Monday, July 11, 2011

Can We Use GDP to Predict the PSEi?

A month ago, one of our avid readers ingeniously tried to perform some sort of fundamental analysis for the market as a whole using the market's total capitalization and GDP. The ensuing discussion led to a promise by yours truly to determine if there is a statistically significant relationship between GDP and the PSEi. Thanks to a timely reminder by another reader (or are you the same one?) a few days ago, here are the results of the promised analysis (pardon the mathematical/technical nature of this post, it couldn't be helped).

Getting the data

Historical PSEi prices are freely available from Yahoo! Finance, while the Philippines' historical macroeconomic data may be downloaded from the website of The World Bank.

Preparing the data

To facilitate the statistical comparison between frequently quoted data (i.e., the PSEi, which is quoted daily, weekly, or monthly) and annual data (i.e., GDP), we would need to annualize the former. One way to do this is to get the annual average of monthly PSEi prices, which, in my opinion, is better than just using end-of-year prices since the average approach smooths out price fluctuations within the year; of course, the downside of any attempt to annualize the PSEi data is significant loss of detail, an issue that cannot be avoided, however.

For the purpose of our analysis, I have decided to use both GDP and per capita GDP in constant US dollars (which is the same as "in current pesos"). Finally, I also computed for the annual growth in GDP, per capita GDP, and average PSEi for an alternative approach in the analysis. You may download the data set and the results of the analysis by clicking this link.

Processing the data

Plotting the data series across time, we see a general  increasing trend in all series from 2000 to 2009. To determine if the relationship between the series (GDP vs. PSEi, PCGDP vs. PSEi) are statistically significant, we would have to perform simple regression analysis, a statistical analysis tool that is available in Excel (by installing the Data Analysis toolpack).

Analysis results

Let's start with GDP vs. PSEi: how strongly is GDP correlated with PSEi, if at all? The regression analysis output from Excel is shown below.

If you recall your college statistics, these highlighted values are the ones that matter the most in regression analysis.  A high "R Square" or coefficient of determination, like what we have here, tells us that we have a "good" model, or that there is a strong relationship between our independent variable (i.e., GDP) and the dependent variable (i.e., PSEi). Another indication of the strength of the relationship between GDP and PSEi is the low p-value of the coefficient of GDP in our model; specifically, the results of our analysis tell us that the coefficient of GDP is significant at the 0.01 level of significance (which means that there's a 99% chance that we are right).

The analysis results of our other models are also significant, as shown below, although less so for the relationship between GDP growth and PSEi growth.

Using the results and limitations of the analysis

So, can we use GDP to predict the PSEi? Even if the results of our analysis seem to indicate that we can, I would not recommend it.Our analysis suffer from very important limitations that limit the usefulness of the results: first, having a limited number of observations casts doubt on the persistence of the observed trends; second, our findings are limited to how the stock market could behave on average in a span of one year and so do not capture daily, weekly, or even monthly fluctuations in the market, which renders the results irrelevant for short term plays. What good is it to have "good" results and models, then, if we cannot even apply them to real world decision making? Well, even with its limitations, our analysis is not completely useless. At the very least, the results tell us that if the economy is expected to grow the following year, then the stock market, as represented by the PSEi, is likely to follow suit. Also, these findings are a sign that long-term trends in the stock market have some fundamental basis, and that investors may be rational in the sense that they drive prices up (or down, as the case may be) when there is valid reason to do so.