StickyKurtosis
Kurtosis refers to the measurement of the degree to which a given distribution is more or less ‘peaked’ relative to the normal distribution. The concept of kurtosis is very useful in decision-making. In this regard, we have 3 categories of…
Covariance and Correlation
Covariance Covariance is a measure of how two variables move together. The sample covariance of X and Y is calculated as follows: $${s}_{XY}=\frac{\sum_{i=1}^{N}\left(X_i-\bar{X}\right)\left(Y_i-\bar{Y}\right)}{n-1}$$ The formula above implies that the sample covariance is the mean of the product of the deviations in the two random variables and…
Measures of the Shape of a Distribution
Because the deviations from the mean are squared when calculating variance, we cannot determine whether significant deviations are more likely to be positive or negative. In order to identify other crucial distributional traits, we must look beyond measures of central tendency,…
Measures of Dispersion
Measures of dispersion are used to describe the variability or spread in a sample or population. They are usually used in conjunction with measures of central tendency, such as the mean and the median. Specifically, measures of dispersion are the…
Measures of Central Tendency and Location
The center of any data is identified via a measure of central tendency. A measure of central tendency for a series of returns reveals the center of the empirical distribution of returns. They include mean, mode, and median. Measures of location include measures…
Other Return Measures
Other Return Measures Gross and Net Return The gross return is generated by an asset manager before deducting management costs, custody costs, taxes, or any other costs not directly connected to the generation of return but related to the management…
Annualized Returns
In order to properly compare a return obtained during a shorter time frame to other returns, it can be necessary to annualize the return. That is annualizing daily, weekly, monthly, and quarterly returns. Non-Annual Compounding Interest may be paid semiannually,…
Money-Weighted and Time-Weighted Rates of Return
Money-Weighted回报率Money-Weighted return considers the money invested and gives the investor information on the actual investment return. Calculating money-weighted return is similar to calculating an investment’s internal rate of return (IRR). As such, the money-weighted rate…
Measures of Return
Financial assets are primarily defined based on their return-risk characteristics, facilitating portfolio construction from the universe of available assets. Regarding returns, there are different ways of measuring returns. Financial market assets generate two different streams of return: income through cash…
Interest Rates
The time value of money is a concept that states that cash received today is more valuable than cash received in the future. If a person agrees to receive payment in the future, he foregoes the option of earning interest…
Risk-Neutrality in Derivative Pricing
Remember that the value of an option is not affected by the real-world probabilities of the underlying price increments or decrements but rather by the expected volatilities (\(R^u\) and \(R^d\) ), which are required to price an option. We can…
