DOI: 10.5817/FAI2018-1-2 No. 1/2018
21
Stock Prices and the Rate of Return Analysis:
The Case of Warsaw Stock Exchange
Magdalena Jasiniak
University of Lodz
Faculty of Economics and Sociology, Corporate Finance Department
Rewolucji 1905 No 39, Lodz, Poland
E-mail: magdalena.jasiniak@uni.lodz.pl
Abstract: The main aims of this article are to verify whether rates of return might
be determined by stock prices and to evaluate low price anomaly on the example
of Warsaw Stock Exchange. The author states that cheap assets characterized by
nominally lower prices are more attractive to buy and bring higher profits in
comparison to assets described as expensive. In order to verify the hypothesis,
database of 13789 quotations from 1.07.1999 to 30.12.2013 was created. The
sample was divided into three groups – cheap, average, and expensive stocks.
Finally, the statistical analysis was conducted using 2924 records including only
cheap and expensive units. Statistical analysis confirms that low–priced assets
generate higher profits and lower losses.
Keywords: face nominal effect, low price anomaly, behavioral finance, capital
market anomalies, investment risk
JEL codes: G02, G11
Introduction
The final effect of investment process is determined not only by strictly economic
factors but also psychological aspects. Emotions and risk tolerance affect human
behavior and determine the investment decisions. Economic psychology mainly
focuses on consumer behavior and explains the processes that are related with
purchasing goods and services. These analyses are mostly used in marketing
strategies. However, the aspects of behaviorism are also observed on stock
exchange market.
In the process of investment, the rational behavior means that investor analyses
all possible choices, assigns importance to possible options and chooses the best
one. In predicting a future event people are impartial and objective. This procedure
maximizes the subjective expected utility. However, due to certain limitations of
time and limited access to information, investors avoid rational methods and use
faster and simpler procedures. Additionally, they are influenced by behavioral
biases which sometimes cause irrational and contradictory decisions.
There are many studies describing behavioral biases and capital market anomalies,
however, they mainly focus on developing markets. Polish Stock Exchange Market
was established in 1991 thus it is relatively young and much smaller than other
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significant markets; still, it is developing fast. Till 2017 it was classified as an
emerging market, since then, FTSE Russel has classified the Polish Market as
developed.
Among many anomalies studied on capital markets, low price anomaly is not widely
explored, especially in the case of Poland. To the best author’s knowledge, there
was only one study conducted by Zaremba et al. (2014, 2016) focusing on this
phenomenon.
Low price anomaly describes the phenomenon when the value of low priced stocks
increases faster in comparison to stocks with relatively high prices. This is in
contrast to the theory of market efficiency. Stock prices should not affect investors
decisions.
This paper analyzes whether the face nominal effect observed at consumer market
also occurs at the stock exchange market. The main aim of this article is to verify
whether investors are influenced by face nominal effects on stock market exchange.
The author states that cheap assets characterized by nominally lower prices are
more attractive to buy and bring higher profits (as a consequence of increased
demand) in comparison to assets described as expensive. The paper presents the
results of a preliminary study focused on the relation between nominal values of
stock prices, investors’ willingness to purchase, and profits achieved in one-month
and one-year periods. It is assumed that investors are more willing to buy stocks
at lower prices. The increase in demand is one of the determinants that influence
the stock price increase and finally the rates of return. As a consequence, it is
expected that low priced stocks generate higher profits than high priced stocks.
1 Behavioral Biases on Stock Exchange Market
According to H. Simon (1979), people’s decisions are not optimal but rather
satisfying and they include psychological context. H. Shefrin and M. Statman
(1985) stated that investors are motivated by willingness to achieve profits but this
aim is balanced between the fear of loss and hope of spectacular profit.
