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Download preview PDF. Box , Blindern, O, Oslo, Norway. You can also search for this author in PubMed Google Scholar. Reprints and Permissions. Benth, F. Statistical Analysis of Data from the Stock Market. In: Option Theory with Stochastic Analysis.

Springer, Berlin, Heidelberg. Publisher Name : Springer, Berlin, Heidelberg. Print ISBN : Online ISBN : Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Skip to main content. Search SpringerLink Search. In business and investment terms, expected value is used by risk managers in scenario analysis when calculating whether an investment is worth the appropriate level of risk the firm is willing to take on.

The quality and depth of statistical analysis now made possible by computing means EV can be calculated on data sets that were previously regarded as unworkably massive. These can be of enormous value in helping investment professionals to arrive at forecasts for investment returns, particularly when used in conjunction with measures of variance and standard deviation see below.

Normal distribution can be charted along a single horizontal axis that represents the total spectrum of values within a given data set. Half of that data set will have values that are higher than the mean and half will have values lower than the mean. Most data points will lie close to the mean and the rest will tail off in each direction. Negative skewness will distort the bell curve to the left and positive skewness will have the opposite effect.

When examining an asset's annual returns over a period of time, the professional investor will look for investments that show positive skewness — returns that are greater than the historical average. This has, in some circumstances, proved disastrous for investors, however. When market bubbles form, an asset can show positive skewness, prompting investors to buy at the top of the market.

Then, when the skew turns negative, they may be tempted to sell at a loss. Kurtosis is another measure of deviation from normal distribution, but looks at the extremes. This introduces the well-known investment term "tail risk". A distribution model that is said to have a fat tail is a sign of kurtosis. Tail risk arises when the possibility that an investment could move more than three standard deviations see below from the mean is greater than a normal distribution model.

Variance is used as a data analysis tool to examine how each individual value in a set of numbers differs from the arithmetic mean of that data set. If you take the data set 2, 4, 5, 8 and 9, the arithmetic mean adding all and dividing by number of data points, i. If you simply take the deviation from the mean by subtracting it from each number, i. The sum of all these numbers, and any other set of numbers will always be zero.

To arrive at the variance, take the difference between each number in the data set and the arithmetic mean and square it. The variance is therefore, 6. Variance is also used in risk management to help determine the level of risk an investor might take when purchasing a certain asset, but usually as the square of standard deviation, which we'll examine next. The standard deviation is simply the square root of variance, but is one of the most important measures in statistical analysis.

When applied to annual returns on an investment, standard deviation can help determine the historical volatility of that investment. Once you have worked out the variance, it is simple. The variance of the set 2, 4, 5, 8 and 9 as above is 6. The standard deviation of this set is the square root of 6. Standard deviation is a fundamental risk measure in investment that most professional fund and portfolio managers use to help calculate likely returns from an investment.

Knowing the returns on an investment over several previous years, the mean or average return can be calculated, and from that the standard deviation tells the investment manager the likely volatility on the average return. If the return each year has been within the standard deviation then it is a stable investment. If the return in some years is outside the standard deviation it is more volatile. Traders use statistical analysis to plot the returns on risky investments in a portfolio.

When two or more risk assets move in tandem, they are said to have high, or positive covariance. Positive covariance isn't particularly welcome in an asset portfolio. One can expect a higher degree of returns from risk assets, but also a higher degree of losses when things go wrong — and you don't want two or more risky assets going wrong at the same time. Low, or negative covariance provides an asset portfolio with greater diversification, because when one risk asset is not performing well, other risk assets should be offsetting that poor performance.

Simple correlations can be seen when comparing two charts side by side. The eye can spot simple matches between peaks and troughs. For a more accurate gauge of correlation, however, the correlation coefficient can be worked out by dividing the sum of the covariance of the variables in question by the sum of their standard deviations. The answer should come between the range of 1 and A positive value means there is a positive correlation between the two variables.

The closer to 1, the more highly correlated the two are. The opposite effect will be seen in a negative coefficient. This type of statistical analysis is used by fund managers to determine how well their fund is performing compared to its benchmark index. The best-known regression model in finance is the capital asset pricing model CAPM which helps investors arrive at asset pricing and cost of capital. Simply put, regression is the degree to which the price of an asset, or other variable, is influenced by another set of variables.

For example, it is possible using regression formula to work out the probable effect on an Australian gold miner's shares from rising gold prices, rising domestic interest rates and a fall in the US dollar. R-squared is the statistical analysis of the relationship between a fund, particular asset or security and its benchmark index. For example, an equity fund will have a firm relationship with the index it tracks - if the fund is sector based, then it should have a close resemblance to that sector's sub-index on a main stock index.

Remember that without some knowledge also of the market conditions in which certain assets and securities thrive, statistical analysis alone is of little reliable use. But together with analysis of economic factors such as balance sheet and profit and loss, or historical returns, statistical analysis can help reassure investors on those hunches.

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