Daily statistics summarize how a stock's return has behaved — day over day — over the past year. Rather than looking at a single price chart, these statistics compress the entire year's trading days into a handful of numbers that present insights into volatility, average returns, and directional trends at a glance.
Also known as the mean return, the average daily return represents the arithmetic average of all close-to-close daily returns over the trailing one-year period. It is calculated by adding together every daily percentage return and dividing by the total number of trading days. The result provides a simple measure of the stock's average daily performance of historical returns. A positive average daily return indicates that, on average, the stock has gained value from one trading day to the next during the period analyzed. Conversely, a negative value suggests that losses have outweighed gains. While this can provide insight into the stock's overall direction and momentum, the mean should never be viewed in isolation. One important limitation of average return is its sensitivity to extreme observations, often called outlier days. A stock that barely changes for most of the year but experiences one or two exceptionally strong days may show a surprisingly high average return despite relatively modest day-to-day performance. Likewise, a handful of severe declines can drag the mean lower than what investors typically experience on a normal trading day. For this reason, investors often compare average return with other distribution statistics. Together, these metrics provide a more complete picture of return quality, consistency, and risk. Average daily return is most useful as a broad measure of historical performance, helping investors determine whether a stock's long-term daily trend has generally been positive, negative, or neutral.
Standard Deviation
Standard deviation of daily returns, commonly represented by the Greek letter σ (sigma), is one of the most widely used measures of market risk. It is a core component of volatility, and it measures how far daily returns tend to deviate from the average return over a given period. In practical terms, it shows how much daily price movement investors can typically expect from a stock. For example, if a stock has a daily standard deviation of 1.2%, most daily returns will generally fall within approximately ±1.2% of the average return. Stocks with low standard deviations tend to experience more stable and predictable price movements, while stocks with high standard deviations often exhibit larger swings in both directions. Higher standard deviation means higher daily volatility and larger swings in both directions. The difference between standard deviation and volatility is that volatility is standard deviation as a function of time - represented by the equation Volatility = σ x √T
Median Return
The median return represents the middle value of all daily returns after they have been arranged from lowest to highest. Unlike the average (mean), the median is not heavily influenced by unusually large gains or losses, making it one of the most reliable measures of a stock's "typical" trading day. To understand the median, imagine sorting every daily return from worst to best. The median is the return that sits directly in the middle, with half of all trading days producing higher returns and half producing lower returns. Because it focuses on the center of the distribution rather than the arithmetic average, it often provides a clearer picture of what investors can generally expect on a normal day. Comparing the median to the mean can reveal important characteristics of a stock's return profile. When the median is significantly lower than the mean, the stock's average performance may be heavily influenced by a small number of exceptionally strong trading days. This pattern is often seen in growth stocks, speculative stocks, or securities that occasionally experience large rallies. Conversely, if the median exceeds the mean, the stock may suffer occasional large declines that drag down the average. Many professional investors consider the median a better indicator of consistency because it is resistant to outliers. A stock with a strong median return and moderate volatility may provide a more dependable return profile than one whose average return is driven primarily by a handful of extraordinary gains. Used alongside mean return, skewness, and standard deviation, the median helps investors determine whether historical performance reflects typical daily behavior or is heavily dependent on rare market events. A stock with a lower median than mean suggests that the stock has big swings.
Mode Return
The mode is the daily return value that occurred most frequently during the trailing one-year period. Unlike the mean and median, which focus on central tendencies of the entire dataset, the mode identifies the return level that investors encountered most often. In financial markets, exact daily return values rarely repeat because stock prices fluctuate continuously. To make the calculation meaningful, daily returns are rounded to two decimal places before determining the most frequently occurring value. This allows the mode to capture the most common return range rather than requiring identical returns. A mode near 0.00% often suggests that the stock spends much of its time experiencing relatively small day-to-day price changes. This is common among mature, lower-volatility companies where daily movements are generally modest. Conversely, a mode located farther from zero may indicate that the stock frequently experiences directional price movement or elevated volatility. The mode becomes particularly useful when compared with the mean and median. If all three values are similar, the return distribution is generally balanced and consistent. However, large differences between them can reveal the presence of outliers, skewed distributions, or unusual return patterns. For example, a stock may have a mode near zero but a substantially positive mean, indicating that a few exceptionally strong trading days contributed significantly to overall performance. Although the mode is less commonly discussed than average return or standard deviation, it provides valuable insight into what investors are most likely to experience on a typical trading day. When combined with other statistical measures, it helps create a more complete understanding of the stock's return distribution and behavioral characteristics.