Literature describes many investors’ behaviors that are driven by non–rational
factors. The most popular is the theory of perspective described by Kahnemann
and Tversky (1979). This theory is an alternative to theory of expected utility and
explains that the perception of risk differs depending on previously experienced
profits or losses. According to this theory, an experienced loss drives investors to
riskier behavior. In contrast, Thaler and Johnson (1990) explained the risk
tolerance by previous experience in the following way: previously experienced loss
increases the fear of risk and prior earning increases risk appetite. It was also
confirmed by Nofsinger (2006).
Samuelson and Zeckhauster (1988) observed that investors are more willing to
maintain stocks they previously bought, being convinced that they it will ensure
profits and focusing only on the market information that confirms this assumption.
23
Many studies also proved that investors are influenced by stock prices and their
nominals. The results of Neiderhofer (1965, 1966), Neiderhoffer and Osborne
(1966), Harris (1991) and other studies show that investors are more convenient
with stocks whose price ends with a whole or a half or less than quarters or eighths.
Goodhart and Currio (1990) observed the decimal price clustering phenomenon.
The price clustering quoted by Harris (1991) and Grossman et al. (1997) reflects
implicit agreements in price negotiations. Rounding up prices speeds up and
simplifies negotiations. The theory of Christie and Schultz (1994), developed by
other authors (for example: Godek (1996), Kandel and Marx (1997)) refers to the
use of price clustering as a way of maintaining a larger spread than would be the
case in full competition. According to Kahn et al. (1999), sellers exploit the
advantage of memory-economizing with investors who tend to cut the observed
prices rather than memorize their full value or round off the price and only then
remember it. Such behavior is also observed in other markets.
Numerous studies have highlighted another anomaly related with stock prices – low
price anomaly. Low price anomaly is an anomaly which means that stocks with low
prices bring higher return rates that stocks with high prices. The first excessive
research in this area was conducted by L. Fritzemeier (1936) on the example of
New York Stock Exchange. Fritzemeier concluded that stocks below $10 grow faster
than stocks over $100. According to the scope of growth or decline probability of
achieving above-average profits (as well as above-average losses) - shares with a
value of up to 10 $ are characterized by the highest amplitude of fluctuations as
opposed to companies whose shares reached prices above $ 100.
Next, the phenomenon was also observed by Goodman and Pevy (1986) and
Branch and Chang (1990). Bhardwaj and Brooks (1992) also positively verified low
price anomaly but additionally also proved that the effect of January is in fact the
effect of low-price shares.
Waelkens and Ward (1997) studied low price anomaly on the example of
Johannesburg Capital Market. They found that the highest investment risk is
associated with the cheapest and the most expensive stocks but the anomaly is
diverted and only most expensive shares generate excessive returns.
According to T. Odean (1999), investors are more willing to sell assets with higher
prices than those with lower prices. However, this phenomenon was strongly
related with the disposition effect and the effect of such behavior appeared to be
negative. The high stocks could bring higher benefits than the low ones.
Hwang and Lu (2008) also stated that the strategy of buying low-price shares can
bring above-average rates of return and explained it by nominal price illusion. If
there are two securities with the same characteristics and a significantly different
nominal price, the same rate of return causes that the increase in the share price
is higher in the case of shares with a higher nominal price. Investors naively
interpret this phenomenon that high-price shares are too expensive to grow further
and expect stock prices at a low nominal price to increase faster.
24
Low price anomaly also refers to catering theory and stock splits (Baker et al.
2009). When investors prefer stocks at a low nominal value, managers do stock
split and deliver assets at expected prices. This is based on the assumption that
nominal value of stocks matters for the investors and as a result, the expected rate
of return is related with stock price.
Studies conducted on Polish Stock Exchange by Zaremba and Żmudziński (2014)
stay in contrast. In that case the low price effect was diverted. It was observed
that stocks with high prices generate higher profits than low priced stocks. Studies
conducted by Biegańska et al. (2016) on the example of M&A transactions proved
that in the case of stocks at lower prices the probability of profits is higher than in
the case of high valued stocks. The question is whether this phenomenon might be
observed to a wider extent.
