Saving for retirement: A thought experiment

In an earlier post, I discussed worry-free investing which was based upon the work of Zvi Bodie. Determining how much to put away for retirement depends on so many different factors that is becomes hard to come up with a "correct" number. There are so many variables such as:

• Inflation rate: By this I don't mean just the widely publicized consumer price index (CPI), since one's spending habits may differ quite a bit from the way the CPI weights the various classes.
• Tax rates: This would relate to current and future income tax rates (federal, state, and local) as well as sales tax rates. This is also affected by where one chooses to live in retirement.
• Returns on investments: This includes things like interest rates and the movement in stocks and bond prices.
• Social security payments: With the financial problems facing the government, it's hard to say what sort of payments social security would be able to make in the future.
• Changes in income: One would normally have more income with age because of experience, but that seems to be changing nowadays with folks losing a job and being forced to accept a lower income.
• Changes in expenses: As one goes through the years, what we spend on changes.  In younger years, one may not need to spend much.  In middle age there is often added costs of supporting a family.  As we age, depending on our health, there may be a lot of expenses for medical care.
• Life span: Perhaps the most crucial one. One may not be around during one's planned retirement years!  But it's probably better to leave behind an estate than to live one's golden years in poverty.

But for the purpose of this exercise, we're going to ignore all of that.

Let's say I make 100 pieces of gold for every year that I work, with no change in income, and no loss of income at any point during my working life. Further, let's assume that what a piece of gold buys today, it will also buy n years from now, where n > 0. In other words, a piece of gold will buy in retirement exactly what it buys today. Let's assume that there are no taxes.

Now, for every year I work, I get 100 pieces of gold. Let's say I spend 50 pieces of gold each year and save the remaining 50. Thus, for every year that I work, I have basically bought one year of retirement. In other words, if I work 30 years, I can have 30 years of retirement. If, on the other hand, I spend 25 pieces of gold each year, I have bought 3 years of retirement for every year of work. And if I spend 75 pieces of gold, I have bought only one year of retirement for each 3 years of work. This, of course, ignores the time value of money as well; i.e. there was no attempt to invest the money during the working years, but also bear in mind that any kind of investing necessarily involves risk.

So if we look at the average working life of about 40 years until retirement (age 25 to 65), and we need to plan to live to age 105, a retired life of 40 years, then using this simple example, we need to be able to save 50% of our income. In general, if I work x years, and need to plan for a retirement of y years, then I need to restrict my spending to [x/(x+y)] × 100% of earnings. Put another way, if I save m% of my income each year, then I buy one year of retirement for every (100-m)/m years of work. If we want to account for taxes, then these percentages would apply to the post-tax income.

Perhaps the biggest drawback of this example is that it does not account for social security. At lower income levels, social security tends to replace a significant portion of that income, and would therefore require a significantly lower savings rate. However, at higher income levels social security contributes far less to replacing that income.

Anyway, this is just a thought experiment and is not practical by any means. But I thought I'd write it up nevertheless.

(A few days after writing this post, courtesy of A.Word.A.Day, I found out of the existence of the word gedankenexperiment, which means "thought experiment". Had I known of it before this post, I might have used it in the title.)