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
Since 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…
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…
Other Return Measures
Other Return Measures Gross and Net Return The gross return is what an asset manager earns before subtracting various costs such as management fees, custody fees, taxes, and other administrative expenses. However, it does account for trading costs such as…
Annualized Returns
To compare returns over different timeframes, we need to annualize them. This means converting daily, weekly, monthly, or quarterly returns into annual figures. Non-Annual Compounding Interest may be paid semiannually, quarterly, monthly, or even daily – interest payments can be…
Money-weighted and Time-weighted Rates of Return
Money-weighted Rate of Return The 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). The money-weighted rate of return…
Measures of Return
Financial assets are primarily defined based on their return-risk characteristics. This definition approach helps when building a portfolio from all the assets available. It’s noteworthy that there are different ways of measuring returns. Financial market assets generate two types of…
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…
One-Period Binomial Model
The law of arbitrage dictates that the value of any two assets (or portfolio of assets) whose payoffs are identical in all possible future scenarios at a given time must also be identical today. Unlike forward commitments that offer symmetric…
