## May 20, 2008

### What is the equivalent rate of return on social security?

Here's a question:

If you were able to save the Social Security tax payments for your whole life in a retirement account, then what % rate return on your money would you have to earn in order to gain retirement income equivalent to Social Security retirement benefits?

Basically what I'll be doing is comparing the return you get from Social Security as a retirement system to the return you might get with a private retirement fund.
This is actually a pretty complicated question to answer. There are a few parts to answering this. First we need to know how much money you make over the years. Second we need to know how much social security would pay out for retirement benefits. Third we need to know what it would cost to buy that benefit in an inflation adjusted annuity. Lastly we will have to figure the rate of return to save the amount needed to buy the annuity.

1. What is the income earned?

I'm going to simply pick income levels to test with. I'll use 3 different figures to get an even range. I'm going to use values that are multiples of the approximate per income level to equate to low, middle and high income. Starting with the per income level of \$27,239 for 2006 I'll use that as the low income value. Then 2 times that value or \$54,478 for a middle income and finally quadruple the per income value for \$108,956 for the high income value.

 Income Low \$ 27,239 Middle \$ 54,478 High \$ 108,956

2. What are the social security benefits?

The Social Security website has a Social Security Quick Calculator that will estimate your Social Security benefits at retirement age.

Using the calculator we can figure the Social Security retirement benefit for someone who is about to retire. I put in a birth date of 6/15/1943 and earnings for he current year of \$27,239. The amount \$27,239 is the per capita income for 2006 so this is an estimate of average wage. With these figures the calculator estimates that the Social Security benefit would be \$884 a month at age 66 in 2009. Using the same birth date an income of \$54,478 results in benefit of \$1,369 and an income of \$108,956 gives benefit of \$2,010.

 Income Benefit Low \$ 27,239 \$ 884 Middle \$ 54,478 \$ 1,369 High \$ 108,956 \$ 2,010

Note that the benefit rates are not proportional. They are 0.032, 0.025 and 0.018 respectively. So the low income person is getting a higher return from each \$1 they put in than the higher income person. The social security system is a progressive tax system.

3. How Much would an annuity cost?

I'll use the Vanguard annuity information to figure the cost of an annuity equivalent to the Social Security retirement benefits. I'm going to figure the annuity costs two ways, for married couple and for a single person. The annuity for a married couple is more expensive since it will cover the potential life span of two individuals rather than one. I'll use the birth date of 6/15/1943 for both spouses and chose an inflation adjusted annuity thats tied to CPI similar to how Social Security benefits have a COLA (cost of living adjustment). Using the quick quote method on Vanguards site I can figure the cost to buy such an annuity today for a given monthly payment starting in 2009. The result annuity costs are as follows:

 Married Single Income Benefit Annuity Cost Annuity Cost Low \$ 27,239 \$ 884 \$ 191,567 \$ 149,989 Middle \$ 54,478 \$ 1,369 \$ 296,613 \$ 232,224 High \$ 108,956 \$ 2,010 \$ 435,448 \$ 340,910

4. What rate of return on the saved money would we need to get to buy the equivalent retirement benefits?

I used an Excel spreadsheet to figure the rate of return required to get enough savings accumulated to buy the annuities. I did this by plotting out the savings every year from 1961 to 2008 and adding the 15% contribution of wages (employee and employer) for each year. Then I multiplied the savings each year by a fixed % rate. I changed the % rate until using trial and error I got savings equivalent in 2008 to the cost of the annuity and then this % rate is the Rate of Return (ROR) required to buy the annuity. I hope this makes sense. I'll give a quick demo of this trial and error method with a short example. Say I want to have \$500 in 3 years. If I save \$100 per year then what % return would I need to accumulate \$500? I'll start with a 5% return rate which results in \$331. I increase to 10% and get \$364. I jump up to 33% and get \$545. Now I know the rate is between 10% and 33%. I try 20% and get \$437. I'm starting to narrow in and I know its between 20-33%. I keep narrowing down until I get to 27.8%

Using my method to calculate rate of return, I can find the % return you would need to make on your money in order to buy the annuity equivalent to the social security payment.

The results are:
 Married Single Married Single Income Benefit Annuity Cost Annuity Cost ROR ROR Low \$ 27,239 \$ 884 \$ 191,567 \$ 149,989 7.0% 5.6% Middle \$ 54,478 \$ 1,369 \$ 296,613 \$ 232,224 5.6% 4.2% High \$ 108,956 \$ 2,010 \$ 435,448 \$ 340,910 3.8% 2.2%

So there you have it: By my figuring, the return rate from social security varies from 2.2% to 7.0% The typical worker is probably in the middle range of 4-5%.

Keep in mind that this does not count the value of disability insurance. Also keep in mind that I'm just doing rough figuring here and my information is only as good as the data I have to work with.

Here are some further sources of information on this topic:
• First off there is a study from the Social Security Administration that discusses rate of returns from SS. That study has return numbers ranging from 0.44% to 9%. The low of 0.44% is for a high income single person retiring in 2069 and the high of 9% for a low income one earner couple who retired in 1985.
• Heritage foundation has a calculator to estimate the return from social security versus private retirement accounts. The results I get there range from -0.29% to 2.97%
• Another calculator to estimate returns can be found at the Political Calculations blog. Their results seem to be in the 0.3% to 5.6% range depending on situation.
• The paper Rate of Return from Social Security from Federal Reserve bank of San Francisco stated that : "The authors find that, under current OASI rules, today's lowest paid workers (those in the bottom 20% of the income distribution based on lifetime earnings) can expect internal rates of return between 4% and 5% after adjusting for inflation (Panel A). Today's middle income workers can expect real rates of return between 1% and 2%."