User:Quebec/Consumption smoothing

Consumption smoothing is an economic concept stating that people want to optimize their standard of living over their lifetime. In other words, "people seek to smooth spending over their lifetimes in order to obtain the greatest satisfaction from their limited resources, and the problem to be solved is how high this standard of living can be".

To maintain their standard of living (purchasing power) after retirement, investors need to build up financial assets by saving a portion of their employment income during their work years. How much saving is actually needed to achieve this is a difficult question.

Traditional approaches to retirement planning start either with a savings rate goal (e.g., "save 10% of your income"), or an income replacement goal (e.g., "replace 70% of your pre-retirement salary"). These approaches are likely to result in either a sudden drop or an abrupt increase of purchasing power at retirement, because they can lead the investor to save either not enough, or too much. A more rational approach is to start with the explicit aim to smooth consumption over one’s remaining lifetime, calculate this optimal consumption amount, and adjust other parameters accordingly.

This article explores the consumption smoothing approach to retirement planning in two steps. We first look at an ideal world example to illustrate the concepts. We then present a method that takes real world factors, such as taxes and variable salaries, into account.

In the ideal world
To illustrate the concept of consumption smoothing, here is an example presented in chapter 4 of Chapurat et al. (2012). A 25 year old person is about to start working, plans to retire at 65, and plans to die broke at exactly 90. There is $3000 in a savings account, and no debt. The initial salary, payable at year end, will be $50,500, and will grow at a real (after-inflation) rate of 1%. All valuation rates are 3% real (return on investment, discount rate for human capital, etc.). Yearly consumption is to remain constant in real terms. The following table shows the results of the calculations, in today’s dollars, with human capital and financial capital given at the beginning of each year:


 * {| class="wikitable" style="text-align:center"

The following graphs illustrate the variations in human capital, financial capital, salary, consumption, and yearly savings.
 * align="center" style="background:#f0f0f0;"|Age
 * align="center" style="background:#f0f0f0;"|Gross human capital
 * align="center" style="background:#f0f0f0;"|Financial capital
 * align="center" style="background:#f0f0f0;"|Salary
 * align="center" style="background:#f0f0f0;"|Consumption
 * align="center" style="background:#f0f0f0;"|Savings
 * align="center" style="background:#f0f0f0;"|Savings rate
 * 25||$1 372 536||$3 000||$50 500||$48 334||$2 156||4.3%
 * 26||$1 363 212||$5 246||$51 005||$48 334||$2 661||5.2%
 * 35||$1 240 356||$54 036||$55 783||$48 334||$7 439||13.3%
 * 45||$999 502||$185 839||$61 620||$48 334||$13 275||21.5%
 * 55||$605 986||$432 799 ||$68 066||$48 334||$19 722||29.0%
 * 64||$72 275||$791 969||$74 443||$48 334||$26 099||35.1%
 * 65||$0||$841 827||$0||$48 334||-$48 344||n.a.
 * 75||$0||$577 132||$0||$48 334||-$48 344||n.a.
 * 85||$0||$221 403||$0||$48 334||-$48 344||n.a.
 * 89||$0||$46 936||$0||$48 334||-$48 344||n.a.
 * }
 * 64||$72 275||$791 969||$74 443||$48 334||$26 099||35.1%
 * 65||$0||$841 827||$0||$48 334||-$48 344||n.a.
 * 75||$0||$577 132||$0||$48 334||-$48 344||n.a.
 * 85||$0||$221 403||$0||$48 334||-$48 344||n.a.
 * 89||$0||$46 936||$0||$48 334||-$48 344||n.a.
 * }
 * 85||$0||$221 403||$0||$48 334||-$48 344||n.a.
 * 89||$0||$46 936||$0||$48 334||-$48 344||n.a.
 * }
 * }





The details of how such calculations are performed are given in Chapurat et al. (2012). . It is possible to adjust consumption so that it has an upward trend (for patient investors) or downward trend (for impatient investors). One can also change the discount rate, etc.

In the real world
The calculations in the previous section ignore the effect of taxes, government pensions and benefits (OAS, CPP/QPP), RRSP limits, salary fluctuations, and unpredictable investment returns. In the real world where such factors are at play, more flexible tools are needed.

A method of calculating the savings rate each year, that takes into account one’s salary, taxes, portfolio balance, etc. and that smooths future consumption has been developed by FWF member longinvest. He calls this The After-Tax Spending Plan and writes that the spreadsheet "informs us about the 'equilibrium' monthly spending amount, given the current state of things: current age, planned retirement age, current salary, current portfolio balance, and currently accrued QPP (and eventually CPP) pension".

EXPLAIN THE CALCULATIONS IN EXCRUCIATING DETAIL

INSERT LINK TO SPREADSHEET