When I write posts, I face the same dilemma as a researcher presenting results. If you have hung around the research circuit for a while, you notice that there are different ways of thinking about exactly the same thing. Some focus on the detailed technical aspects of the calculations: “This is described by this ginormous equation”. Others focus on the basic understanding: “Here is a simple toy model, that …”.

In myField, the difference between toy models and the complex computer simulations I run is about 50%. This means that the toy models are pretty good and a useful way to think about the problem. They are also quite useful to mark out unchartered space (damn you, competing researchers!).

The same holds for the model presented yesterday.

Suppose we pick a 10% savings rate. This means for every \$10 we make, we save \$1 and spend \$9. After 9 years we have \$9 saved. These \$9 can be spent in the 10th year during which nothing is saved . After 10 years, we thus have \$0 in savings. This is how the math works.

While it is possible to work on and off, professional careers certainly “discourage” sabbaticals. Therefore we will have to stack them. (Yes, the calculations are approximately linear. What about compound interest? I’ll get to that!).

Thus if we pick the 10% rate, we could work 18 years, saving \$18 and then taking 2 years off. Or we could work for 27 years and take 3 years off at the end (after which we need a job “to make ends meet”).

Reinvested compounding returns will change this. If the return rate is high (10%), it will change fundamentally. If the return rate is low, it won’t change very much. I submit that there is a real and present risk that the return rate will be low.

Hopefully I do not need to repeat that it is easy to find 30 year periods in the S&P500, where the return rate has been in the low-middle single digits! Yet, this fact is ignored by practically all personal finance bloggers and book authors who gladly use 10% (historic average) or even 12% (from the 1980-2000 bull run). Ignore it at your peril. Seriously, I’m concerned, but it’s hard to be heard against the chorus of the majority.

So which rate should be used?

Going with the present aggregate P/E of 17, the earning yield is 5.8%. I will ignore taxes, but they would influence the above number to the tune of 0-30%, so 5.8 would turn into 4.1-5.8%.

Historic inflation rates have been 3-4%, but what really matters are future inflation rates (see comments below). Subtracting this from 5.8%, we get 1.8-2.8% or rounding off 2-3%. Using the law of 72, this gives doubling rates of about 25-35 years. Of course this is only the case if all the money was invested in the beginning which is not the case. If it is invested annually, the money won’t double, rather it will end adding somewhere between 0 and 100% to the invested amount. Let’s say 50%. Hence saving \$27 over a period of 27 years will turn into \$40.5 in inflation adjusted dollars, which will allow about 4.5 years of retirement. (Warning, if anyone complains about accuracy, I will post the annuity equations along with a long and boring explanation on how uncertainties in the input parameters eradicates any kind of technical improvements).

So when compound interest is assumed along with an earnings yield based on current numbers (which may change, but still influence everything invested currently), then saving 10% means that after 27 years of working, your retirement would last not 3, but 4.5 years. Therefore 10% is probably a decent savings rate if you plan to work until you are physically and incapable of working anymore. It is probably too little, if you plan to spend decades playing golf.

Originally posted 2008-09-12 07:57:32.