Case 11.2: Forecasting COLAs

Tarrows, Pearson, Foster and Zuligar (TPF&Z) is one of the largest actuarial consulting

firms in the United States. In addition to providing its clients with expert advice on

executive compensation programs and employee benefits programs, TPF&Z also helps

its clients determine the amounts of money they must contribute annually to defined

benefit retirement programs.

Most companies offer two different types of retirement programs to their employees:

defined contribution plans and defined benefit plans. Under a defined contribution

plan, the company contributes a fixed percentage of an employees earning to fund the

employees retirement. Individual employees covered by this type of plan determine

how their money is to be invested (e.g., stocks, bonds, or fixed-income securities), and

whatever the employees are able to accumulate over the years constitutes their retirement

fund. In a defined benefit plan, the company provides covered employees with

retirement benefits that are usually calculated as a percentage of the employees final

salary (or sometimes an average of the employees highest 5 years of earnings). Thus,

under a defined benefit plan, the company is obligated to make payments to retired

employees, but the company must determine how much of its earnings to set aside

each year to cover these future obligations. Actuarial firms such as TPF&Z assist companies

in making this determination.

Several of TPF&Zs clients offer employees defined benefit retirement plans that

allow for cost of living adjustments (COLAs). Here, an employees retirement benefit is

still based on some measure of his or her final earnings, but these benefits are increased

over time as the cost of living rises. These COLAs are often tied to the national consumer

price index (CPI), which tracks the cost of a fixed-market basket of items over

time. Each month, the Federal government calculates and publishes the CPI. (Monthly

CPI data from January 1991 through March 2016 is given in the file CPIData.xlsx that

accompanies this book.)

To assist its clients in determining the amount of money to accrue during a year for

their annual contribution to their defined benefit programs, TPF&Z must forecast the

value of the CPI 1 year into the future. Pension assets represent the largest single source

of investment funds in the world. As a result, small changes or differences in TPF&Zs

CPI forecast translate into hundreds of millions of dollars in corporate earnings being

diverted from the bottom line into pension reserves. Needless to say, the partners of

TPF&Z want their CPI forecasts to be as accurate as possible.

a) Apply a regression model with linear trend factors and seasonal (quarterly) indices to make forecasts for the next 3 months in 2016.

b) Use the Holt-Winters method to re-do Question 4, incorporating additive seasonality effects.