Coefficient of variation PDF

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coefficient of variation The coefficient of variation shows the extent of variability of data in a sample in relation to the mean of the population. In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments. (how risky is to get the expected return). Ideally, if the coefficient of variation formula should result in a lower ratio of the standard deviation to mean return, then the better the risk-return trade-off. Note that if the expected return in the denominator is negative or zero, the coefficient of variation could be misleading. The coefficient of variation is helpful when using the risk/reward ratio to select investments. For example, an investor who is risk-averse may want to consider assets with a historically low degree of volatility relative to the return, in relation to the overall market or its industry. Conversely, risk-seeking investors may look to invest in assets with a historically high degree of volatility In finance, the coefficient of variation allows investors to determine how much volatility, or risk, is assumed in comparison to the amount of return expected from investments. The lower the ratio of the standard deviation to mean return, the better risk-return trade-off Distributions with a coefficient of variation to be less than 1 are considered to be low-variance, whereas those with a CV higher than 1 are considered to be high variance.

Based on the calculations above, Fred wants to invest in the ETF because it offers the lowest coefficient (of variation) with the most optimal risk-to-reward ratio Let us consider the case of a rational investor, who is risk-averse and at the same time, wants decent returns on his investment. He is looking to invest in either stock A of a blue-chip company or gold. Both are safe investment options. Here stock A has a mean annual return of 9% p.a. and a standard deviation of 13.5%, whereas gold has a mean annual return of 7% and a standard deviation of 11%.

If the investor looks at just the returns, stock A is the better choice as the performance is higher. But he needs to check for the coefficient of variation for both the cases. It will take into account the risk factor, as well. In the case of stock A- Standard deviation of stock A/ Mean annual return of stock A 15.5/9= 1.72 In the case of Gold- Standard deviation of gold/ Mean annual return of gold 11/7= 1.57 Therefore it is safer to invest in gold than stock A as the coefficient of variation is lesser for gold. It means that there is a lesser chance of volatility in returns from investing in gold.

Coefficient of variation vs Standard Deviation The greater the standard deviation, the greater the risk of an investment. However, the standard deviation cannot be used to compare investments unless they have the same expected return. For instance, consider the following table. The coef coefficient ficient of variation is a better measure of risk, quantifying the dispersion of an asset's returns in relation to the expected return, and, thus, the relative risk of the investment. Hence, the coefficient of variation allows the comparison of different investments. So while the standard deviation measures the dispersion of returns, the coefficient of variation measures their relativ relative? e? Dispersion

The greater the standard deviation of securities, the greater the variance between each price and the mean, which shows a larger price range. A large dispersion shows how much the return on the fund is deviating from the expected normal returns. Because it is easy to understand, this statistic is regularly reported to the end clients and investors.

s.d -> by how much share prices may move from the expected return – it is volatile – No Comparison coefficient of V -> how much risks is invovled -> that volatility is risky! – Comparison

Similarly, financial analysts use the coefficient of variability to assess the volatility of returns for financial investments across a wide range of valuations. In this context, higher coefficients indicate a more significant risk owever, if your kilograms variable has a higher coefficient of variability than megapascals, then you know weight is relatively more variable than strength.

The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The higher the coefficient of variation, the greater the level of dispersion around the mean. It is generally expressed as a percentage. Without units, it allows for comparison between distributions of values whose scales of measurement are not comparable.

When we are presented with estimated values, the CV relates the standard deviation of the estimate to the value of this estimate. The lower the value of the coefficient of variation, the more precise the estimate.

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