Volatility Definition
In finance, volatility is a statistical measurement of up and down asset price fluctuations over time. If an asset has rapid dramatic price swings, volatility will be high. If prices are consistent and rarely change, volatility is low. Volatility can be measured as the annualized standard deviation.
Volatility as Measure of Risk
Volatility is often used to measure risk. Many common measurements of risk, such as beta, utilize volatility in calculations. It makes sense that an asset that has had huge price swings is more risky than an asset that is …

Normal distributions (a bell curve) of asset returns is a key assumption made by many financial models, including the capital asset pricing model(CAPM) and the Black-Scholes option pricing model(BSM). However, actual asset returns may not be so normal.
Normal Distributions Overestimate the Improbability of Unlikely Market Events
Using a normal distribution, events that diverge from the mean by five or more standard deviations, known as a five-sigma event, are very rare and ten-sigma events are nearly impossible. For example, the 1987 market plunge represents a change equalling 22 standard deviations. The odds …

“By far the most significant event in finance during the past decade has been the extraordinary development and expansion of financial derivatives. These instruments enhance the ability to differentiate risk and allocate it to those investors most able and willing to take it - a process that has undoubtedly improved national productivity growth and standards of living.” -Alan Greenspan
Financial derivatives are financial instruments that “derive” value from an underlying item such as an asset or index. The use of derivatives provides exposure to the linked underlying item without necessitating the …

The Sortino ratio is a financial ratio, similar to the Sharpe ratio, that measures the risk-adjusted return of investments or portfolios. Unlike the Sharpe ratio, the Sortino uses downside-volatility(sometimes referred to as semi-volatility) as the denominator instead of standard deviation. The use of downside-volatility allows the Sortino ratio to measure the return of “negative” volatility.
Downside deviation differentiates “positive” volatility from “negative” volatility, unlike standard deviation. Standard deviation is the square root of volatility. However, using standard deviation as a measure of risk may not be completely accurate. For example, assume …

The Sharpe Ratio is a formula used to measure risk/return. The ratio describes the amount of extra return received for the extra volatility of a more risky asset. The higher the Sharpe Ratio, the greater returns are for each unit of risk. The Sharpe Ratio is calculated by subtracting the risk free rate or return from the return of the portfolio and then dividing by the portfolio’s standard deviation. By using the Sharpe Ratio, investors can theoretically compare risk adjusted returns of investments or portfolios that have different returns and …

A Mortgage-Backed security(MBS) is a debt obligation (bond) that represents claims to the cash flows from pools of mortgage loans. Mortgage providers sell the loans to an Agency or company that packages or pools loans together for sale to investors, creating a MBS. As the loans are paid, the MBS owner receives payments of interest and principle. Because mortgagors are have the option to pay more than the required monthly payment(curtailment) or pay off the loan in its entirety(prepayment)the monthly cash flow is not completely known in advance, increasing risk. …