2 Nominal Value of Assets and the Rates of Return – Research
Results
Research was conducted on data collected from Polish Stock Exchange Market. In
order to verify the hypothesis, a database of 13,789 quotations from July 1, 1999
to December 30, 2013 was created. Only those companies were included that were
recommended by brokerage analysts.
Brokerage recommendations are important in the process of investing and support
the investment decisions made by individual investors. These reports contain
extensive analyses made by financial analysts, including an assessment of the
company's financial situation based on all available information and containing a
message indicating its further development prospects (Keller, Pastusiak, 2015).
The author made an assumption that in the case of positive recommendations, the
share prices of a given company are expected to increase. In the case of negative
recommendations, share prices are expected to decline.
Shares of companies that received neutral recommendations were excluded from
the study.
At first, the database was divided into two groups – those with positive brokerage
recommendation (buy or accumulate) at moment t (date of recommendation issue)
and those with negative recommendations (sell or reduce) at moment t. Next, the
sample was divided into three groups – cheap, average and expensive stocks –
according to group structure.
It has been assumed that investors perceive cheap shares as those worth up to 10
PLN. The value is understood here as the opening price at time t set as at the date
of publication of the recommendation. The anchor here is the value of the money
banknote and a two-digit value. Within this group, shares were divided up to 0.50
PLN, from 0.50 to 1 PLN, from 1 PLN to 5 PLN, and from 5 PLN to 10 PLN, assuming
that the anchor determines here the values of coins. The next group are shares
from 10 PLN to 100 PLN and are considered as a neutral group. It has been assumed
that expensive shares will be those with three-digit prices. The following division
25
was made in this subgroup - shares with a value from 100 PLN to 250 PLN, from
250 PLN to 500 PLN, and over 500 PLN. Such a division is a proposition of the
author and is based on round pricing.
Finally, shares price structure in the group of positive and negative
recommendations is as follows:
Table 1 Shares price structure in the group of positive and negative
recommendations
Share price
Recommendations
positive negative
up to 1 PLN 80 21
from 1 to 10 PLN 1,746 369
from 10 to 100 PLN 5,732 1,279
from 100 to 1000 PLN 2,000 440
above 1000 PLN 86 14
9,644 2,123
Source: Own elaboration
The number of shares in groups of positive and negative recommendations and its
structure according to shares differ. Additionally, the number of negative
recommendations issued is much lower than the positive ones, which may influence
final conclusions. On the other hand, both samples represent the market and are
sufficient for the following study.
In the case of positive recommendations, the analysis is conducted between the
group of shares priced below 1 PLN and above 1000 PLN. In the case of negative
recommendations low- and high–priced stocks are defined as those with price below
10 PLN and above 100 PLN. The reason why these groups are extended is that
there are not enough units in the sample of shares priced up to 1 PLN and above
1000 PLN. Neutral stocks were excluded from the analysis in both groups.
The author verified the rate of return after one year measured by 250 trading
sessions and one month measured by 21 trading sessions in order to verify whether
the phenomenon occurs in short and long period. The periods proposed are typical
for analyses conducted within the capital market. The analysis was conducted
separately in the group of positive and negative brokerage recommendations and
the results were compared.
The results of analysis conducted among the group of positive recommendation are
presented below.
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Table 2 Rate of return (%) of low and high prices – positive recommendations
in one-year period
Characteristic Low prices High prices
Mean 0.721046 0.350316
Standard error 0.218695 0.067061
Median 0.230882 0.201948
Standard deviation 1.956066 0.632657
Variance 3.826192 0.400255
Range 13.2 2.616643
Minimum -1 -0.91028
Maximum 12.2 1.706362
Sum 57.68366 31.17815
Number of units 80 89
Source: Own elaboration
The descriptive statistics indicate that the average rate of return in the case of low
priced stocks is higher than in the case of high priced stocks (0.72 and 0.35,
respectively). In the case of low priced stocks, the rate of return is characterized
by higher variance and the range of minimum and maximum rates is definitely
higher. The highest return rates amounted to 12.2% in the case of low priced stocks
and only 1.7% in the case of high priced ones.
The statistical significance of means was verified by using t statistics for means and
variances. The zero hypothesis assumed that the difference between the average
return rates of low- and high-priced stocks is equal to 0.
Zero hypothesis: the difference between both means = 0
Sample 1:
N=80, mean = 0.721046, std. error = 0.218695
Residual std. error = 0.0244508
95% confidence interval for the mean from 0.672378 to 0.769714
Sample 2:
N=89, mean = 0.350316, std. error = 0.0670615
Residual std. error = 0.0071085
95% confidence interval for the mean from 0.33619 to 0.364443
The test statistic: t (167) = = (0.721046 – 0.350316)/0.0243572 = 15.2205
Double–sided critical area p = 2.25e-033
One–sided critical area = 1.125e-033
The test confirms that the means are different. Additional test of variances was also
conducted.
27
Zero hypothesis: the difference between both variations = 0
Sample 1:
n = 79, variation = 0.568327
Sample 2:
n = 86, variation = 0.317299
T statistic: F(78, 85) = 1.79114
Double–sided critical area p = 0.008892
(One–sided critical area = 0.004446)
Variation in the group of low- and high–priced stocks differs. In the next step the
author verified the coefficient of variation indicator as a standard measure of risk.
CV is evaluated as a standard deviation (δ) divided by mean (µ).
𝐶𝑉 =
δ
µ
(1)
CVlow-priced stocks = 2.712817
CVhigh-priced stocks = 1.805961
According to the results, in one-year period, capital investments in low–priced
stocks are more efficient judged by profits but also characterized by higher risk in
comparison to high–priced stocks. In that sense, low price anomaly occurs. In the
short time period, some different tendencies are observed.
Table 3 Rate of return (%) of low and high prices – positive recommendations
one-month period
Characteristic Low prices High prices
Mean 0.06637 0.03664
Standard error 0.01848 0.01231
Median 0.04919 0.03708
Standard deviation 0.16528 0.11419
Variance 0.02732 0.01304
Range 0.92087 0.66368
Minimum -0.3423 -0.3305
Maximum 0.57858 0.33319
Sum 5.30978 3.15084
Number of units 80 86
Source: Own elaboration
28
Nominally, the rate of return in the case of low–priced stocks is higher than in high–
priced stocks (0.07 and 0.04, respectively). Also in the case of low–priced stocks it
is possible to achieve higher rates of return – the maximum amounts to 0.58. In
comparison, in the case of high–priced stocks, the maximum rate of return possible
to achieve in period analyzed amounts to 0.33.
However, as the following test presents – statistically both means are equal but the
variances are not. It means that although the average rate of return in both groups
of shares is equal, the variability is higher in the case of low–priced stocks, which
also influences the risk of transactions.
Zero hypothesis: the difference between both means = 0
Sample 1:
n = 80, mean = 0.0663722, std. error = 0.165277
Residual std. error = 0.0184785
95% confidence interval for the mean from 0.0295917 to 0.103153
Sample 2:
n = 86, mean = 0.0366377, std. error = 0.114186
Residual std. error = 0.012313
95% confidence interval for the mean from 0.0121561 to 0.0611192
The test statistic: t(164) = (0.0663722 - 0.0366377)/0.0219212 = 1.35643
Double–sided critical area p = 0.1768
(one–sided critical area = 0.08841)
Zero hypothesis: the difference between both variances = 0
Sample 1:
n = 80, variance = 0.0273164
Sample 2:
n = 86, variance = 0.0130385
Test statistic: F(79, 85) = 2.09506
Double–sided critical area p = 0.0009112
(one–sided critical area = 0.0004556)
In this case, as means are statistically equal, risk measured by coefficient of
variation depends on standard deviation, which is higher in the case of low–priced
stocks. According to this, capital investment in low-priced stocks in one-month
period are less efficient thus the average rate of return is the same as in the case
of high–priced stocks but the variability is higher.
