Valuation Model

Valuation Model Analysis of Portfolios

Portfolio manager style analysis is a fairly common procedure in today's technologically advanced institutional investor community. Rather than rely on the promotional literature or salesmanís presentation from a money manager or mutual fund, pension fund managers and others use statistical methods to look at the actual investments to determine the characteristics of a manager's style. Styles such as "growth", "income", "indexed", "value" and others have been used to describe the investment objectives of investment managers in both their literature and by outside observers.

Most services that describe these investment "styles" will provide some sort of definitions for each, even if the managers do not. Most style definitions are the result of an analysis of more fundamental portfolio characteristics such as beta, P/E, yield, market capitalization, industry and portfolio turnover. Certain weighted average fundamental characteristics of a portfolio are correlated with certain styles. For example, we would expect to see high weighted average dividend yield in portfolios characterized as "income" oriented.

But what is the relationship between the manager's "style" and the manager's method of stock selection? What is the criteria? The particular valuation techniques used by investors to achieve their style goals is often not apparent. In addition, many of the most popular ìtechnicalî models, such as Estimate Revision and Relative Strength are used by a broad cross-section of money managers, regardless of style.

In too many cases the stated style of the manager differs from the characteristics of the fundís investments. We may likewise assume this to be the case when examining the stock selection methods, or "valuation models" of the institution. Regardless of the managerís stated style or valuation models, it follows that the characteristics of the portfolio should provide some evidence of the models actually used. This basic principle is the foundation of the analytics developed by Valuation Technologies.

An oversimplified example of this principle can be related to a common selection method such as "neglected stocks", meaning stocks that are neglected by institutional investors and/or have few analysts providing coverage. If a manager states that he only invests in neglected stocks, and that he sells stocks when they become popular, then we should find related characteristics in the portfolio. We should see that the analyst coverage of all stocks purchased is less than the mean for all companies.

Examining stocks sold, we should see, at minimum, a weighted average analyst coverage which exceeds that of all stocks. Since not all stocks will perform as the manager anticipated, there will be some sales of stocks which the manager feels will not reach his objective. This fact will be reflected by sales of some still neglected stocks, thus lowering the average popularity of stocks sold. But generally we should see stocks sold reflecting the sales criteria of the manager.

Company Model Scores

The first step in analysis of manager stock selection methods is the examination of the stocks themselves. Just as stocks have individual financial and market characteristics such as earnings per share, market capitalization, dividend yield and total return; each stock has a characteristic "forecast return" when valuation models are applied.

Valuation models, like the dividend discount model, attempt to "fairly price" each stock, and then derive expected returns based on the current price of each stock moving toward fair value. Returns-based models, on the other hand, directly seek company attributes correlated with subsequent residual returns. Our database, updated monthly, contains both types of models and related forecast returns for each of over 7000 stocks and ADR's.

For each model, after the returns are calculated, the companies are divided into groups based on their returns. For example, if we were grouping in percentiles, the universe of companies would be divided into 100 groups based on their returns. After the stocks are divided into groups, each group is assigned a score ranked from high to low. The top group receives the highest score and the bottom group receives the lowest score.

Standardizing Scores

To better compare stocks across models or over time, we then standardize the scores. Standardizing preserves the order of the scores, but rescales the distribution so it has a set mean and standard deviation. In effect, it puts the results of the various models all on the same scale.

It is most common to standardize variables to have an average of zero and a standard deviation of one. By standardizing a variable this way, you can immediately determine a stockís relative position above or below the universe average, without looking at any other numbers. A stock with a score of 1.5 is a stock that scores 1.5 standard deviations above average. Any stock whose score is negative is below average.

Truncating

In our analysis, it is useful to truncate the distribution of company model scores to exclude any extreme values that may have resulted from data anomalies. Since many of our analytical techniques are based on a variableís squared value, extreme values can affect results drastically. Generally, we truncate the distribution of company scores to an outer limit of three standard deviations from the mean. This results in company scores between 3 and -3, with zero representing the mean.

More technically, winsorization is the technique we use to truncate distributions. It is a repeating, circular procedure where outlying values are pulled in towards the center of the distribution. This lowers the standard deviations set in our original standardization. Re-standardizing to force the mean and standard deviation back to zero forces some results beyond the 3, -3 limits, so we repeat the process. This brings the outlying extremes closer and closer to 3, -3 with each repeated calculation.

To avoid unnecessarily long calculations, we allow the final distribution to have a few scores slightly outside the three standard deviation limit. This is why a few models will have company scores that may lie between 3 and 3.2 or between -3 and -3.2.

We now have company scores for all twelve valuation models and approximately 55 other variables such as trading activity an size. The scores represent the relative position of that company regarding its expected total return resulting from the application of each model or variable.

Portfolio Analysis

Our method of portfolio analysis is based on an examination of the equity holdings as reported in the manager's quarterly filings with the SEC and/or the quarterly reports of public mutual funds.

First, we determine three components of the portfolio; the current holdings, stocks which were net purchases during the previous quarter and stocks which were net sales. Beginning with the institutionís net purchases, for each valuation model we determine the highest and lowest company scores, as well as the capitalization weighted mean and standard deviation of company scores. This statistical analysis is repeated for the current portfolio holdings and for the net sales. The result is a statistical picture of the portfolio activity as it relates to all 12 valuation models, as well as selected additional variables such as trading activity and size.

As shown in this sample, the company scores under the neglect model for the net purchases of the SAMPLE ABC Fund range from 3.06 to 0.06, and the weighted mean score is 1.44. We can conclude that the portfolio purchases consisted of stocks with above average scores in the neglect model, but we cannot yet determine if this was any more than coincidence.

In order to determine if we can conclude that these purchases were by design, we must test for statistical significance. We perform a variation of the "T" statistic on the distribution of company scores for the buys, holds and sells for each model to determine models with the highest statistical significance.

For a specific institution, we use only those models with the highest statistical significance to determine its likelihood to buy or sell specific stocks. These are also the models used in analysis of holders of a particular company to determine interests of investors and the current value drivers of the stock.

In the attached example, statistically significant models are usually indicated by a narrow range of high and low scores. Additional significance can be seen in the trend in scores from the buy to sell components.

Comparison with Company Scores for Targeting Potential Buyers

Now we have enough information to match the models used by institutions with the model scores of a specific company. To identify institutions likely to purchase a particular stock, we examine the statistically significant models found within the purchases portion of each portfolio. The subject company's scores are then compared to the distribution of scores for purchases by the institution.

Specifically, each institution is given a numerical rating representing its purchase potential. The list of potential purchasers is limited first by size and trading activity variables. If the companyís score lies outside an institutionís distribution of scores for the variables trading activity and size, that institution is eliminated from consideration. Second, the institutional list is limited to those with at least one statistically significant valuation model which includes the company's score in the range of scores for purchases.

For each of the surviving institutions, the company score is given a rating dependent upon its position within the range of purchase scores of statistically significant models. The result is then multiplied by the "T" value of the model for that institution. This weights the companyís score by the degree of statistical significance of the model within the portfolio. For example, if the company has identical ratings in two models used by an institution, the score for the more statistically significant model would be higher. The total of these scores is determined for each institution. The institution with the highest number is the most likely to purchase the companyís stock. We then rank all institutions high to low based on their likelihood to purchase the company's stock.

Comparison with Company Scores to Find Potential Sellers

The above calculations also apply to determine the most likely sellers of a company's securities. Institutions examined are limited to current holders of a company's stock, and calculations are based primarily on net sales of the portfolio during the previous quarter.