Today’s Wall Street Journal’s Money & Investing section had an excellent article by E.S. Browning on measuring investments by real-world returns. He quotes this research by Thornburg Investment Management. (The Journal article quoted numbers through 2005, I could only find the 2004 Thornburg article so I’m using 2004 numbers to avoid confusion)

The example discussed in the article is the S&P 500 since 1926.It is common knowledge that the S&P has returned about 10% per year since then. Put another way one dollar invested in the index in the start of 1926 would have appreciated to $2,531.44 at the end of December 2004. This annualizes out to a rate of 10.43%.

Thornburg after running the numbers net of inflation, taxes, and fees and found a starkly different story. That same $1 in real (post tax, fees, and inflation) terms would only be worth $44.80. Which only annualizes out to a rate of only 4.96%. They assumed fees of .2% of assets yearly, inflation of 3.04%, and then you can work out that they assume taxes to average out to 2.23% of assets per year. Since we’re talking about annual rates, we can use simple arithmetic to calculate the effects on returns so long as all percentages are in terms of assets per year. APY is implicitly a percentage of assets.

In an IRA, things fare quite a bit better since you get to add back in some or all of the value lost to taxes.

With a Roth IRA, since you’ve paid taxes on the money already, you get to add back all of those taxes and you get a historical return of 7.19%.

With a traditional IRA or 401(k) things are a bit more complicated. You have to deflate the real value of your money by the tax-rate when it is withdrawn. You get to compound at 7.19% yearly, but you have to take out taxes on the back end, and the amount of taxes you’ll take out depends on 1) the amount of income and 2) the tax rate at that time (for me, that’s about 42 years from now).

I ran the numbers simplistically, assuming a 33% tax on withdrawals and a withdrawing everything at the end of 20, 30, and 40 years. This Resulted in effective rates of 5.06%, 5.77%, and 6.12% respectively. Bear in mind, that this is a simplification and because you’re only withdrawing a small amount per year.

## Monday, February 06, 2006

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## 3 comments:

Excellent post. With all the financial books and blogs touting 10% compounded returns (as if you can keep the whole 10%) from the compounding of the stock market, it is a breath of fresh air to see the REAL return, after the expenses of life.

However, it is incorrect to take the difference as the REAL return. I may be wrong, but my calculated real return from the given data is 4.62%.

Although the real return is low, I believe the stock market is the best way to increase one's wealth.

Alex,

I am not sure how you got the 4.62% number. I took 4.96% directly from the thornburg article I refferenced. I was able to confirm 4.96% using the follwoing formula in excel =rate(79,,-1,45.8).

If I was using the numbers in the Journal article, I came up with 4.92% using the same formula. The difference is because the Journal used data through 2005 and I was only able to find the thornburg article through 2004.

Your final analysis is exactly the same as Thornburg's. The rates are low, but they could be lower. http://tinyurl.com/chf2p

Despite everything, stocks are the way to go.

I did not calculate the return using payment period, present value, and future value. If I did, I would have gotten an answer close to 4.96%.

Instead, I calculated the real return using a variance of this formula:

(1+nominal return) / (1+inflation) = (1+real return)

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