KEEP CALM and LOOK AT THE FUNDAMENTALS
- On March 9, 2020, the US stock market’s favorite index S&P500 fell 7.6%, the biggest daily drop since the 2008 financial crisis.
- The flight to safety lowered the yield on the 10-year US Treasury bond to below 0.5%.
- Energy stocks were hardest hit; XLE, the energy sector ETF lost more than 20% of its value.
Blame it on the corona virus, blame it on the bad timing of the Saudis and the Russians to get into a price war. Heck, for all I care, blame it on the weather.
The important thing is that it happened …and it wasn’t supposed to.
One of the fundamental assumptions of Economics and Finance is that asset values are log-Normally distributed. Which is to say that changes in asset prices (the return on assets) are Normally distributed. Many of us who stick their neck out in the marketplace know that this assumption does not hold. Normal distribution does not allow for outliers, yet we observe outliers. And we trade based on this assumption anyway. We hedge our portfolios, we trade options, and we diversify with methods all based on the Normality assumption.
I updated my charts showing the distribution of daily market (S&P500 index) returns for 4575 trading days between January 2, 2002 and March 9, 2020. First, let’s calculate and review some statistics. Moments of a distribution are the expectation of the observations to 1st, 2nd, 3rd, and fourth power. Moments can tell us a lot about the shape and the likelihood of the observations. First moment tells us the mean, second moment is related to the standard deviation, the third moment gives us skewness (which direction is it leaning?), and the fourth moment is kurtosis; roughly speaking, a measure of the likelihood of outliers.
In the table below I calculated these statistics for actual observations (the red bars) and also for the corresponding normal distribution (the green line).
|Mean Return||Standard Dev||Skewness||Kurtosis||Prob(return < -4σ)|
|Return on actual observed S&P 500||0.02%||1.18%||-0.29||10.1||0.415%|
|Return on log-Normally Distributed S&P500||0.02%||1.18%||0.00||3.0||0.003%|
If returns were really “Normal”, we would expect a 4.72% or more loss in one day once in every 125 years.
But in the last 18 years it happened on average about once a year.
Notice how many times we observe daily returns outside of the green normal bounds. Interestingly, these happen around the mean return (complacent times) and on both ends (driven by fear or greed).
It is unimaginable that economic fundamentals work like this, that 5% of the working population lose their jobs in one day, production increases by 4% in one day, the price of goods and services sold in the market increase or decrease by 6% in one day.
Yet the stock market gyrates left and right.
People get overly fearful or irrationally exuberant about the cumulative effect of small fundamental changes in the future. These small effects exaggerated by the human imagination are then communicated instantaneously through numerous channels making everyone act in the same direction.
If everyone does the same thing, normality is broken. Imagine all the molecules in your coffee cup “deciding” to move in the same direction, and the coffee jumping out of your cup. This does not happen in truly random systems.
Suggested Data References in This Article (ALTADATA Marketplace)
- Standardized Income Sheets
- Standardized Balance Sheets
- Valuation Ratios and Growth History
- Petroleum & Other Liquids Prices
Please share your thoughts.