Lognormal and Normal Distribution

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Normal Bell Curve Distribution Data sets like the height of humans, marks obtained by 45 pupils in a class, etc.

This distribution of normal distribution options points is called the normal or bell curve distribution. For example, in a group of individuals, 10 may be below 5 feet tall, 65 may stand between 5 and 5. This range-bound distribution can be plotted as follows: Similarly, data points plotted in graphs for any given data set may resemble different types of distributions.

Three of the most common are left aligned, right aligned and jumbled distributions: Note the red trendline in each of these graphs. This roughly indicates the data distribution trend.

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The normal distribution is symmetrical around the central value with half the values on each side. A lot of real-life examples fit the bell curve distribution: Toss a fair coin many times say times or more and you will get a balanced normal distribution of heads and tails.

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Roll a pair of fair dice many times say times or more and the result will be a balanced, normal distribution centered around the number 7 and uniformly tapering towards extreme-end values of 2 and The height of individuals in a group of considerable size and marks obtained by people in a class both follow normal patterns of distribution.

Risk and Returns Any investment has two aspects: risk and return.

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Investors look for the lowest possible risk for the highest possible return. The normal distribution quantifies these two aspects by the mean for returns and standard deviation for risk.

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For more, see " Mean-Variance Analysis. This mean value or expected value signifying return can be arrived at by calculating the average on a large enough dataset containing historical daily price changes of that stock.

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The higher the mean, the better. The higher the standard deviation, the riskier the investment, as it leads to more uncertainty.

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Here is a graphical representation of the same: Hence, the graphical representation of normal distribution through its mean and standard deviation enables the representation of both returns and risk within a clearly defined range. A dataset which has a mean of 1.

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Knowing these values for each selected asset i. But can this be extended to a portfolio of multiple assets? Individuals start trading by buying a single stock or bond or investing in a mutual fund.

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Gradually, they tend to increase their holdings and buy multiple stocks, funds or other assets, thereby creating a portfolio. In this incremental scenario, individuals build their portfolios without a strategy or much forethought.

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To achieve this objective, the assets to be included in the portfolio should not be selected solely based on their own individual merit but instead on how each normal distribution options will perform relative to the other assets in the portfolio. In a nutshell, Ways to make money online with defines how to best achieve portfolio diversification for the best possible results: maximum returns for an acceptable level of risk or minimal risk for a desired level of returns.

Ideally, the positive performance of one asset in the portfolio will cancel the negative performance of other assets.