“Be careful – you are using the same data to predict as the model itself. You used past data to determine how stocks have behaved 1 year in the future based on the P/E that the index had (average ranges). Then you plot the “prediction” of that past data as a backcasted chart. Obviously it will show the same curve, because you used the very same data to determine the ranges in the first place :)” – Deepak Shenoy
Excellent comment on my last post: Predicting stock market returns, by one of the most prolific analytical finance practitioners in India. (If you aren’t already, you should be a regular reader on his website: www.capitalmind.in and following him on twitter @deepakshenoy)
The point Deepak made is absolutely valid and hence I figured the response deserved a post of it’s own. He’s alluding to a basic but an oft-repeated mistake in drawing inferences from data when the same data is used for developing a model and testing as well. It’s like if we dug out every instance in test cricket when a left-handed opener had a century partnership and made a claim that “left-handed openers result in century partnerships”.
Learning the impact of P/E on returns
The key to determining whether an inference from data can be generalized or is specific to only that data is to test the inference on a separate set of data. In this case, our data consists of index levels from Jan 1999 (June in case of CNX 500) along with corresponding valuation measures: Price-to-Earnings, Price-to-Book, Dividend Yield. Note that there are plenty of other measures that could potentially be used like ‘Market Cap to GDP’, ‘Forward earnings’ etc. In fact, a paper analyzing returns on the US market concluded the the single best predictor of index returns was ‘investor portfolio allocation to equities’.
We break down the data into two sets; We use data from Jan 1999 to Dec 2010 (11 years) to learn about the relationship between the valuation metrics and future returns. and then use the remaining data, from Jan 2011 to Jan 2015 (4 years) to test the relationship we learnt.
Next, we run a simple linear regression (I used R), plotting Returns versus P/E for the learning dataset. Outcome shown below.
What we learnt from the data (but haven’t tested yet):
- Future returns are inversely related to current P/E. Higher the P/E today, lower the returns in the future
- For every unit increase in P/E, future returns drop by just over 6%
- However, the relationship is far from perfect. R-squared of 53% implies that about 53% of future return is explained by current P/E, which is quite significant. But it also says that almost half of whatever drives future returns is not explained by P/E
The above analysis makes for nice enough reading but how do we know it has any bearing on the present? For that we use the remaining data, from 2011 to 2015
- The predicted values ‘roughly’ track the actual performance, with obvious errors in some phases. e.g. The simple model overestimates the returns during Jul ’12 to Mar ’13 while underestimating them in Sep ’13 (meaning the extent to which markets rose between Sep ’13 and ’14)
- The prediction for 2015 implies a gradual decline with 1 year returns turning negative by the 3rd quarter (Sep ’15). Simply put, this implies the Nifty is likely to be at ~8,000 in Sep 2015, the same level that it was in Sep 2014
This is an exercise in historical analysis. Even if what we learnt is material, remember current P/E statistically only explains about half of future return. Other factors like liquidity, interest rates, oil prices, global macros, all will have a say on where markets actually end up. Last and probably most important, whether Indian companies finally start showing earnings growth will be where the rubber meets the road which will decide where Indian markets go in 2015.
The single greatest predictor of stock market returns – Philosophical Economics
Open Source statistical analysis – R Project
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