The ups and downs of volatility

Imagine the year is 1974. You’re contemplating saving for your older years. Your plan is to put aside 1000 per year at the end of each year until 2017. Suddenly, a man comes from the year 2017 and informs you that between 1974 and 2017, the S&P500 will average 10.983% annual return. You do some quick back-of-the-napkin math, because you know how to do exponents quickly, and you calculate that that means that a dollar today will become $98.02 by the end of 2017. Not bad! Now, Mr. Future Man also tells you that there will be some good years and some bad years. (It turns out the best year would be 1995 with a 37.20% gain, and the worst year 2008 with a 36.55% loss. However, Mr. Future Man refuses to tell you the years, as he mumbles something about the space-time continuum.)

Now Mr. Future Man makes you an offer – instead of living in the fear and doubt that comes with big ups and downs in the market, Mr. Future Man is willing to let you invest in his secret fund, the ISF (for Impossibly Smooth Fund), which guarantees a 10.983% annual return with no volatility. You must stick to your same plan, however. Invest $1000 at the end of each year until 2017. Do you take him up on his offer? At first, the decision seems clear. If you put a dollar in the S&P500 today or a dollar in the Impossibly Smooth Fund (ISF), by 2017 that dollar would be $98.02, and there wouldn’t be any bumps along the way. All the money, no fear. You decide to invest with Mr. Future Man, and he keeps his promise of a flat 10.983% return through 2017.

However, your twin brother had the same idea as you, but Mr. Future Man does not visit him, so he invests $1000 per year at the end of each year in the S&P500. The end of 2017 rolls around and you’ve both made your final contribution. You tally things up, and you find that you have $883,302.62. Not bad for $44,000 invested. Your brother shows you his brokerage statement, and it shows a balance of $968,590.47 – more than $85,000 above your balance. What happened? Did you get the same average return, but without the bumps?

It turns out that volatility is your friend when you’re saving. Remember the mantra of “buy low, sell high”. While you’re saving up, if there are bad years, that’s an opportunity to buy low. With the Impossibly Smooth Fund there are no years for you to buy low. It’s all steady growth. Note: volatility is not a guarantee of better returns. If the returns happen in different orders, it could be anything from much worse, to much better. However, based on tens of thousands of randomizations that I ran on my computer, a volatile fund is more profitable than a non-volatile one more often than not, if you invest steadily over the years. Also note: the inverse is true. During times when you are withdrawing money rather than contributing money, a more volatile fund will serve you worse than a more steady fund with the same return.

Here are the numbers:

Year End of year contribution Actual S&P500 return End year year balance in S&P500 fund ISF return End of year balance in ISF fund
1974 $1000 -25.90% $1,000.00 10.983% $1,000.00
1975 $1000 37.00% $2,370.00 10.983% $2,109.83
1976 $1000 23.83% $3,934.77 10.983% $3,341.55
1977 $1000 -6.98% $4,660.12 10.983% $4,708.56
1978 $1000 6.51% $5,963.50 10.983% $6,225.70
1979 $1000 18.52% $8,067.94 10.983% $7,909.46
1980 $1000 31.74% $11,628.70 10.983% $9,778.16
1981 $1000 -4.70% $12,082.15 10.983% $11,852.10
1982 $1000 20.42% $15,549.33 10.983% $14,153.81
1983 $1000 22.34% $20,023.05 10.983% $16,708.32
1984 $1000 6.15% $22,254.47 10.983% $19,543.40
1985 $1000 31.24% $30,206.76 10.983% $22,689.85
1986 $1000 18.49% $36,791.99 10.983% $26,181.88
1987 $1000 5.81% $39,929.60 10.983% $30,057.43
1988 $1000 16.54% $47,533.96 10.983% $34,358.64
1989 $1000 31.48% $63,497.65 10.983% $39,132.25
1990 $1000 -3.06% $62,554.62 10.983% $44,430.15
1991 $1000 30.23% $82,464.89 10.983% $50,309.91
1992 $1000 7.49% $89,641.51 10.983% $56,835.45
1993 $1000 9.97% $99,578.77 10.983% $64,077.68
1994 $1000 1.33% $101,903.16 10.983% $72,115.34
1995 $1000 37.20% $140,811.14 10.983% $81,035.76
1996 $1000 22.68% $173,747.11 10.983% $90,935.92
1997 $1000 33.10% $232,257.40 10.983% $101,923.41
1998 $1000 28.34% $299,079.15 10.983% $114,117.66
1999 $1000 20.89% $362,556.78 10.983% $127,651.21
2000 $1000 -9.03% $330,817.90 10.983% $142,671.14
2001 $1000 -11.85% $292,615.98 10.983% $159,340.71
2002 $1000 -21.97% $229,328.25 10.983% $177,841.10
2003 $1000 28.36% $295,365.74 10.983% $198,373.39
2004 $1000 10.74% $328,088.02 10.983% $221,160.74
2005 $1000 4.83% $344,934.67 10.983% $246,450.82
2006 $1000 15.61% $399,778.98 10.983% $274,518.51
2007 $1000 5.48% $422,686.86 10.983% $305,668.88
2008 $1000 -36.55% $269,194.81 10.983% $340,240.49
2009 $1000 25.94% $340,023.95 10.983% $378,609.11
2010 $1000 14.82% $391,415.50 10.983% $421,191.74
2011 $1000 2.10% $400,635.22 10.983% $468,451.23
2012 $1000 15.89% $465,296.16 10.983% $520,901.23
2013 $1000 32.15% $615,888.88 10.983% $579,111.82
2014 $1000 13.52% $700,157.05 10.983% $643,715.67
2015 $1000 1.36% $710,679.19 10.983% $715,414.96
2016 $1000 12.25% $798,737.39 10.983% $794,988.98
2017 $1000 21.14% $968,590.47 10.983% $883,302.62