The Nasty Mathematics of Volatility

Ancient library at Ephesus, Turkey

Long-time readers of ITA Wealth Management note we are paying more attention to portfolio risk and the volatility of individual securities than we did when this blog first started.  Below is an example of why this is an important concept to consider when managing a portfolio.  This basic idea is discussed in Chapter 8 of Adaptive Asset Allocation, a book authored by Adam Butler, Michael Philbrick, and Rodrigo Gordillo.

Suppose you invest $1,000 and the average return is 5% per year over a five-year period.  The first year the return is 5 percent, the second year it is 10 percent, the third year it is negative 15 percent, the fourth year it is 10 percent and the final year it is 15 percent.

After five years the $1,000 becomes $1276 if the return is exactly 5 percent per year.  Now we do the math for the actual event where the gains and losses vary from year to year, but still average 5 percent per year.

• $1,000 x 1.05 = $1050
• $1050 x 1.10 = $1155
• $1155 x 0.85 = $982 (rounded)
• $982 x 1.10 = $1080
• $1080 x 1.15 = $1242

$1242 is less than $1276 so we actually increase the portfolio at a lower rate than the 5 percent average.  This is just a more detailed calculation or reminder that a gain of (100%) is required to recoup a 50% loss.

Some of us are old enough to remember when load mutual funds were charging an 8.3% load fee.  For every $1,000 invested, we started out with only $917.  No-load funds reminded prospective investors that it required a little over a 9% gain to get back to even.  Historically, that is equivalent of losing one year of investing.  Fortunately, those days of the “heavy” load fees are history.

While we cannot prevent the market from wobbling from day to day, we can limit portfolio volatility by using the Position Sizing worksheet found in the latest version of the Kipling Tranche spreadsheet.  Applying absolute momentum with SHY as the cutoff is another way to keep us clear of two and three sigma draw-down events.  Those are the ones that really are portfolio killers.