A3 in cell B3, etc. This will produce the ten answers that you need without much typing.
A more advanced application is to use a formula that involves a built-in spreadsheet function, such as MEAN. If there are numbers in cells A1 through A10 (the first ten cells down the first column of the spreadsheet), then entering =MEAN(A1:A10) into another cell will compute the arithmetic average of those ten numbers.
Spreadsheets and Redington Immunization
In my video “Actuarial Exam 2/FM Prep: (Lack of) Redington Immunization in a Spreadsheet” embedded below, I use a spreadsheet in the context of immunization of liability cashflows by asset cashflows.
The definition of Redington immunization involves derivatives of present value functions. However, the results of Exercise 7.2.3 from “The Mathematics of Investment and Credit“, 7th Edition, by Samuel A. Broverman confirm that we can think of Redington immunization in terms of certain summations. These summations are computed in the spreadsheet.
In the first example of this video, based on the October 2018 Society of Actuaries Sample Exam Problem #127, the liabilities are actually not Redington immunized by the assets, in spite of the fact that present values and durations have been matched. This means that the following summation facts are true for this example: 1) 
In the second example from the video, conditions (1) and (2) from above hold, but the two parts of condition (3) become equalities, because that example is at the “boundary” of Redington immunization. The derivation for this example is done in another video, “Actuarial Exam 2/FM Prep: Modifying an Asset Cashflow to Achieve Immunization”, embedded below.