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Why the Volatility Smile?

Average returns are hardly ever average.



Stock markets have been more volatile than investors think. Those seeking average returns have been surprised with negative returns more than one year in every four.


Reading through the Northern Trust (NT) 2014 Outlook one might wonder if their eyes were going buggy. NTGA presents a chart (reproduced below) that suggests that the frequency of returns have been below zero or above 25% … 56% of the time. Seriously?

S&P 500 Frequency of Returns 1926-2012

Read the chart as follows: Average annual returns, from 1926 – 2012, were 11.8% but annual returns have only been average (that is, between 10% – 15%) 7% of the time. And they’ve been negative 28% of the time … more than one year in every four. (Data here. Click chart for larger picture). Find the NT 2014 Outlook here.

The Law of Large Numbers

Stock market returns are supposed to be normal-ish. The Central Limit Theorem (aka the law of large numbers) says that the distribution of returns (like stock market returns) should exhibit a sort-of-like traditional normal bell curve. A key assumption, however, is that returns are independent from one another. So, yesterday’s return doesn’t affect today’s return.

But That’s Not What Happens

Clearly, stock market data don’t always fit nicely with the theory. Sometimes, in a market crisis, say, the individual buy and sell decisions that drive supply and demand for stocks are no longer independent. Individual decisions no longer offset. They become collective and the result is herd behaviour. The foundational assumption for a normal distribution (independent returns) breaks, returns cluster at the extremes and the bell-shaped curve curls up at the ends creating fat tails … a Volatility Smile (to borrow a phrase from the option trading world).

The chart below is the same as above, except the line is added to show the volatility smile. (Click chart for larger picture).

S&P 500 Volatility Smile

Fun with Statistics

Investors may not appreciate the frequency of extreme occurrences … the fat tails, (I didn’t) … it’s worth digging in to the data.

First, the chart scale is a bit misleading. Were the scale below zero and above 25% to show the same 5% ranges like the mid-ranges of the chart, then the tails would flatten and the curve would be more normal. Still, investor concerns are negative returns so the scale is a helpful reminder that annual returns have been less than zero 28% of the time. The chart is a good way to help investors think about risk and not just return.

Second, the data (see here) indicate that the average annual return over the first 21 years (1926 – 1946) was 8.9% however all but two annual returns during those 21 consecutive years were either negative or above 20%. No wonder brokers were leaping from window ledges. Throw out the first 21 years of annual returns and the tails would flatten and the curve would be more normal.

Third, annual returns can be misleading. Take the same period 1926 – 2012 but consider instead monthly returns (or weekly, or daily); the intra-year returns could flatten the tails as well.

Fourth, one could question the relevance of data from 1926 and instead look at the more recent data. This makes sense. The last 40-years, say, have seen massive changes due to technology, Globalization, turnover in composition of the S&P 500 index, regulation etc. If one instead took the 38 year period from 1975 – 2012 the average annual return was 9.6% but still the stock market delivered negative returns 21% of the time (one year in every five) and above 25% returns 24% of the time. Again, fat tails. Not what investors expect. (Chart data here. Click on chart for larger picture).

S&P 500 Frequency of Returns 1975-2012

Stock Markets are Volatile. (Duh)!

The NT report shows that the U.S. stock market has been volatile. And, here’s some unhappy news, the Canadian stock market has been even more volatile delivering negative returns 32% of the time since 1988. (Data here. Click chart for larger picture).

S&P TSX Frequency of returns 1988 - 2012

This explains why, in part, many pension plans have been gradually reducing their allocations to Canadian stock markets. (See PIAC’s composite asset allocation).

The pessimist might say that in 25 out of 87 years (28% of the time) the U.S. stock market has delivered a negative annual return. The optimist, might counter with in 62 out of those same 87 years (72% of the time), the U.S. stock market delivered positive returns. Those are good odds.

Be diversified by asset class, region, currency (and maybe sector). Have stocks (U.S., Canadian, EAFE, EM), bonds (at least Canadian, probably shorter duration) and real estate (REITs) in your portfolio. Use the PIAC composite average asset allocation as a guide.

Be mentally prepared. Investors, happy with average returns are not likely to expect negative returns one year in every four. Have cash or cash-like short bonds. Extremes happen more often than investors think and market corrections are an opportunity to buy low.

Consider rebalancing. Use volatile markets to your advantage. See Rebalance? How? When? and Buy Low and Sell High Made Easy.


Next time? How to not-Market time – and update.
Doug Cronk CFA PRM is a Pension Investment Officer
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