The Titanic is overrated

Who survived on the Titanic?

Decision trees not only help with many investment questions, such as whether one should currently buy small or large caps. They are also helpful in answering the question of who was most likely to survive the sinking of the luxury liner “Titanic”.

Since the stock bubble burst in 2000, stocks in small cap stocks have outperformed large cap stocks. According to various valuation metrics, however, small caps are now very expensive compared to large caps. It should be said at this point that, compared to large caps, small caps are overvalued by around 25% according to our estimates, which means they are historically expensive. The universe for the calculation was the MSCI World Share Index, which was divided into “small” and “large” companies. What is the best forecast that can be made taking into account all other available information, such as the steepness of the yield curve?

Combination of different methods

To answer this question, the intelligent combination of various quantitative methods appears to be particularly promising. In the following, the two methods “cointegration” and “decision tree” are linked in order to investigate whether small or large caps are likely to be the more attractive investments in the second half of 2006.

So-called cointegration models are ideally suited to “only” using observable data - in this case profits, cash flows or dividends and interest - to “calculate” a “fair” rating line and from this, in turn, “calculate” the undervaluation or overvaluation in percent. Then the relative valuation of the small caps compared to the large caps as well as various other valuation variables (e.g. valuation of the world stock market) are calculated. One possible further use of the estimated under- and over-valuation is to incorporate it into a return equation. The greater the overvaluation of small caps compared to large caps today, the lower the future relative returns. Such a method makes it possible to estimate a specific adjustment speed.

No cash injection for smaller companies

In the following, the above valuation information is used in a decision tree together with other relevant variables, such as the interest rate curve. The easiest way to explain the advantages of a decision tree is with the example of the “Titanic”: Which questions have to be asked in which order in order to find out what was decisive for survival or non-survival? For example, should you ask first about gender and then about passenger class - or vice versa? It is important that a decision tree can recognize non-linear relationships. For example, it would be possible that the probability of survival in the third grade did not depend on gender, while in the first grade it was strongly influenced by gender. These non-linearities are almost impossible to map in conventional econometric models.

The main disadvantage of the decision tree is that it is even more sensitive to overfitting than econometric models. You can use it to describe the past almost perfectly, but the model is not at all suitable for forecasting. In econometric models, overfitting occurs when you use too many explanatory variables; in decision trees, when you ask too many questions.

Back to the real problem of whether you should invest in small or large caps. The graphic shows a “small caps versus large caps” decision tree for the MSCI world stock market. The first question is: Was the MSCI world stock market undervalued by more than 24% a month ago? If so, small caps did better 79% of the time over the next month. Where is the logic behind this question? If stocks are valued very favorably overall compared to bonds, then loan-financed company takeovers and loan-financed going private are worthwhile. Since large companies generally buy up small companies and going private is more difficult with large companies than with small ones, small caps develop better than large caps when loans are cheap compared to stocks.

In the case of high credit differences (credit spreads) alone, which indicates a high risk of bankruptcy, small caps performed worse despite the high undervaluation of the global stock market (in 67% of all cases). This is plausible since smaller firms suffer more from the consequences of a credit crunch. They are often dependent on bank loans and cannot rely on political financial injections based on the motto “too big to fail”.

Unless the global stock market is grossly undervalued, the next most important question is whether value stocks are cheap versus growth stocks. If this was the case, the small caps outperformed in 71% of all cases. In contrast, if growth stocks were valued relatively cheaply, the steepness of the yield curve determined whether large caps performed better. It is interesting in this context that the relative valuation of growth versus value stocks is classified by the decision algorithm as more informative than the relative valuation of small versus large caps. If the yield curve was steeper than 3.2% a month ago, the small caps outperformed in almost all cases.

Brisk going-private activities

Where are we today The stock markets are undervalued, but not exactly “dirt cheap”. Historically, growth stocks are valued at low prices versus value stocks, and the yield curve is flat. In this data constellation, large caps performed better than small caps in 62% of all cases. The main reason why small caps could still outperform for a while is the current wave of takeovers. Loans with a relatively bad rating are currently cheap because interest rates and credit spreads are low. In Europe you can currently buy a “BBB” bond with a ten-year term at around 5.2% and become the owner of a high “free cash flow yield” of 6.5%. Small caps are expensive compared to large caps, but small and large caps are cheap compared to medium or poor quality bonds.

That is why we are currently observing brisk going-private activity, which means that there are many privately-loan-financed purchases from companies with high cash flows. Since smaller companies can be bought more privately and the same applies to company takeovers, the relatively expensive valuation of the small caps compared to the large caps does not fully come into play. The algorithm recognizes the above logic in part by first asking about the valuation of stocks versus bonds. In our investment strategy, we assume that large cap stocks will outperform slightly and have slightly overweighted them. If interest rates rise sharply and stocks are no longer cheap compared to loans, the high valuation of small caps compared to large caps would attract more attention. At this point at the latest, an aggressive shift into large caps would be advisable.

Men must go under

And who survived on the "Titanic"? The most important question to ask first is gender. If it was a female passenger, the question of class became a question of survival. If the passengers were male, the question "Child or adult?" the most important question of survival. All first and second grade male children survived. As a grown man, on the other hand, the question of which class you were promoted to was of secondary importance.

* Thomas Härter is Chief Strategist at Swisscanto Asset Management in Zurich.