Risk prediction capabilities of P/E during market downturns.

Bahhouth, Victor ; Maysami, Ramin Cooper

INTRODUCTION

Stock market crashes shake the financial markets stability around the globe at each occurrence. The aftermath of these negative swings is devastating on investors. The stock market crash of 2000 destroyed more than $8 trillion of investors' wealth, for example (Nofsinger, 2001), while in 2008 the stock market lost more than 50% of its value with dramatic repercussions on the economy in general and on the investors in particular.

The purpose of this study is to identify a reliable measure of risk during periods of negative price swings. The study tests the reliability of one of the most widely used measures of risk, beta (B), during such negative price swings and tests the predictive power of price-earnings ratio as an alternative to beta in measuring risk.

LITERATURE REVIEW

Researchers do not agree on the factors that causing these stock market downturns. Sornette (2003) argued that the major cause of the market crashes was the exaggerated expectations of future earnings by investors who overlooked the economic fundamentals--people invested in companies that promised high returns but whose financials were unable to meet these promises. Ofek and Richardson (2002), in discussing the stock crash market of the year 2000, discussed the wide gap between price and their fundamental values in the period that preceded the 2000 market freefall.

Zuckerman and Rao (2004) related the market crash of 2000 to the main features of trading in Technology stocks early in the 1990s, during which investors and stock traders were unable to explain the wide fluctuations in prices of Internet stock, and failed to predict its implications on the broader markets. Baigent and Massaro (2005), meanwhile, in their analysis of the 1987 market crash concluded that "portfolio insurance" was the most plausible explanation for the rapid downturn. They discussed the important role of derivative securities in contributing to the escalation of market capitalizations through the first nine months of 1987.

The capital pricing asset pricing model (CAPM) remains the most dominant theory in the investments literature, relating beta as a measure of relevant risk to the return from a financial asset. There is documented research, however, pointing to the use of financial measures as an explanatory variable in stock markets return analysis. Fama and French (1992), for example, showed evidence of the relationship between return and size, price-to-book ratio, and prior returns. The pointed to the incremental return with a risk component not explained in the assets pricing model. Aras and Yilmaz (2008) used price-earnings, dividend yield and market-to-book ratio to predict returns in emerging markets. Ang and Bekaert (2003) discussed the reliability of using price-earnings ratio to predict future dividend growth. In the same direction, Lamont (1998) argued that price-earnings ratio has independent predictive power for excess returns. Lewellen (2001) similarly highlighted the predictive power of financial ratios in determining returns.

Conventionally, however, beta remains the dominant measure of relevant systematic risk. This paper tests the reliability of using beta in predicting riskiness of investment in financial assets:

[H.sub.0]: Beta is a reliable measure of risk.

Additionally, we examine the use of price-earnings ratio as an alternative measure:

[H.sub.0]: Price-Earning ratio (P/E) is a predictive measure of risk.

RESEARCH MODEL

The purpose of the study is to examine the reliability of beta as a measure of risk by predicting the stock price movement during negative price swings and to test the predictive power of a price-earnings ratio as a measure of risk during the same period. The procedure used is to identify two groups of stocks (dependent variable). The first group consists of stocks that observed a sharp negative price movement during a crash period (Y = 0), and the second group are those stocks that did not have a negative sharp price movement during the same crash period (Y = 1). The independent variables are beta and price-earnings ratio, which are both used independently and jointly. The model requires the use of a non-metric dependent variable and metric independent variables in identifying these two groups of stocks.

We employ the Binary Logistic Regression Model (BLRM) used by Olujide (2000) to predict corporate financial distress using financial ratios. Logistic regression is superior to the linear regression model where normality assumptions of the independent variables are not met. It is simpler to read and to interpret because its values are bound to a range between zero and one (Tsun-Siou, Yin-Hua & Rong-Tze 2003).

Hence the logistic regression model is used to test the reliability of using beta (independent variable) in identifying the stock price movement during negative price swings, i.e. risk (dependent variable); as well as in evaluating the predictive power of price-earnings in classifying stocks into two groups (dependent variables): stocks that were adversely affected during negative price swings (assigned a binary value of 0); and stocks that were less adversely affected during negative price swings (assigned a binary value of 1).

