28 Asset Valuation

Association for Investment Management and Research

Market-to-Book Ratios and Positive and Negative Returns on Equity

Martin A. LeibowitzJournal of Financial Statement Analysisvol. 4, no. 2 (Winter 1999):2130

The author evaluates the correlation between return on equity (ROE) and the market-to-book ratio (P/B). The relationship is not linear but has a J shape. The rela-tionship between positive ROE and P/B is positive, but the relationship between negative ROE and P/B is inverse. The distinction between negative and positive ROE is important in valuing start-up companies.

Literature on the relationship between return on equity (ROE) andthe market-to-book ratio (P/B) indicates a positive correlationexcept in lower percentiles. Unlike earlier studies that do notdistinguish between the correlation when ROE is negative andwhen it is positive, the author evaluates the relationship when thisdistinction is present.

Three factors indicate that the relationship between ROE and P/Bmay be inverse if ROE is negative. First, negative earnings may beassociated with positive expected future earnings if the negativeearnings reflect accelerated expenses. In cases such as start-upcompanies, a positive P/B incorporates future expected earningsdespite negative earnings in the present period. Second, negativeearnings may reflect transitory items that do not influence cashflow and thus do not reduce price, again contributing to a negativecorrelation between P/B and ROE. Third, transitory negative earn-ings may influence cash flow, causing both price and ROE todecrease. The larger the negative transitory items are, the largerthe increase in P/B above unity, and vice versa. Because the medianP/B approximates unity, the expected correlation between ROEand P/B for these items approximates zero.

Martin A. Leibowitz is at the Sy Syms School of Business at YeshivaUniversity. The summary was prepared by Charles F. Peake, CFA, theUniversity of Maryland at Baltimore County.

Asset Valuation 29

The CFA Digest Summer 1999

Although previous studies have aggregated data into portfolios, theauthor evaluates results for individual companies. After the authoreliminates companies with negative equity and extreme observa-tions, his sample contains 19 years of Compustat data with at least3,000 observations for each year. The data show positive P/B foreach percentile but negative ROE in the lower percentiles and apositive correlation for the entire data set. An initial plot of the datashows a nonlinear J-shaped curve, in which companies with anegative ROE show a negative relationship with P/B and compa-nies with a positive ROE are positively related to P/B.

The author next partitions the data into companies with negativeROE and those with positive ROE and presents correlation coef-ficients for the full set, for companies with positive ROE, and forthose with negative ROE. The correlation for the full set is positiveand consistent with earlier data. The partitioned data, however,show that both Spearman and Pearson correlation coefficients areconsistently positive for companies with positive ROE and consis-tently negative for companies with negative ROE.

Annual cross-section regressions test whether the distinctionbetween negative and positive ROE contributes to explaining firmvalue. Simple regressions of P/B on ROE do not show statisticallysignificant results, but the insertion of dummy variables to distin-guish between positive and negative ROE results in statisticallysignificant coefficients for each of the 19 years. The results arefurther improved when P/B is regressed on ranked ROE.

The author concludes that a positive correlation exists between P/B and positive ROE but a negative correlation exists between P/Band negative ROE. Distinguishing between positive and negativeROE in cross-section analysis results in significantly greater expla-nation of variations in P/B. Failure to distinguish between positiveand negative ROE results in spurious correlations. This finding isespecially important for valuing start-up companies.