Motivation

This project aims to provide a potential explanation to the value premium puzzle. The main idea is to investigate the behavior and strategies of two different types of investors/analysts (agents hereafter). The first type includes agents who are thriving among their peers. They are the top performers for given tasks, and desire to maintain their status. Lets label this group "top performers". The second type includes agents who are not top performers, and desire to improve their status and performance among their peers. Let this group be labeled as "status-seekers".

Our hypothesis is two-fold. We assume that the top performers adopt strategies that are sufficient to outperform their peers, and help maintain their status at the same time. In other words, they seek less risky choices (fearing a significant loss in status upon failure) with potential high returns (to continue outperforming). On the other hand, the status-seekers are aware of the top performers' strategy. Their skill level does not allow them to outperform their peers by adopting a similar strategy. Thus, we assume that they are forced to adopt more risky strategies to improve their status.

The next series of assumptions try to create a setup to help explain the observed trends for the value premium puzzle. Choices of higher risk could possibly have lower average returns compared to top performer strategies, a feature assumed in order to account for the top performers' dominance on average. However, it is possible that the distribution of returns from high-risk choices dominates the corresponding low-risk distribution at the tails. The high-risk p.d.f. could either be more right-skewed or have thicker tails compared to the low-risk pdf. As a result, a status seeker being fully aware that cannot outperform his peers with low-risk strategies, attempts high-risk strategies with a ``lottery''-type of payoff. The reason is that the status-seeker values status more than average returns, and aims to win the lottery as the only alternative option to outperform his peers.

We would like to test these hypotheses in the data. The problem setup implies that top performers invest on value stocks, while

status-seekers invest on growth stocks with potential lottery payoffs. Currently, we plot these distributions and perform tests to

verify our claim.

Description of data

We choose two dates (cross-section points) to calculate stock returns. Growth and value stocks are identified through the market to book ratio. We consider the ratio's value on the initial date only to label stocks as growth or value (those that qualify, not all stocks). The alternative use of the M/B ratio on both dates could exclude firms whose stock was initially growth, but has evolved to a value stock (or at least is no longer growth stock) within the period considered.

In order to calculate the M/B ratio, we merge data from the Daily Stock File (DSF) and its header (DSFHDR) in CRSP with the

Fundamental Annual (FUNDA) data in COMPUSTAT. The linking set CCMXPF_LINKTABLE from CRSP is used to properly link the libraries. Firms that have been liquidated in between the given cross-section points are excluded, but care is taken to include

events such as M&As that result in changes to data headers (tickers, names, etc). Penny stocks (below a set threshold, typically $10.00) are excluded, but a limited number of stocks above the threshold price and negative book value are included. However, the ranking among stocks is done by the absolute value of M/B. Further filters include

- Choose only Ordinary Common Shares (share codes "10", "11"). Other authors may include preferred stock, other tangible assets, etc.
- Include only certain link types ("LC", "LU", "LS", "LN") between CRSP and COMPUSTAT
- Exclude dummy IIDs (existing company, non-existent security)
- Sanity check for price (CRSP negative prices record the average of bid/offer spread)
- Sanity check for outstanding shares (reported in units within CRSP and in thousands within COMPUSTAT)
- Market capitalization upper and lower limits

The M/B ratio calculation includes unavoidably numbers reported on different dates. Since the accessible data on firm fundamentals are only those with annual periodicity (due to USC subscription to WRDS), we use the past fiscal-year-end reporting date that is closest to our chosen cross section date. This approach coincides most of the times with the standard method that Fama & French have established, when the reported fiscal-year-end date is close to December. However, we force the use of the closest past fiscal-year-end date for cases where this date is end of March for some firms.

Given the difference between the selected date (first cross-section point) "CS" and the most recent past fiscal-year-end date "FYE", a straightforward way to define the M/B ratio is

M/B* = [ stock price(CS) x outstanding shares(CS) ] / [ book value per share(FYE) x outstanding shares(FYE) ]

= [ market value CRSP(CS) ] / [ book value COMPUSTAT(FYE) ]

However, there are cases where a firm has more than one class of shares, and one or more classes are not traded. Data for such classes are not included in CRSP data, but are included in the calculation of the firm's book value by COMPUSTAT. As an approximate correction for such cases, we use the following M/B ratio

M/B = [ market value COMPUSTAT(FYE) ] / [ market value CRSP(FYE) ] x M/B*

Preliminary results

We perform a series of normality tests on the distribution of returns from growth and value stocks. All normality tests that are performed (Shapiro-Wilk, Kolmogorov-Smirnov, Anderson-Darling, and Cramér-von Mises) have high power by construction. Due to the tail thickness (always present) and skewness (whenever evidenced) of the growth and value stock distributions, the tests always reject the null hypothesis of normality. Thus, we rely primarily on graphical methods to understand the properties of these distributions for various cross-sections considered.

The major trend is that the distribution of returns from value stocks stochastically dominates to first order the corresponding distribution of returns from growth stocks. For such cases, investing on growth stocks has no advantage compared to portfolios of value stocks. The distribution of growth and value stock returns is skewed to the right. However, the left tail of the distribution is thicker for growth stocks, while the right tail of the distribution is thicker for value stocks. As a result, large losses are more probable with growth stocks, while large gains are more probable with value stocks.

However, there exist time periods that the right tail of the distribution from growth stocks is thicker than the corresponding tail of the distribution from value stocks. This implies that long positions in certain growth stocks during such periods may result in larger positive returns compared to value stocks. The distribution of growth stocks is skewed to the right. The distribution of value stocks is primarily symmetric, although with the right tail longer and the left tail shorter compared to the normal.

The set of diagnostic plots includes

- Histograms and quantile-quantile (QQ) plots for each of the distributions of returns from growth and value stocks. The QQ plots compare each distribution to the normal.
- A comparison of the cumulative distribution functions of returns between growth and value stocks.
- A
quantile-quantile (QQ) plot between the two distributions of returns
from growth and value stocks. A
point (x,y) on the plot corresponds to one of the quantiles of the
value distribution (y-coordinate) plotted against the same quantile of
the growth distribution (x-coordinate).If the two distributions
compared are similar, the points on the QQ plot will approximately lie
on the benchmark line
*y*=*x*. If a point lies above the benchmark line, then for this quantile the value distribution dominates the growth distribution (and vice versa).

Major trends (Period: 02/17/1993 - 02/18/1998)

Growth stock tail dominance (Period: 02/21/1996 - 02/18/1998)

Growth stock tail dominance (Period: 10/05/1989 - 02/13/1991)