The results of analysis conducted among negative recommendations is presented
below. In this situation, the analysis concentrates on losses. Stocks that are
expected to lose value received negative recommendations.
29
Table 4 Rate of return (%) of low and high prices – negative recommendations
– in one-year period
Characteristic Low prices High prices
Mean -0.05847 -0.12629
Standard error 0.031235 0.030257
Median -0.00437 0.016502
Standard deviation 0.615262 0.643273
Variance 0.378548 0.4138
Range 5.164841 4.963525
Minimum -3.94481 -3.85496
Maximum 1.220028 1.108567
Sum -22.6874 -57.0816
Number of units 388 452
Source: Own elaboration
As descriptive statistics show, in both cases, the rate of return is negative.
However, in the case of low-priced stocks the loss is lower than in the case of highpriced
stocks (-0.05% and -0.13%, respectively). The variance of both samples is
similar. Despite visible differences, this relation is not statistically significant.
Zero hypothesis: the difference between both means = 0
Sample 1:
N=358, mean = -0.0623703, std. error = 0.610748
Residual std. error = 0.032279
95% confidence interval for the mean from -0.125851 to 0.00111063
Sample 2:
N=452, mean = -0.126287, std. error = 0.643273
Residual std. error = 0.030257
95% confidence interval for the mean from -0.185749 to -0.0668244
The test statistic: t (808) = (-0.0623703 - -0.126287)/0.0445101 = 1.436
Double–sided critical area p = 0.1514
One–sided critical area = 0.0757
The zero hypothesis is positively verified. It means that statistically both means are
equal. The same conclusions appear in the case of variance analysis.
30
Zero hypothesis: the difference between both variances = 0
Sample 1:
n = 388, variance = 0.378548
Sample 2:
n = 452, variance = 0.4138
Test statistic: F(451, 387) = 1.09313
Double–sided critical area p = 0.3658
(One–sided critical area = 0.1829)
In the long time period – one year, capital investments in low- and high-priced
stocks are equal according to the average rate of return and variability. Risk
measured by coefficient of variation is also the same. The efficiency of investing in
both groups of stocks is similar.
In the short time period, the tendencies differ.
Table 5 Rate of return (%) of low and high prices – negative recommendations
– in one-month period
Characteristic Low prices High prices
Mean -0.04213 -0.12629
Standard error 0.009962 0.009962
Median -0.03311 0.016502
Standard deviation 0.19674 0.643273
Variance 0.038707 0.4138
Range 2.264028 4.963525
Minimum -1.51413 -3.85496
Maximum 0.7499 1.108567
Sum -16.4313 -57.0816
Number of units 390 452
Source: Own elaboration
In one-month period, losses generated by low-priced stocks are much lower than
in the case of those high-priced. However, the sample of high-priced stocks is more
diversified in terms of rate of return. Despite the assumption that stocks in this
sample are expected to generate losses, in the case of high-priced stocks, profits
at 1.11 are available – versus 0.75 in the case of low-priced stocks. Verification of
the hypotheses about means and variations is presented below.
31
Zero hypothesis: the difference between both means = 0
Sample 1:
n = 390, mean = -0.0421314, std. error = 0.19674
Residual std. error = 0.00996233
95% confidence interval for the mean from -0.0617182 to -0.0225447
Sample 2:
n = 452, mean = -0.126287, std. error. = 0.643273
Residual std. error = 0.030257
95% confidence interval for the mean from -0.185749 to -0.0668244
The test statistic: t(840) = (-0.0421314 - -0.126287)/0.0338647 = 2.48504
Double–sided critical area p = 0.01315
(one–sided critical area = 0.006574)
The statistic test confirms that the means are different. Similar conclusions might
be formulated for the variances.
