Written by Monty Agarwal, MA Capital Management
Summary
- Following up on our statistical analysis of the January effect, we did a similar exercise on the first quarter returns to see if they told us anything about the rest of the year.
- A positive Q1 has in the past, 92% of the time, led to a positive year as well; but a negative Q1 does not tell us much about whether the year will be positive or not.
- While the data is limited, after we combine the analysis of a positive first quarter and the size of the first quarter returns, there is enough statistical significance to say that Q1 returns do bode well for the rest of 2014.
A few months ago we did a statistical analysis of the January effect to see if the magnitude of January returns has any bearing on the rest of the year. We determined that while a positive January leads to a positive year 92% of the time, a negative January does not tell us much about whether the year will be positive or not.
We decided to conduct the same exercise on the first quarter returns of the S&P 500 to see if we could get some statistical answers about the rest of the year.
Correlation Analysis
We took the quarterly and annual returns of the S&P 500 price index from 1952-2013 and ran a correlation matrix between Q1 returns and the returns for the rest of the year. We made sure that the correlation study for the rest of the year did not include Q1 returns, but only Q2 through Q4 returns so as not to have Q1 returns influence the rest of the year’s returns.
We found there was a 0.15 correlation between how Q1 does and the how rest of the year performs. Extending the study to other quarters we found that Q1 had the highest correlation to the performance of the sum of the remaining 3 quarters.
Correlation of Quarterly Returns to the Rest of the Year’s Returns, S&P 500 (1952-2013)
- Q1: 0.15
- Q2: 0.13
- Q3: 0.05
- Q4: -0.05
Two Factor Analysis
Clearly Q1 has the strongest bearing on the S&P 500 performance for the rest of the year, so we decided to take a deeper look into the relationship. The next step was to conduct a 2 factor analysis. The 2 factors would be the direction of Q1 returns and the size of those returns and to see if they would give us more information on the annual returns. We broke out Q1 returns ranging from -15% to +15% and tallied the corresponding average annual returns as well as the percentage of positive years for each period.
Size of Q1 returns versus annual returns and percentage of positive years, S&P 500 (1952-2013)
(Source: Tiger Technologies, Yahoo Finance)
The way to read the above table is as follows:
1. There was 1 year when Q1 returns were between -13% and -11% and that year the annual returns were -12%.
2. There were 2 years when Q1 returns were between -11% and -9% and the average annual returns during those 2 years were -8% and 1 year was positive while 1 year was negative.
Here is a summary of the results from our finding:
1. 23 out of 59 or 39% of the years had negative Q1 returns, but out of those 23 years, only 10 years or roughly 43% of the years were negative as well.
2. But what if Q1 returns were positive? This is where it gets interesting. Q1 returns were positive in 36 out of 59 years and of those 36 years, 33 or 92% of the years were also positive.
Conclusion: A positive Q1 has in the past, 92% of the time led to a positive year as well, but a negative Q1 does not tell us much about whether the year will be positive or not.
Q1 2014
So what does our statistical analysis of Q1 2014 tell us about the expectation for the rest of 2014? In Q1 2014, the S&P 500 was up 1.7% which at first glance looks very positive for the rest of 2014.
The analysis above showed that a positive Q1 has led to a positive year 92% of the time and a Q1 return between +1% and +2% has led to a positive year 100% of the time with average returns of 11%.
(Source: Tiger Technologies, Yahoo Finance)
- Since 1952 there have been 3 years when Q1 returns fell between 1% and 2%.
- All 3 years turned out to be positive.
Conclusion: While the data is limited, after we combine the analysis of a positive first quarter and the size of the first quarter returns, there is enough statistical significance to say that Q1 returns do bode well for the rest of 2014.
