Tag: statistics

If you have studied finance or are listening to the news around the end of the year, the one thing you usually hear about is the January effect in the stock markets. The January effect is the hypothesis that socks increase much more in January than any other month.

Why? One theory is that prices go up because of year-end selling. To defer taxable capital gains to future years, by realizing capital losses in the current year, security holders will sell before the end of the year and then re-buy securities in January. Thus increasing the demand for securities in that month. In practice however, this theory doesn’t hold much mustard because tax rules like the 30-day rule (see the section on the superficial losses discussion here).

Is there such thing as a month effect in the stock market?

If I am writing this blog you probably guessed it that there is such a thing. But it is not the January effect but rather a December effect.

Lets look at the data

I took the last 30 years (1987-2017) of data for the four (4) majour US stock indices (each representing different slices of the stock market):

• S&P 500 (large-cap stocks)
• Russell 2000 (small-cap stocks)
• NASDAQ (mainly technology stocks)
• Dow Jones (mainly industrial stocks)

I clean up the data and test the statistical significance of the returns in each month and compare them to the distribution of average returns over the preceding 30 years. Because I want to look at what investors get paid for holding risky assets, I use excess return to measure performance. Excess returns are the market return minus the rate paid to hold riskless assets (known as the risk-free rate). For the risk-free rate I used the 3-month Treasury Bill rate.

Results

Based on the results presented in the table below,  I see significantly positive returns in the month of December.  December sees on average about 2% growth in the market as compared to any other month, after accounting for variability of across time. In fact, over the past 30 years, only 6 Decembers have seen a decline in the SP500 index.

Interestingly the Dow seems to be additionally have a pronounced April effect.  I wonder what that could be?

Critique on the t-statistic

For those interested, in the table below I present the statistical results (t-statistic) for all months with significant excess return.  Recent research on the topic of statistical significance in the field of finance has come to the conclusion that t-stats might not be a powerful enough indicator of the significance of the finding. As such, I have published an additional indicator as suggested by  Harvey, Liu, Zhu (2015).  This is a more stringent criterion of significance designed to combat data-mining bias. Harvey et al. suggest using t-statistic bigger than 3.0 as an indicator of significance. Currently most researchers use 2.0. Even with this more stringent criteria December does stand out as a month with significantly positive market returns. Even the Dow April effect passes this more stringent test.

Results for each market are presented in the following tables: