'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Which means for our asset as example:- Looking at the total return, or increase in value of -40.4% in the last 5 years of Liberty Global, we see it is relatively lower, thus worse in comparison to the benchmark SPY (57.1%)
- During the last 3 years, the total return, or increase in value is -18.9%, which is smaller, thus worse than the value of 32% from the benchmark.

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Which means for our asset as example:- Looking at the annual return (CAGR) of -9.9% in the last 5 years of Liberty Global, we see it is relatively lower, thus worse in comparison to the benchmark SPY (9.5%)
- Compared with SPY (9.7%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of -6.8% is lower, thus worse.

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (21.5%) in the period of the last 5 years, the historical 30 days volatility of 33.9% of Liberty Global is greater, thus worse.
- Compared with SPY (17.9%) in the period of the last 3 years, the 30 days standard deviation of 30.2% is larger, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- Looking at the downside risk of 23.6% in the last 5 years of Liberty Global, we see it is relatively greater, thus worse in comparison to the benchmark SPY (15.5%)
- Looking at downside volatility in of 21.5% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.5%).

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Using this definition on our asset we see for example:- The risk / return profile (Sharpe) over 5 years of Liberty Global is -0.37, which is lower, thus worse compared to the benchmark SPY (0.32) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of -0.31 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.41).

'The Sortino ratio improves upon the Sharpe ratio by isolating downside volatility from total volatility by dividing excess return by the downside deviation. The Sortino ratio is a variation of the Sharpe ratio that differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative asset returns, called downside deviation. The Sortino ratio takes the asset's return and subtracts the risk-free rate, and then divides that amount by the asset's downside deviation. The ratio was named after Frank A. Sortino.'

Which means for our asset as example:- Looking at the ratio of annual return and downside deviation of -0.52 in the last 5 years of Liberty Global, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.45)
- During the last 3 years, the downside risk / excess return profile is -0.43, which is smaller, thus worse than the value of 0.58 from the benchmark.

'Ulcer Index is a method for measuring investment risk that addresses the real concerns of investors, unlike the widely used standard deviation of return. UI is a measure of the depth and duration of drawdowns in prices from earlier highs. Using Ulcer Index instead of standard deviation can lead to very different conclusions about investment risk and risk-adjusted return, especially when evaluating strategies that seek to avoid major declines in portfolio value (market timing, dynamic asset allocation, hedge funds, etc.). The Ulcer Index was originally developed in 1987. Since then, it has been widely recognized and adopted by the investment community. According to Nelson Freeburg, editor of Formula Research, Ulcer Index is “perhaps the most fully realized statistical portrait of risk there is.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.57 ) in the period of the last 5 years, the Ulcer Index of 24 of Liberty Global is higher, thus worse.
- During the last 3 years, the Ulcer Ratio is 26 , which is higher, thus worse than the value of 10 from the benchmark.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -48.2 days of Liberty Global is lower, thus worse.
- Looking at maximum reduction from previous high in of -48.2 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-24.5 days).

'The Maximum Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Which means for our asset as example:- Compared with the benchmark SPY (439 days) in the period of the last 5 years, the maximum days below previous high of 505 days of Liberty Global is greater, thus worse.
- During the last 3 years, the maximum days under water is 505 days, which is higher, thus worse than the value of 439 days from the benchmark.

'The Average Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (106 days) in the period of the last 5 years, the average time in days below previous high water mark of 195 days of Liberty Global is greater, thus worse.
- During the last 3 years, the average days under water is 181 days, which is larger, thus worse than the value of 149 days from the benchmark.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of Liberty Global are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.