cashflow Archives - Infinity is Really Big

March 1, 2019March 1, 2019

New Video: Internal Rate of Return

Lecture 5 on Financial Mathematics for Actuarial Science

Financial Math for Actuaries, Lecture 5: Internal Rate of Return (IRR), a.k.a. Yield Rate

I have been working on developing video resources for Bethel University‘s course on Financial Mathematics for Actuarial Science for the past couple of years.

Mostly this has consisted of making many very detailed problem-solving and conceptual videos … Read the rest

February 22, 2019February 22, 2019

New Video: Immunization, Part 6

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 … Read the rest

February 20, 2019February 21, 2019

New Video: Immunization, Part 5

Redington immunization is a concept that can be defined in terms of derivatives of present value functions.

Given asset cashflows $A_{0},A_{1},A_{2},\ldots,A_{n}$ and liability cashflows $L_{0},L_{1},L_{2},\ldots,L_{n},$ each set of flows occurring at times $t=0,1,2,\ldots,n,$ the expressions $P_{A}(i)=\displaystyle\sum_{t=0}^{n}A_{t}(1+i)^{-t}$ and $P_{L}(i)=\displaystyle\sum_{t=0}^{n}L_{t}(1+i)^{-t}$ represent the present values of these cashflows, as functions of an arbitrary periodic interest rate $i.$

If we let $h(i)=P_{A}(i)-P_{L}(i)=\displaystyle\sum_{t=0}^{n}C_{t}(1+i)^{-t},$ where $C_{t}=A_{t}-L_{t},$ then we say the liabilities are Redington immunized … Read the rest

February 4, 2019February 12, 2019

New Video: Immunization, Part 3

Immunization of a liability cashflow by an asset cashflow can help to cushion a company when interest rates change, but is it always possible?

My most recent video is “Actuarial Exam 2/FM: Liabilities Not Immunized by Assets in Spite of PV and Duration Matching” (Financial Math for Actuarial Exam 2 (FM), Video #171. October 2018 SOA Sample Exam, Problem #127). … Read the rest

January 30, 2019January 31, 2019

New Video: Immunization, Part 1

It is very important for any business, including any insurance company, to be able to meet their financial liability obligations.

A major class of liabilities that insurance companies must plan for are the claims from their customers. For example, if a person buys car insurance, then the insurance company would be obligated to pay for, among other things, some or … Read the rest