Saturday, January 30, 2010

How Reliable is The January Barometer?

With 2010's first month of trading in the record books, the perennial references to "The January Barometer" are being espoused ad nauseum, and throughout a variety of media outlets. In a January 29th WSJ article - "January Proves Tough for Stocks" - the venerable newspaper makes the following statement:

"History suggests that a weak January performance is a worrisome sign for the rest of the year...In years when the Dow has risen in the first month of the year, the median rise for the rest of the year is 10.4%. In years when the Dow has fallen, the median rise for the next 11 months is just 0.28%" 

Feeling dissatisfied with the statistical methodology (Given January % Return > 0, median return) used above, I set out to apply a regression analysis to the data. I pulled data on the S&P 500 for every year from 1952 to 2009, setting each year's January % Return as the explanatory (X) variable, and the subsequent full year % Return as the response (Y) variable. The results are plotted below to provide a visual:
In the event that a strong relationship between X and Y existed, the plot above would display at least some modicum of linearity. This isn't quite the case. In fact, the r-squared value for this data is 0.1012, meaning that only 10.12% of the variation in Y (entire year's stock market return) is explained by X (return in January). However, I realize that regression analysis of this nature is not very resistant to outlying/extreme values; that is, a few extreme observations have the potential to significantly affect the portion of Y's variation that is attributable to X. For this reason, I arranged January's % returns into quartiles, calculated the inter-quartile range (IQR), and deleted any observations that fell greater than 1.5*IQR from either the first or third quartile. Interestingly, only two observations throughout a 57 year period passed the above test for being considered "extreme" - the S&P 500's return during January 2001 and January 2009. I deleted both observations, and recalculated below:
After removing the two extreme values, the new r-squared value is 0.1544 ( 15.44% of Y explained by X) - a near 50% improvement, but still well below any reasonable threshold which might prove the predictive value of January. 

In conclusion, I will not be using January's stock market decline as a basis for any prediction concerning the full year performance of the S&P 500. That determination is better made - in my opinion - by recognizing that not all recoveries are created equally, via close monitoring of the mortgage market's response to the Federal Reserve's exit from it's mortgage backed security purchase program, and by examining the structural implications of sustained double digit (real) unemployment.

*long several S&P 500 stocks Sphere: Related Content

Saturday, January 23, 2010

Quantitative Assessment of House Price Distributions

This weekend, as I found myself inundated in quantitative finance problem sets, I decided it might be worthwhile to apply some quant methods to real estate. After all, we're in the midst of a recession whose numerous causes - and/or exacerbating factors - include a multi-year decline in median home prices across virtually every geographical market. Furthermore, a larger proportion of Americans own a home than own equity securities. My experiment began with market selection; I wanted to compare two housing markets within relative geographical proximity. I also wanted the comparison to be between markets that have suffered comparably during the recession, and are perceived as good long-term housing bets for reasons such as population and demographic trends, weather etc. After brief deliberation, I decided that tonight's matchup would be between Atlanta and Charlotte.

To begin, I pulled data from the S&P Case-Shiller Home Price Index (monthly) from January 2000 to October 2009. I then converted the index value to a periodic rate of return for each month, using the natural log function. That data was then summarized in histogram format below:

The two distributions are somewhat similar at first glance, although Atlanta appears more skewed to the left. Atlanta's most frequently observed interval (bin) of return is also a bit higher than Charlotte's. However, in this instance I'm most interested in providing an investor with a general idea concerning the risk associated with a house purchase in each of these markets. To do so, I computed the mean and standard deviation for each city's returns. Furthermore, I calculated the (theoretical of course) probability that a given month's return would be less than zero for each market:

The Conclusion: Although the monthly return could conceivably be higher for an Atlanta house, there is a 45.75% probability that a given month's return will be less than zero - negative that is. In Charlotte, that figure is only 39.54%. Furthermore, it's important to note that the Atlanta data is characterized by a fatter left tail; that is, Atlanta has experienced multiple months of >2% price declines, while Charlotte's returns all fall above -2%.

Clearly, there are many variables that influence house prices, not all of which are even subject to attempted forecasting. However, I would venture to say that the method above provides a reasonable illustration of the relative risk associated with a real estate investment in the two subject markets.

*no positions in either Charlotte or Atlanta real estate. I am licensed to sell real estate in NC however. Sphere: Related Content