Monday, March 29, 2010

What is the Average Return Rate of the Stock Market?

Much ado has been made about the prudence of long-term investing in the stock market.  Mutual funds are often quoted as having 10%/year long-term growth.  Burton G. Malkie (author of A Random Walk Down Wall Street) recommends the average investor would do better by purchasing an unmanaged index fund (specifically the Wilshire 5000 for the U.S. market) over a managed mutual fund.  This post will track stock market returns by considering historic S&P 500 data from 1871-2009 pieced together by  Robert Shiller (author of Irrational Exuberance).  I say pieced together because the modern S&P 500 didn't exist until 1957.
The above graph plots the history of a $1 investment in 1871.  The bottom curve (blue) shows the price history of index, while the top curve (red) shows the price history of an investment with dividends reinvested.  The index itself tracks inflation closely (the index has an average return rate of 3.91%/year -- not much higher than the 3.26%/year that the CPI data gives).  The investment with dividends reinvested has an average annual return rate of 8.61%/year.  To calculate these rates, I took the ratio of the value of the investment at one year to the value from the previous year.  I then took a geometric mean of these values to come up with the average return rate.

The below graph is somewhat more interesting because it has been CPI-adjusted. All values are given in 2009 dollars.

Once again, the top curve (red) shows the investment history with dividends reinvested, while the bottom curve (blue) is an inflation-adjusted price history of the index.  In this case the index has an average return rate of 1.80%/year, while the dividends-reinvested investment has a return rate of 6.41%/year.  The following histogram shows the spread in returns for the inflation-adjusted, dividends-reinvested case:


If history repeats itself, a long-term investor can expect to earn an inflation-adjusted 6.41%/year in the S&P 500.  After a 15% capital-gains tax, the investor will be left with a 5.45%/year investment (some fraction of which will be lost to a financial adviser/firm). At 5.45%/year, the investment should double in just under 13 years (the doubling time is given by 100%*ln(2)/investment rate).  This 5.45%/year is significantly less than the 10%/year I seem to remember mutual fund advisers quoting.  This leads me to believe that the real way to get rich (other than, you know, earning money) is to maximize your personal savings rate (the American average being 6.98%/year).

Copyright © 2010 Peter Dolph





Sunday, February 28, 2010

What is the U.S. Personal Savings Rate?


Disposable personal income is the amount of income left over after taxes have been paid.  Personal savings is the amount of income left over after personal consumption expenditures and debts have been paid.  The personal savings rate is the ratio of personal savings to disposable personal income.  The U.S. Department of Commerce's Bureau of Economic Analysis has kept a record of the personal savings rate since 1959.  Since then, the personal savings rate has averaged 6.98% with a standard deviation of 2.75%.  In the past 20 years, Americans have saved at a much lower 4.18%.
The Federal Reserve Bank of St. Louis and the Federal Reserve Bank of Kansas City both have interesting articles that compare the U.S. personal savings rate to that of other countries (notably Germany and Japan).

To tie things in with CPI inflation data, below is a plot showing the annual inflation rate vs the personal savings rate.

Copyright © 2010 Peter Dolph











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