Saturday, January 10, 2009

Why is Warren Buffett a Cheapskate?

Warren Buffett was notorious for frugality in his younger years.  He has mellowed a bit, but the various stories always make him seem eccentric at best and if one were less charitable, just plain goofy.

One explanation, from the book, Snowball, is:
 ...a small sum could turn into a fortune.  He could picture the numbers as vividly as the way a snowball grew when he rolled it across the lawn.  Warren began to think of time in a different way.  Compounding married the present to the future.  If a dollar today was going to be worth ten some years from now, then in his mind the two were the same.
Most people don't think this way. Everyone knows that when you are young, you can afford to take risks, and as you grow closer to retirement, you need to invest more conservatively. You are effectively diversifying over time. This is one case where what everyone knows is simply wrong.

John Norsted, a paleo blogger, has discussed this at length on his website.  Per Norsted, 
If there is one thing I would like people to learn from this paper, it is to disabuse them of the popular notion that stock investing over long periods of time is safe because good and bad returns will somehow "even out over time." Not only is this common opinion false, it is dangerous. There is real risk in stock investing, even over long time horizons. This risk is not necessarily bad, because it is accompanied by the potential for great rewards, but we cannot and should not ignore the risk.
Norsted continues:
While the basic argument that the standard deviations of the annualized returns decrease as the time horizon increases is true, it is also misleading, and it fatally misses the point, because for an investor concerned with the value of his portfolio at the end of a period of time, it is the total return that matters, not the annualized return. Because of the effects of compounding, the standard deviation of the total return actually increases with time horizon. Thus, if we use the traditional measure of uncertainty as the standard deviation of return over the time period in question, uncertainty increases with time.
I'll try to make this a bit simpler. An individual typically wants to compound her (his) savings over her (his) working life, and end up with a terminal amount at retirement that is the right number to fund her (his) lifestyle.  We care about the final number.  In a simplistic example, if a person starts with a fixed sum at age 20 and makes no further contribution, the terminal amount will be the product of the annual returns over 45 years [times the initial investment].  With annual returns expressed as factors, like (1+r1) x (1+r2) x (1+r3) .... (1+r45).  r is the return and the number refers to the percentage return in that particular year.  Like (1.05) x (1.15) x (1.01) etc. High School algebra: AxB = BxA.  The order of the terms is totally irrelevant.  The return in year 1 is exactly as important as the return in year 45.  

Lets say the r's are selected from a uniform distribution of 2% to 8%.  Like drawing a slip of paper out of a hat with an equal number of 2%'s, 3%'s, etc.  The average annualized return could be just as easily be 2% as 8% after the first pick.  Draw a larger sample and the mean annual return will tend to get closer to 5%.  But normal people don't care about their annualized returns.  They care about their accumulated dollars.  The predictability of their terminal return decreases the longer the series.

In 1948, consider that Buffett could have debated if he wanted to spend an extra dollar on a meal.  If he ordered the T bone instead of a burger, that dollar, compounded at 20% over 60 years would amount to $56,000.  Even today, a Saudi Prince would balk at $56,000 to upgrade from a burger to a steak.  

After his early 20's, Buffett never held a job and never made more in salary then his living expenses.  So he really did take his small stake and simply run it up to a huge number.  Sort of. 

Real life is more complex, but the basic idea is that retirees spend dollars, not annualized returns.  Returns are multiplicative, so it doesn't matter how you order the good years and the bad years.  Losses in the early years are exactly as harmful as losses in later years.  

Norsted does a great job in the cited paper.  I am skipping over the nuances and complexity of how this would play out in more complex scenarios, but Norsted discusses them.  In addition, these findings are true using the currently maligned normal distribution.   Any adjustment for "fat tails" or "black swans" simply strengthen the argument.



1 comment:

K T Cat said...

I never thought of it this way. Thanks!