Zero hypothesis: the difference between both variances = 0
Sample 1:
n = 390, variance = 0.0387067
Sample 2:
n = 452, variance = 0.4138
Test statistic: F(451, 389) = 10.6907
Double–sided critical area p = 7.029e-103
(one–sided critical area = 3.515e-103)
The results show that the variances are different. Risk of transactions is calculated
below:
CVlow-priced stocks = 4.66983
CVhigh-priced stocks = 5.09362
Risk analysis indicates that investments in low-priced stocks are lower. The
variability of the sample is less diversified. Additionally, these stocks generate lower
losses. It might be concluded that in short-term period, investments in low-priced
stocks, negatively recommended are more efficient, which might be crucial for
those investors who tend to keep losing positions.
Conclusions
Studies conducted in the area of behavioral finance proved that investors do not
behave rationally and make decisions influenced by psychological factors. However,
the question is whether the perceived price is one of the factors that strongly
influence investors decision. The low price anomaly indicates that low-priced stocks
32
are attractive to buy and generate higher profits. On the other hand, market
analytics communicate that purchase of low-priced stocks is riskier and they are
usually issued by companies in a bad financial condition.
The low price anomaly has not been widely verified for the Polish capital market.
Current studies proved that the effect is diverted. The author within this study
proposed a different approach and has classified stocks in certain price ranges due
to people’s tendency to price clustering and nominal price perception. In addition,
the author uses recommendations as an important factor supporting investment
decisions and provides analysis conducted separately in the groups of positive and
negative recommendations.
On the basis of the analysis conducted, it may be concluded that in the case of
stocks positively recommended by stock analysts, low-priced stocks generate
higher profits on average in one-year period. However, this is related with a higher
variability and risk of investment. This phenomenon does not occur in short-term
period, one month. Statistically, the average rate of return does not differ but the
variability and investment risk is higher in the case of low-priced stocks.
In the case of negative recommendations, when losses are expected, in one-year
period, the efficiency of investing in both groups of shares is similar in contrast to
one-month investments. In short-time period, low-priced stocks generate lower
losses and are characterized by lower risk.
Based on the final results related with nominal price of stock and rate of returns
they generate; it might be concluded that low-price anomaly occurs on Warsaw
Stock Exchange market but it is limited. One of factors is the price below which
stocks might be defined as low. The author assumed 1 PLN for positive and 10 PLN
for negative recommendations, however, this is just a proposition and needs further
verification based also on the market condition.
The analysis conducted provides additional conclusions related with
recommendations. First of all, it should be noticed that the number of negative
recommendations is much lower than the number of positive ones. It indicates that
the phenomenon of excessive optimism also occurs on Warsaw Stock Exchange and
as a result, stock analysts tend to over-evaluate their predictions. On the other
hand, within the group of negatively recommended stocks, there are those that
generate profits. Results also differ in long- and short-time period. This may
suggest that the efficiency of brokerage recommendations is low, which might be
a presumption for further analysis in this area.
References
Baker, M., Greenwood R. and Wurgler, J. (2009). Catering Through Nominal Share
Prices. The Journal of Finance, 64(6), pp. 2559-2590.
33
Biegańska, K., Jasiniak, M., Pastusiak, R. and Pluskota, A. (2016). Efekt
Zakotwiczenia w Transakcjach Fuzji i Przejęć na Przykładzie Polski. Finanse, Rynki
Finansowe, Ubezpieczenia, 1(79), pp. 585-593.
Bhardwaj, R. K. and Brooks, L.D. (1992). The January Anomaly: Effects of Low
Share Price, Transaction Costs, and Bid‐Ask Bias. The Journal of Finance, 47(2),
pp. 553-575.
Branch, B. and Chang, K. (1990). Low Price Stocks and the January
Effect. Quarterly Journal of Business and Economics, pp. 90-118.
Christie, W.G. and Schultz, P.H. (1994). Why do NASDAQ Market Makers Avoid
Odd‐Eighth Quotes? The Journal of Finance, 49(5), pp. 1813-1840.
