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EDIT - The title may mis-lead some. (See discussion below with SMK.)
The message here is that you should not use arithmetic average, but geometric average. This is well known by financial professionals, but often not known by individuals. As volatility goes to zero, so does the difference between an arithmetic and geometric average. Don't confuse yourself into thinking that it is OK to use an arithmetic average when computing "average" gain.
You should expect that profession articles, books, or other professional services communication will not mistakenly use an arithmetic average. However, be suspicious of casual investors, as my experience indicates this is a frequent error.
--------------------------Original post--------------------------
On the SimpleAllocation.com website, we frequently mention "lower volatility" being a benefit of using our model. Most people have a sense that volatility is only important because it can cause them emotional stress to see their portfolio value drop; though they don't mind the upside volatility.
There is more to volatility though, than just the emotional roller coaster it can create. Volatility actually reduces return. We'll say it a different way - two investment strategies can have the same average gain, yet very different total return.
How can this be? Here is a very simple example: If I have $1, and I make 10% each year for 3 years, then at the end of the 3 years I have $1.33. ($1 + $1 * 10% = $1.1, $1.1 + $1.1 * 10% = $1.21, $1.21 + $1.21 * 10% = $1.33). Clearly the average gain was 10%/year.
Now lets say I have variable gain each year; 20% the first year, -5% the second year, and 15% the third year. That is still an average gain of 10%/year. But at the end of 3 years, I only have $1.31.($1 + $1 * 20% = $1.2, $1.2 - $1.2 * 5% = $1.14, $1.14 + $1.14 * 15% = $1.31)
OK, so with constant 10% gain, I got $1.33 after 3 years, and with a more variable but still 10%/year average gain, I wound up with $1.31. That doesn't seem like too big of a deal. Well, each year these issues compound; the more time that passes, the bigger the difference will become. Also the more volatility, the bigger the differences become.
The data below is a simulation of variable versus constant gain. (Link to the Google spreadsheet used to create the chart and data.) Notice that the constant gain model on the left has a 9.07% gain, each year, for 20 years, just as the variable gain model on the right has an average annual gain of 9.07%. Yet at the end of 20 years, the constant gain account has $5.67, yet the variable gain account balance is only $4.47. (Both accounts started with $1.00) In this case the volatility was 17.32%. (That is the standard deviation of the annual gains was 17.32%)
How does this compare to the "real" market volatility? SPY, an S&P500 index ETF, since 1994 has had:
An average annual gain of 9.86%
A volatility of 19.54%
Resulting in a average annualized gain of only 7.99% ("Average annualized gain" is the equivalent "constant gain".)
Investing in the S&P500, you would only have achieved 81% of the gain you might have thought you would achieve by looking at the average annual gain.
The moral of the story is that just because two strategies have the same average annual gain, does not mean they will generate the same return. Lower volatility generally means better total return.
(Edit) So how should you calculate "average gain"?
To compute the return, solve this equation for compound_return: (compound_return)^time = (final_value / starting_value)
compound_return = 10^(log10(final_value / starting_value) / time)
Where "^" means: raise to the power of
I.E. you start with $1, end with $5, over an 8 year period.
compound_return = 10^(log10(5/1)/8) = 1.2228, or 22.28% annual return.
Check this by noting that 1.2228^8 = 5.
Thanks for reading!
The message here is that you should not use arithmetic average, but geometric average. This is well known by financial professionals, but often not known by individuals. As volatility goes to zero, so does the difference between an arithmetic and geometric average. Don't confuse yourself into thinking that it is OK to use an arithmetic average when computing "average" gain.
You should expect that profession articles, books, or other professional services communication will not mistakenly use an arithmetic average. However, be suspicious of casual investors, as my experience indicates this is a frequent error.
--------------------------Original post--------------------------
On the SimpleAllocation.com website, we frequently mention "lower volatility" being a benefit of using our model. Most people have a sense that volatility is only important because it can cause them emotional stress to see their portfolio value drop; though they don't mind the upside volatility.
There is more to volatility though, than just the emotional roller coaster it can create. Volatility actually reduces return. We'll say it a different way - two investment strategies can have the same average gain, yet very different total return.
How can this be? Here is a very simple example: If I have $1, and I make 10% each year for 3 years, then at the end of the 3 years I have $1.33. ($1 + $1 * 10% = $1.1, $1.1 + $1.1 * 10% = $1.21, $1.21 + $1.21 * 10% = $1.33). Clearly the average gain was 10%/year.
Now lets say I have variable gain each year; 20% the first year, -5% the second year, and 15% the third year. That is still an average gain of 10%/year. But at the end of 3 years, I only have $1.31.($1 + $1 * 20% = $1.2, $1.2 - $1.2 * 5% = $1.14, $1.14 + $1.14 * 15% = $1.31)
OK, so with constant 10% gain, I got $1.33 after 3 years, and with a more variable but still 10%/year average gain, I wound up with $1.31. That doesn't seem like too big of a deal. Well, each year these issues compound; the more time that passes, the bigger the difference will become. Also the more volatility, the bigger the differences become.
The data below is a simulation of variable versus constant gain. (Link to the Google spreadsheet used to create the chart and data.) Notice that the constant gain model on the left has a 9.07% gain, each year, for 20 years, just as the variable gain model on the right has an average annual gain of 9.07%. Yet at the end of 20 years, the constant gain account has $5.67, yet the variable gain account balance is only $4.47. (Both accounts started with $1.00) In this case the volatility was 17.32%. (That is the standard deviation of the annual gains was 17.32%)
How does this compare to the "real" market volatility? SPY, an S&P500 index ETF, since 1994 has had:
An average annual gain of 9.86%
A volatility of 19.54%
Resulting in a average annualized gain of only 7.99% ("Average annualized gain" is the equivalent "constant gain".)
Investing in the S&P500, you would only have achieved 81% of the gain you might have thought you would achieve by looking at the average annual gain.
The moral of the story is that just because two strategies have the same average annual gain, does not mean they will generate the same return. Lower volatility generally means better total return.
(Edit) So how should you calculate "average gain"?
To compute the return, solve this equation for compound_return: (compound_return)^time = (final_value / starting_value)
compound_return = 10^(log10(final_value / starting_value) / time)
Where "^" means: raise to the power of
I.E. you start with $1, end with $5, over an 8 year period.
compound_return = 10^(log10(5/1)/8) = 1.2228, or 22.28% annual return.
Check this by noting that 1.2228^8 = 5.
Thanks for reading!
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