Index Fund Returns

A Better Way to View Investment

Have you ever invested through a bank, or perhaps a mutual fund online? Perhaps they gave you a selection of options and gave you a bunch of averages: the 1 month return, 1 year return, 5 and 10 year average return, and so on. But how much money will you make? If you invested $1 today and came back in 40 years, how much money would they give you? After fees and inflation and taxes, it's not clear. That's why I came up with a better way of visualizing this.

These are the S and P 500 index fund graph with its dividends, and the inflation rate in the USA with the consumer price index, since around the 1800's. Even if you subtract the inflation and add the dividend return to the nominal return of the S and P 500, you've omitted taxes and fees, and still have almost no idea how much money can actually be made through investing.

I built a compound investment calculator (in Python 3.4) that takes functions for amount added every year, capital gains taxes, dividend returns every year, taxes on dividends, rate of return every year and inflation every year. I applied the S and P 500 returns to this data and came up with a money multiplier table (below):

Between the years 1975 and 2015, the X represents the year invested, Y the year removed, and Z is the multiplier. For example, if I invested $5000 in the S and P 500 through Vanguard at a .05% fee in Texas and I am roughly in the middle class (not through a 401k), if I take the $5000 out in 2014, I'll have $15,000 after tax and fees in 1975 dollars. If that investment was in California or New York, it would be $13,300.

States like New Hampshire, Texas, and Washington have no state capital gains tax; states like California and New York have about a 9% capital gains tax on the middle class. Middle class Americans living in California will have approximately the same multiplier as the wealthiest 1% of Americans living in New Hampshire.

Fees Effect On Your Investment

Investments in Vanguard's S and P 500 index fund carry a fee of .05%, but what affect would a 2% fee have on your savings? A 2% fee is a typical fee you'd see on a managed mutual fund, and these fees are applied on your entire account holdings every year. Everything below assumes 0% state capital gains taxes.

Be wary of the fees! A 2% fee is not like a 2% capital gains tax — the 2% fee compounds just like interest, causing the Texas 1975-2014 multiplier to go from 3.01 to 1.37, effectively costing the investor half their money.

Historical 40 Year Compounded Returns

For both a tax deferred 401k investment and regular investment, these graphs represent the multiplier if X amount of money is invested each year for 40 years, starting on the x-axis year. States without capital gains taxes, assuming 15% federal capital gains tax (middle class). The shaded regions represent a range of possible multipliers given a combination of investments in the S and P 500 and 10 year T bills.

Notice, you never lose in the stock market — at least not in the S and P 500 over 40 years. None of the multipliers, even without a tax deferred 401k plan, dip below 40; you always make at least all your payments back, after inflation, fees, and taxes.

The Big Picture

Using the 401k tax deferred index fund only returns, this is a histogram of all the 40 year multipliers, as defined above. It would be reasonable to expect 90-150 times your yearly contribution. The data more closely resembles an exponential distribution, so I fit a gamma curve. This has a profound implication: the difference between having a $450,000 retirement fund and a $1,250,000 retirement fund, even when you diversify your portfolio, is mostly just luck.