Fritzmeier, L.H. (1936). Relative Price Fluctuations of Industrial Stocks in Different
Price Groups. Journal of Business, 9(2), pp. 133-154.
Godek, P.E. (1996). Why Nasdaq Market Makers Avoid Odd-Eighth Quotes. Journal
of Financial Economics, 41(3), pp. 465-474.
Goodman, D.A. and Peavy, J.W.III. (1986). The Interaction of Firm Size and PriceEarnings
Ratio on Portfolio Performance. Financial Analysts Journal, 42(1), pp. 9-
12.
Goodhart, C. and Currio, R. (1990). Asset Price Discovery and Price Clustering in
the Foreign Exchange Market. Working paper, London School of Economics.
Grossman, S., Miller, M.H., Cone, K.R., Fischel, D.R. and Ross, D.J. (1997).
Clustering and Competition in Asset Markets. The Journal of Law and Economics,
40(1), pp. 23-60.
Harris, L. (1991). Stock Price Clustering and Discreteness. The Review of Financial
Studies, 4(3), pp. 389-415.
Hwang, S. and Lu, C. (2008). Is Share Price Relevant? SSRN Working paper.
Kahn, C., Pennacchi, G. and Sopranzetti, B. (1999). Bank Deposit Rate Clustering:
Theory and Empirical Evidence. Journal of Finance, 54(6), pp. 2185-2214.
Kahneman, D. and Tversky, A. (1979). Prospect Theory: An Analysis of Decision
under Risk. Econometrica, 47(2), pp. 267-291.
Kandel, E. and Marx, L. M. (1997). Nasdaq Market Structure and Spread Patterns.
Journal of Financial Economics, 45(1), pp. 61-89.
Keller, J. and Pastusiak, R. (2015). Rekomendacje Inwestycyjne a Realia
Gospodarcze-nadmierny Optymizmu Wśród Analityków Giełdowych. Ekonomista,
(6), pp. 910-920.
Neiderhoffer, V. (1965). Clustering of Stock Prices. Operations Research, 13(2),
pp. 258-265.
34
Neiderhoffer, V., (1966). A New Look at Clustering of Stock Prices. Journal of
Business, 39(2), pp. 390-413.
Neiderhoffer, V. and Osborne, M. (1966). Market Making and Reversal on the Stock
Exchange. Journal of the American Statistical Association, 61(316), pp. 897-916.
Nofsinger, J. R. (2006). Psychologia inwestowania. Gliwice: Helion.
Odean, T. (1999). Do Investors Trade Too Much? The American Economic Review,
89(5), pp. 1279–1298.
Samuelson, W. and Zeckhauser, R. (1988). Status Quo Bias in Decision
Making. Journal of Risk and Uncertainty, 1(1) pp. 7-59.
Shefrin, H. and Statman, M. (1985). The Disposition to Sell Winners Too Early and
Ride Losers Too Long: Theory and Evidence. The Journal of Finance, 40(3), pp.
777-790.
Simon, H.A. (1979). Rational Decision Making in Business Organizations. The
American Economic Review, 69(4), pp. 493-513.
Thaler, R.H. and Johnson, E.J. (1990). Gambling with the House Money and Trying
to Break Even: The Effects of Prior Outcomes on Risky Choice. Management
Science, 36(6), pp. 643-660.
Waelkens, K. and Ward, M. (1997). The Low Price Effect on the Johannesburg Stock
Exchange. Investment Analysts Journal, 26(45), pp. 35-48.
Zaremba, A., Okoń, S., Nowak, A. and Konieczka, P. (2016). The Low Price
Anomaly: The Intriguing Case of the Polish Stock Market. Inzinerine EkonomikaEngineering
Economics, 27(2), pp. 163-174.
Zaremba, A. and Żmudziński, R. (2014). The Low Price Effect on the Polish Market.
Financial 22 Internet Quarterly „e-Finanse”, 10(1), pp. 69-85.