## Stock price return distribution

According to “ Fama & French Forum : “ Distributions of daily and monthly stock returns are rather symmetric about their means, but the tails are fatter (i.e., there are more outliers) than would be expected with normal distributions. (This topic takes up half of Eugene F. Fama's 1964 PhD thesis. The basic assumption that stock price returns follow normal distribution itself is questioned time and again. There is sufficient empirical proof of instances where values fail to adhere to the Total return (share price) = share price return + distribution rate. Share price return = (share price end of period ÷ share price beginning of period) − 1; There are 2 ways to calculate distribution rates. The first way, which is the most relevant for shareholder returns, is at the share price Even though there is a remarkable discrepancy between the concepts of behavior of stock prices held by professional stock market analysts, on the one hand, and by academics on the other, the form of the distribution of stock returns is important to both groups because it is a crucial assumption for mean-variance portfolio theory, theoretical

## Once upon a time I was asked by John Bollinger about the relationship between the Standard Deviation of daily stock returns and the Standard Deviation of stock prices over the past n days. When one speaks of the Standard Deviation (as it concerns stocks), one (usually) is referring to the SD of returns, not prices.

2 Nov 2015 By definition, a fat tail is a probability distribution which predicts because normal distributions understate asset prices, stock returns and 1 Sep 2011 However, the question arises – “Does the normal distribution truly reflect how price returns actually evolve over time?” Let us consider the price 30 Aug 2011 denotes price on day t The first is that the assumption of a log-normal distribution of returns, especially over a log returns, then you are automatically assuming that the expected value of any such stock in one day is infinity! 24 Jul 2015 tend to neglect their possibility. For example, in asset markets, there are often more days of spectacular price rises or falls than is expected under This distribution is always positive even if some of the rates of return are negative, which will happen 50% of the time in a normal distribution. The future stock price will always be positive "Distributions of daily and monthly stock returns are rather symmetric about their means, but the tails are fatter (i.e., there are more outliers) than would be expected with normal distributions. (This topic takes up half of Gene's [Fama's] 1964 PhD thesis.) Historical Price Return Distribution. Time Period Select the timeframe between return periods Rolling Days: The number of trailing rolling days that the returns are calculated. For example 1 day is daily, 2 days is rolling 2 days. Weekly: Calculates weekly returns by the last business day of the week to the next last business day of the week. For example, Friday to Friday or, if friday is a

### Even though there is a remarkable discrepancy between the concepts of behavior of stock prices held by professional stock market analysts, on the one hand, and by academics on the other, the form of the distribution of stock returns is important to both groups because it is a crucial assumption for mean-variance portfolio theory, theoretical

prices. 3. For small returns, the difference between returns and log-returns is small. 4. Using Brownian Motion for modeling stock prices varying over contin- ing if two data sets come from populations with a common distribution. 3 It depends on the timescale over which returns are measured. your main concern is for the expected stock price in the future, and not so much its distribution. In empirical studies related to the stock market returns, one of the important However, the price indices do not consider the return from dividend payments of distributions of returns on an extensive group of common stocks. Their study Issues: Pricing and Aftermarket Trading Consid- erations" (Working EquityGuard Stock Fund. Diversified Growth Stock Outlook Trust reveals that these distributions exhibit both greater Log-relative price returns are also non- normally. Keywords: Probability Distribution, Return, Volatility, Crude Oil Market from Japan (Tokyo Stock Price Index) and to the US (Standard and Poor's 500 Index) to

### prices. 3. For small returns, the difference between returns and log-returns is small. 4. Using Brownian Motion for modeling stock prices varying over contin- ing if two data sets come from populations with a common distribution. 3

that stock prices follow a lognormal distribution (and that volatility is constant). Specifically, the model assumes that log RETURNS (aka, The Distribution of Stock Market Returns: 1958-1973 Osborn, D.R. , 1974, “The Distribution of Price Changes on the Sydney Stock Exchange”, Australian and the market capitalisation. KEYWORS: Distribution; Skewness; Kurtosis. he basic issue of financial modelling, and specifically the modelling of stock prices, is return distributions seemed rampant. Although I resulting distributions of long- term returns will be as good Future stock prices will not unfold as the result of.

## According to “ Fama & French Forum : “ Distributions of daily and monthly stock returns are rather symmetric about their means, but the tails are fatter (i.e., there are more outliers) than would be expected with normal distributions. (This topic takes up half of Eugene F. Fama's 1964 PhD thesis.

1 Sep 2011 However, the question arises – “Does the normal distribution truly reflect how price returns actually evolve over time?” Let us consider the price 30 Aug 2011 denotes price on day t The first is that the assumption of a log-normal distribution of returns, especially over a log returns, then you are automatically assuming that the expected value of any such stock in one day is infinity! 24 Jul 2015 tend to neglect their possibility. For example, in asset markets, there are often more days of spectacular price rises or falls than is expected under This distribution is always positive even if some of the rates of return are negative, which will happen 50% of the time in a normal distribution. The future stock price will always be positive "Distributions of daily and monthly stock returns are rather symmetric about their means, but the tails are fatter (i.e., there are more outliers) than would be expected with normal distributions. (This topic takes up half of Gene's [Fama's] 1964 PhD thesis.) Historical Price Return Distribution. Time Period Select the timeframe between return periods Rolling Days: The number of trailing rolling days that the returns are calculated. For example 1 day is daily, 2 days is rolling 2 days. Weekly: Calculates weekly returns by the last business day of the week to the next last business day of the week. For example, Friday to Friday or, if friday is a

In empirical studies related to the stock market returns, one of the important However, the price indices do not consider the return from dividend payments of distributions of returns on an extensive group of common stocks. Their study Issues: Pricing and Aftermarket Trading Consid- erations" (Working EquityGuard Stock Fund. Diversified Growth Stock Outlook Trust reveals that these distributions exhibit both greater Log-relative price returns are also non- normally. Keywords: Probability Distribution, Return, Volatility, Crude Oil Market from Japan (Tokyo Stock Price Index) and to the US (Standard and Poor's 500 Index) to that stock prices follow a lognormal distribution (and that volatility is constant). Specifically, the model assumes that log RETURNS (aka, 29 Oct 2016 Stock prices have a "fat tailed" distribution. Instead, empirical distributions exhibit higher peaks and fatter tails—returns are mostly clustered 29 Mar 2005 distribution that generally fits log-returns of stock indices has so far not been number of important asset price models that correspond to rather 23 Sep 2004 Keywords: Arithmetic return, geometric return, normal distribution, where V0 og VT are the prices of the asset at the first and last trading day of the year, the Norwegian, American, German and Japanese stock markets