MktNeutral's  Instablog

Following up on Dividend Inc's post about dividend stocks and sentiment, which can be found here, I noticed several semiconductor stocks with high yields.

Semiconductor stocks were on fire on Friday. Is this the beginning of a big rally for the sector or a dead cat bounce after the sector fell hard after Intel’s announcement to buy McAfee? The yield on many of these stocks has become quite high so perhaps this rally in the semis could have legs.

I ran a screen and here is the list of the top semiconductor stocks by dividend yield.

 

It is often said that diversification is the only free lunch in investing. However, the ability to manage risk in the stock market through diversification depends on the level of correlation of stock prices to each other, i.e. how correlated stocks are to one another. If all stocks were perfectly correlated and moved up and down together in tandem, then diversification would offer no risk management advantage over a non-diversified portfolio holding a single stock or an index basket of stocks. Risk management in such a market would be reduced to market timing methods for how to scale in and out of positions as the market moves up and down. If, on the other hand, the return on any given stock were random and independent of the movement of all other stocks, then diversification would offer investors a nearly perfect method for reducing risk. Asset allocation would become a problem of betting on the right stocks. Some stocks would rise while others would fall, and the portfolio manager’s job would be simplified to picking the winners and avoiding or shorting the losers.

In the real world, however, investing follows neither of these contrasting scenarios. Stock returns are not perfectly correlated but they are not independent of one another.  Some days the market goes up sharply and 9 out of 10 listed issues rise. Other days the broad indices are practically flat and some stocks rise while others fall. Thus, the utility of diversification depends on how correlated stocks are to each other, and this is why practitioners have developed many methods for quantifying the level of correlation of stock returns to each other. Knowledge of this correlation level is important to asset managers because it assists them in making decisions such as whether it is worth the effort to build a diversified portfolio of stocks rather than to simply invest in index funds.

Time series analysis offers the most widely applied method for quantifying the global level of correlation in a group of stocks. This method begins with a fixed time interval and stock returns at regular intervals. For example, five years of monthly stock return data could be used to compute the global correlation of a group of country specific stock indices as in the paper by Solnik and Roulet. The same approach could just as easily be applied to long time periods such as years to tick level data on an intraday chart. Pairwise correlation values are computed across each pair of stocks in the group over the fixed interval and then these pairwise correlation values are averaged to arrive at the global level of correlation among the stocks in the group. The average value is usually referred to as the cross sectional correlation and can be estimated over distinct fixed intervals or over a rolling window period. For example, one could compute the 90-day cross sectional correlation of the daily returns of all stocks in the S&P 500 by computing the trailing 90-day correlation of returns for each pair in the S&P 500 and then averaging the pairwise values to find the cross sectional value.

The time series approach has many limitations. First, each pairwise correlation value is computed separately, and second, it is difficult to estimate the change in the correlation because each pairwise value is computed from a moving window in which only one data point changes at each successive time step. This problem can be rectified somewhat if the pairwise correlations are computed using formulae that give more weight to recent data such as exponentially weighted data. However, this solution is somewhat ad hoc and each pairwise value still depends on many historical data points. It is for this reason that people began to look for a method of estimating the global level of correlation in a way such that new estimates are independent of the historical data.

Cross sectional dispersion is a model of global market correlation published by Bruno Solnik and Jaques Roulet in 2000. This model offers an alternative approach for quantifying the level of correlation of stocks. The premise of their model is to compute the standard deviation of the returns of a group of stocks at regular intervals, every month, for example, and to use the standard deviation, which they call the “dispersion”, as a means to derive an estimate for the “instantaneous correlation” of the group of assets. They present empirical data that shows that the long term mean of the cross sectional correlation computed in this manner is very close to the long term value of cross sectional correlation computed using traditional time series approaches.

The math behind the cross sectional dispersion approach is arguably simpler than that of the time series approach. To calculate the cross sectional dispersion of a group of stocks, simply compute the standard deviation of the returns of all stocks in the group over a fixed interval, such as a month. In their paper, Solnik and Roulet use country specific stock indices at monthly intervals as an example, but the method can easily be applied to a group of stocks within a sector or a major index at daily or even intraday periodicities. Now compute the historical value of the volatility for the group of stocks. Let  σ_c denote the cross sectional dispersion and  σ_w denote the volatility of the group of stocks. Then the global level of correlation is given by the formula:

where ρ is the “instantaneous” global level of correlation. Solnik and Roulet derive the formula above using a series of approximations and assumptions. I will not reproduce the derivation here, but I will comment on their results and the utility of their model.

Solnik and Roulet use empirical data from country specific stock indices to show that an estimate of the global level of correlation from their model has a long term average that is approximately equal to the value of the cross sectional average correlation computed with the time series approach. This is comforting, given that their approach makes so many approximations and assumptions. Their data demonstrates cross sectional correlation estimates derived from their dispersion method change more frequently than a value computed using a rolling window with the time series approach.

The greatest advantage of the cross sectional dispersion approach is that it provides more frequent estimates of the current global level of correlation in a group of securities than the time series approach. One of its greatest drawbacks, however, is that the method only offers information about the global level of correlation in a group of stocks and says nothing about the correlation between different components within the group. In fact, one of the assumptions of the model is that every stock has the same correlation to every other stock in the group. As crude as this assumption may appear, the empirical data suggest that it is still a very useful way to estimate the level of co-movement in a group of stocks.

The cross sectional dispersion model offers investors another tool for identifying the utility of diversification in managing the risk of a portfolio. As up to the minute information becomes more readily available to people worldwide, and globalization causes world economies to become more interconnected, it is logical to expect that global stock returns will become more correlated. Investors now need better tools to identify new opportunities for improving the diversification of their portfolios. A combination of the traditional time series approach supplemented with the frequent correlation estimates offered by the dispersion model could be a great way to begin looking for such opportunities. These quantitative methods are no substitution for old fashioned bottoms up analysis, however. Investors should always examine the who, what, where, why and how of the underlying businesses into which they are placing their money and seek to diversify themselves across these fundamental business dimensions as well.