Logistic model takes the following form:

Y(0 -1) = A + [B.sub.1][X.sub.1] + [B.sub.2][X.sub.2]

Reliability of the Model

In testing the reliability of the model, the two following measures are used:

Coefficient of Determination: is similar to that of the ordinary least squares (OLS) regression:

[R.sup.2.sub.Logit] = 1 - [(2L[L.sub.0]/2L[L.sup.1]).sup.1/2]

2L[L.sub.0] is the log-likelihood (represents unexplained variations) of the model without independent variables. 2L[L.sub.1] is the log-likelihood of the research model based on the independent variables that remained in the model and exhibited significant power in explaining the two stock groups. N is the sample size. In general, the interpretation of [R.sup.2.sub.logit] is similar to the coefficient of determination [R.sub.2] in the multiple regressions. It has a value that ranges between 0 and 1; when [R.sup.2.sub.logit] approaches 0, the model is a poor predictor; when [R.sup.2.sub.logit] approaches 1, the model is a perfect predictor.

Hit Ratio: A Z test is performed to test the significance of hit ratio (percentage of correctly classifying the cases). The following formula is applied:

Z test = [P - 0.5 ]/[[0.5 (1 - 0.5)/N].sup.1/2]

where P = hit ratio = proportion correctly classified results, N = sample size.

The "Z-test" tests the significance of the hit ratio. The hit ratio measures the percentage of times the model accurately classifies the cases into the two stock groups i.e. if the model completely explains the dependent variable, the overall hit ratio would be 100%. A level of significance of 5% is used.

DATA COLLECTION

The data is taken from Compustat and covers a twelve-month-period ending October 31, 2008. The study includes the information of 9930 public firms that are traded at NYSE and NASDAQ.

Data Description and Measurement

The data are of two types:

Dependent variable, which is non-metric and reflects the change in prices:

Y(0) = Adversely affected stocks are defined (Risky) as stocks with a decline in price exceeding that of the two markets indices (The two indices declined by almost 50% during the reported period);

Y(1) = Stocks that were not adversely affected (Safe) and represents stocks with a decline in price below that of the average of the two indices.

Independent variables are metric--beta and price-earnings ratio. They are cross sectional type taken at the beginning of the crash period i.e. October 31, 2007.

DATA ANALYSIS

The testing was conducted using a scenario analysis of three steps. The 5% level of significance and enter method (SPSS) were used in the three scenarios.

Step one included beta as an independent variable to predict stock risk using the "Enter" method. Step two used the price-earnings ratio as an independent variable to predict risk. And step three included both beta and price-earnings ratio as measures of risk.

The number of cases removed from the model was 2,113, while the number of cases that remained in the model was 7817. The model correctly classified the stock price movement of 4125 cases, resulting in an overall hit ratio of 52.80%. However, the [R.sup.2.sub.logit] = 0 and was insignificant.

The outcome of step 2 (Table 2) depicts the following:

The number of cases removed from the model was 3,470, while the number of cases that remained in the model was 6,469. The model correctly classified the stock price movement of 4,089 cases, resulting in an overall hit ratio of 63.30%. However, the [R.sup.2.sub.logit] = 0.3% and was significant at a level of 5%.

In step 3 where both beta and price earnings were entered into the model, the summary output (Table 3) signifies the following results:

The number of cases removed from the model was 4,214 and the number of cases that remained in the model was 5,716. The model correctly classified the stock price movement of 3,039 cases, resulting in an overall hit ratio of 53.20%. However, the [R.sup.2.sub.logit] = 0% and was insignificant at a level of 5%.

TESTING RELIABILITY

Testing the reliability of the model is done by using the following two measures:

1 Coefficient of determination (R-Square) value, which represents the proportion of unexplained variation that is explained by the independent variables. Table 4 shows that the coefficient of determination of price-earnings ratio scenario was significant, while it was insignificant for the other two scenarios;

2 Testing the significance of hit ratio is done by using Z distribution. Z critical value at a level of significance of 5% is = 1.65, N = the number of cases included in the model. Table 5 shows that overall hit ratio of price-earnings ratio was significant.

