# Which One Is Better, a Negatively Skewed Return or a Positively Skewed Returns Distribution?

## What is Skewness?

In statistics, the term skewness refers to an asymmetrical or distorted data set distribution of values. When a data set is plotted on the x and y-axis, it can either indicate a normal or skewed distribution.

A normal distribution is represented by a bell-shaped curve produced if there are equal denominations on both positive and negative sides of the mean.

Hence, a normal distribution is symmetrical where mean, median, mode, and mode are equal, and skewness equals zero. (mean=median=mode, skew=0)

On the other hand, a skewed distribution is formed when unequal positive and negative denominations are plotted around the mean.

A skewed distribution is of two types; positive (right-skewed) and negative (left-skewed).

• Positive Skewness:

When a positively skewed distribution is produced on a graph, the tail of the bell-shaped curve is tampered with towards the right due to the concentration of positive values.

The inequality of the positive Skewness can be shown as follows.

(Mean>median>mode)

The value of Skewness will be greater than zero (skew>0).

• Negative Skewness:

Whereas, in the graph of a negatively skewed distribution, the tail of the bell-shaped curve is inclined towards the left due to extreme negative values.

The inequality of the negative Skewness can be shown as follows.

(Mean<median<mode)

The Skewness statistic will be lesser than zero in this case (skew<0).

## Purpose of using Skewness in Finance

Skewness is applied in finance to analyze the probability distribution of financial data, specifically the data on return of investments (ROI).

An investor might invest in different securities like bonds and stocks and then use statistical techniques like standard deviation, skewness, kurtosis, etc., to predict and analyze the return patterns from these investments.

### Predicting ROI using Standard Deviation

Investors or their agents are more likely to determine ROI using standard deviation, but it does not always give accurate results.

This is because standard deviation is to be used for normal distributions only and these investors assume the distribution of their returns to be symmetrical or normal, which is not necessarily true.

Suppose the standard deviation is applied to a skewed distribution.

In that case, it can lead to skewness risk because all three measures of central tendency i.e., mean, median, and mode are not equal in a skewed distribution, as wrongly presumed by investors.

Standard deviation involves calculating the mean or average of the data, then subtracting it from each data point and squaring the difference for each result.

Where, x= value in the data set, μ = mean, N = number of data points

This method depends on ‘average‘ which is only reliable for long-term investors whose ROI can show a normal distribution due to stable investments in several securities over time.

### Predicting ROI using Skewness

For short and medium-term investors skewness is a more suitable technique to predict returns as it takes into account the ‘extreme’ values of the data set along with the average.

Skewness is calculated by obtaining the difference between mean and median, multiplying the difference by 3, and then dividing the result by standard deviation.

Skewness = 3 (mean – median) / standard deviation

Sk2 = 3 X – M d / s

Where, Sk2 = Pearson second coefficient of skewness, X = mean, M d = median, s = standard deviation

This way, skewness risk can be minimized as the difference between mean and median is realized and not wrongly presumed to be equal.

### Interpretation of Positive Skewness of distribution of investment returns

A positively skewed distribution of returns for one period indicates the possibility of regular small losses and rare big profits in the next period.

Generally, a positive skewness is preferred by investors over negative skewness because of the view that few big gains can cover the small losses.

### Interpretation of Negative Skewness of distribution of investment returns

A negatively skewed distribution of returns for one period indicates the possibility of regular small profits and rare big losses in the next period.

Negative skewness is preferred by a few investors like traders for whom stable returns are more important than frequent losses.

Nevertheless, the risk of huge losses should not be ignored as it can nullify the smaller gains.

## Negatively Skewed Return vs. Positively Skewed Returns Distribution

According to financial theory, investors usually prefer positive skewness over negative skewness for predicting future returns.

This means investors are willing to accept frequent small losses to obtain huge gains once in a blue moon.

It might seem irrational to a risk-averse person at first but it makes sense when given another thought. Imagine you were presented with two options:

1. 99% probability of losing \$200 and 1% probability of winning \$10,000. (Positively skewed)
2. 1% probability to lose \$10,000 and 99% probability to win \$200. (Negatively skewed)

For most readers, it will be choice number one, positive skew, controlling for mean and standard deviation.

Because even though the idea of losing money frequently might seem unfavorable, the slightest chance of winning a bigger amount is more tempting.

Similarly, a high probability of obtaining small and stable returns might seem safe and secure yet the slightest fear of losing a big profit is an unacceptable risk.

There is abundant evidence from the literature to support this view. The rationale behind this preference is also explained by the ‘longshot bias’ or ‘lottery-effect’ and “black swans”.

Black swans refer to bad events deemed impossible due to their low probability of occurrence, such as shutting down a well-established MNC.

While longshot bias refers to good events that are deemed possible although having a low probability of occurrence, such as a prize bond lottery.

Black swans being negatively skewed are often ignored and longshots being positively skewed are often overweighed.

## Conclusion

In statistics, the central tendency is important to analyze the data behavior. The structured data is plotted to understand the behavior and decide on its basis.

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Although, data is related to the past and there are certain assumptions. However, it can still help understand the pattern and behavior of different variables.

When structured data is plotted against mean, mode, and median, it can be symmetric, and when these measures are not equal, it’s said to be asymmetric.

In finance, we plot market data to axes for understanding the behavior.

From the ROI perspective, if the data distribution is positively skewed, there is a higher concentration of positive value, a higher probability of losing small values, and a rare chance of gaining significant value.

On the contrary, if the data distribution is negatively skewed, there is a higher concentration of negative values in the population.

In finance, the negative Skewness means a higher probability of winning small amounts with a low probability of losing significant value.

So, it helps investors in what they want to opt for.

A study on Japanese investors confirmed a greater investor inclination towards positively skewed returns.

However, preference for positive skewness is a widely observed phenomenon, not a hard-and-fast rule.

It is also considered an ‘irrational’ approach at certain points in literature. The answer to ‘which skewness is better’ is not absolute; rather, it is conditional upon the type of investor and his/her experience with the stock market.

What types of measures should be used for analyzing the stock?

The following measures can be used for analyzing the stock.

1. Price/Earnings ratio
2. Return on equity
3. Debt to equity
4. Interest coverage ratio
5. Price to book value

This is not an exhaustive list; there may be multiple other measures to analyze the security.

Why should investors look at the liquidity position of the company?

Investors should look at liquidity position if they are more concerned about dividend receipt.

What are two types of analyses to analyze the stock?

Two well-known types of stock analysis include fundamental analysis and technical analysis.