Max / Min
The maximum daily return (Max) and minimum daily return (Min) represent the single best and worst trading days experienced by a stock during the trailing one-year period. These metrics highlight the most extreme positive and negative price movements observed within the dataset. The maximum return identifies the largest one-day gain, while the minimum return identifies the largest one-day loss. These events are often associated with earnings announcements, analyst upgrades or downgrades, mergers and acquisitions, macroeconomic developments, regulatory news, or unexpected company-specific events. In some cases, these extreme moves can dramatically influence investor perception and overall performance statistics. While average return and standard deviation describe typical behavior, maximum and minimum returns reveal what has actually occurred during the most volatile moments. This makes them particularly useful for assessing tail risk and understanding how a stock behaves during periods of market stress or excitement. A stock with relatively low volatility but extremely large maximum and minimum values may be vulnerable to occasional news-driven price shocks. Conversely, a stock with a narrower range between its best and worst days may exhibit more stable behavior and fewer surprises. Risk-conscious investors often pay special attention to the minimum daily return because it reflects the magnitude of downside risk that has historically occurred in a single trading session. At the same time, the maximum return highlights the stock's upside potential and ability to generate large gains. When analyzed alongside standard deviation, kurtosis, and skewness, these metrics provide valuable context regarding the frequency, severity, and asymmetry of extreme price movements.
Kurtosis
Kurtosis measures the shape of a return distribution by evaluating the frequency and magnitude of extreme observations relative to a normal bell-shaped distribution. In finance, kurtosis is particularly important because stock returns often experience unusually large movements that traditional volatility measures may not fully capture. A normal distribution has a kurtosis value of 3. Values significantly above 3 indicate fat tails, meaning extreme gains and losses occur more frequently than would be expected under a normal distribution. High-kurtosis stocks may appear relatively stable most of the time but occasionally experience dramatic price moves due to earnings surprises, economic events, market sentiment shifts, or unexpected news. Low kurtosis suggests a flatter distribution with fewer extreme outcomes. Returns tend to cluster more closely around the center, and large deviations from the average occur less frequently. Such stocks often exhibit more predictable behavior and lower exposure to sudden price shocks. Kurtosis is especially useful when standard deviation alone does not adequately describe risk. Two stocks can have identical volatility levels but very different kurtosis values. In that case, the stock with higher kurtosis may be considerably riskier because its returns are more likely to include rare but significant price swings. Investors and risk managers frequently use kurtosis to identify securities that may be vulnerable to unexpected events. A stock with elevated kurtosis may require additional caution, even if its average return and volatility appear attractive. When combined with standard deviation and skewness, kurtosis helps provide a more complete picture of return distribution characteristics, tail risk, and the likelihood of extreme market outcomes.
Skewness
Skewness measures the asymmetry of a stock's return distribution and helps investors understand whether extreme gains or extreme losses occur more frequently. While standard deviation measures the overall magnitude of price movements, skewness focuses on the balance between positive and negative outcomes. A perfectly symmetrical distribution has a skewness value of zero. Positive skewness indicates a longer tail on the right side of the distribution, meaning occasional large gains pull the average return upward. In positively skewed distributions, the mean is typically greater than the median, and the median is greater than the mode. This pattern often reflects stocks that experience infrequent but substantial upside moves. Negative skewness indicates a longer tail on the left side of the distribution. In these cases, occasional sharp declines drag the average return downward. Stocks with negative skewness may appear stable during normal market conditions but can be vulnerable to sudden and severe losses. Many investors view negative skewness as a particularly important risk factor because downside shocks can have a disproportionately large impact on portfolio performance. Understanding skewness helps investors interpret other statistics more effectively. For example, a stock with a strong average return but significant negative skewness may generate attractive long-term performance while still exposing investors to occasional large drawdowns. Conversely, positive skewness can indicate the presence of rare but meaningful upside opportunities. Together with mean return, median return, standard deviation, and kurtosis, skewness helps describe the complete shape of a stock's return distribution. This deeper understanding allows investors to evaluate not only expected returns and volatility, but also the balance of upside potential and downside risk that may exist beneath the surface.
How to Use These Together
Statistical metrics don't tell the full story of a company. However, they do give some insights into how the stock has performed historically over the past year. Sometimes the importance of each characteristic changes over time depending on the stock and the overall market. We recommend checking investments often, understanding your investments fully, and remembering that historic results aren't indicative of future performance.
As a rule of thumb, Systems Capital often prefers investments with the following characteristics:
Average return that is greater than 0%.
Standard Deviation as close to 0% as possible.
Median as large as possible.
Mode also as large as possible but with all mean, median, and mode, ensure values are greater than daily inflation.
Max that is greater than 0% and as high as possible.
Min that is as small as possible and is ideally still a positive value.
Kurtosis depends on investment goals. Often, we invest in both high and low, but not often normal kurtosis.
Skewness is market dependent, but often near 0.
Suggested Reading
Below are some recommended readings that helped shape Systems Capital's investment philosophy.