LIMITATION OF THE STUDY

There were two limitations in the study: (1) Missing cases--a number of cases in this study had missing variables and were removed from the study as reported in the three scenarios; (2) The external validity of the model was not tested.

CONCLUSIONS

The research output of the study was robust and showed that beta's power was insignificant in predicting stock price movements. It raised a serious question about using it as a measure of risk when it indeed unreliable. On the other hand, the price-earnings ratio exhibited significant power in predicting stock price movements and accordingly was a more reliable measure of risk.

This study poses a real dilemma that we need to address imminently. Should beta's role as the dominant measure of risk be continued? We recommend further research to test the external validity of this model by applying it to other stock markets and or different time frames.

BIBLIOGRAPHY

Ang, Andrew, G. Bekaert (2003), "Stock Return Predictability: Is it There?". Columbia University and NBER, July 2003.

Aras and Yilmaz (2008) Price-earnings Ratio, Dividend Yield, and Market-to-book Ratio to Predict Return on Stock Market: Evidence from the Emerging Markets. Journal of Global Business and Technology, 4(1), Spring 2008.

Baigent, G Glenn, and Vincent G Massaro (2005). "Derivatives and the 1987 Market Crash" Management Research News Patrington, 28(1), 94-105.

Fama, E.F., K.R. French (1992), "The Cross-Section of Expected Stock Returns", Journal of Finance, 47, 427-465.

Lamont, O. (1998), "Earnings and Expected Returns", Journal of Finance, 53, 1563-1587.

Lewellen, J. (2002), "Predicting Returns with Financial Ratios", Journal of Financial Economics, 1-38.

Nofsinger, John (2001). "Psychology and Investing"; http://www.phptr.com / articles /article.asp?p=21917.

Ofek, E. and M. Richardson (2003), 'Dot.Com mania: the rise and fall of internet prices,' Journal of Finance, 58, 1113-1138.

Olujide, J. (2000). Exposure to Financial Ratio Analysis of Three Operating Firms in the Beer Industry in Nigeria. Journal of Financial Management & Analysis, 13, 69-73.

Sornette, D. (2003). A Complex System View of Why Stock Markets Crash. www.goldeagle.com/editorials_03/sornette071603pv.tml.

Tsun-Siou, Lee, Yin-Hua, Yeh and Rong-Tze, Liu (2003). "Can Corporate Governance Variables Enhance the Prediction Power of Accounting-Based Financial Distress Prediction Models?";http://cei.ier.hit-u.ac.jp/working /2003/2003WorkingPapers/wp2003-14.pdf.

Zuckerman E, Rao H. (2004). Shrewd, crude or simply deluded? Co-movement and the internet stock phenomenon. Industrial and Corporate Change. Oxford.13(1), 171.

Victor Bahhouth, University of North Carolina--Pembroke

Ramin Cooper Maysami, University of North Carolina--Pembroke

Table 1 shows the summary output of step 1with the following results:

Table 1: Beta
 Observed Predicted Correctly
 classified

 0 1

Risky stocks 0 3 3689 0.001
Safe stocks 1 3 4122 0.999
 Overall hit ratio 0.528

Table 2--Price- earnings ratio

 Observed Predicted Correctly
 classified

 0 1

Risky stocks 0 1840 1388 0.57
Safe stocks 1 983 2249 0.696
 Overall hit ratio 0.633

Table 3--Beta and Price- earnings ratio

 Observed Predicted Correctly
 classified

 0 1

Risky stocks 0 236 2532 0.085
Safe stocks 1 145 2803 0.951
 Overall hit ratio 0.532

Table 4--Coefficient of Determination--Measure

 Measure Nagelkerke Alpha 5 %
 R Squared

Beta 0.00 Insignificant
Price-earnings 0.03 Significant
Beta and Price earnings 0.00 Insignificant

Table 5--Significance of Hit ratio

 Measure Hit Ratio % N Z value

Beta 52.8 7817 0.56
Price-earnings 63.3 6469 2.16
Beta and Price-earnings 53.2 5716 0.64

 Measure Critical Result
 Value

Beta 1.65 Insignificant
Price-earnings 1.65 Significant
Beta and Price-earnings 1.65 Insignificant