'The total return on a portfolio of investments takes into account not only the capital appreciation on the portfolio, but also the income received on the portfolio. The income typically consists of interest, dividends, and securities lending fees. This contrasts with the price return, which takes into account only the capital gain on an investment.'

Using this definition on our asset we see for example:- The total return, or performance over 5 years of Liberty Global is -21.6%, which is lower, thus worse compared to the benchmark SPY (81.9%) in the same period.
- During the last 3 years, the total return, or increase in value is -9.9%, which is lower, thus worse than the value of 46.1% 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (12.7%) in the period of the last 5 years, the annual performance (CAGR) of -4.8% of Liberty Global is lower, thus worse.
- During the last 3 years, the annual return (CAGR) is -3.4%, which is smaller, thus worse than the value of 13.5% from the benchmark.

'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.'

Which means for our asset as example:- Looking at the historical 30 days volatility of 32.8% in the last 5 years of Liberty Global, we see it is relatively greater, thus worse in comparison to the benchmark SPY (19.8%)
- Looking at historical 30 days volatility in of 34.5% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (23%).

'Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Applying this definition to our asset in some examples:- The downside volatility over 5 years of Liberty Global is 22.7%, which is larger, thus worse compared to the benchmark SPY (14.5%) in the same period.
- Compared with SPY (16.8%) in the period of the last 3 years, the downside risk of 23.4% is larger, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the ratio of return and volatility (Sharpe) of -0.22 in the last 5 years of Liberty Global, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.52)
- Compared with SPY (0.48) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.17 is smaller, thus worse.

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Which means for our asset as example:- Compared with the benchmark SPY (0.7) in the period of the last 5 years, the ratio of annual return and downside deviation of -0.32 of Liberty Global is lower, thus worse.
- Compared with SPY (0.65) in the period of the last 3 years, the downside risk / excess return profile of -0.25 is smaller, thus worse.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Using this definition on our asset we see for example:- The Ulcer Ratio over 5 years of Liberty Global is 32 , which is greater, thus worse compared to the benchmark SPY (6.08 ) in the same period.
- Compared with SPY (6.77 ) in the period of the last 3 years, the Downside risk index of 18 is higher, thus worse.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Applying this definition to our asset in some examples:- Looking at the maximum reduction from previous high of -59.5 days in the last 5 years of Liberty Global, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum drop from peak to valley in of -45.1 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-33.7 days).

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. The Max Drawdown Duration is the worst (the maximum/longest) amount of time an investment has seen between peaks (equity highs). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Using this definition on our asset we see for example:- Looking at the maximum days below previous high of 1078 days in the last 5 years of Liberty Global, we see it is relatively greater, thus worse in comparison to the benchmark SPY (139 days)
- Compared with SPY (119 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 448 days is larger, thus worse.

'The Drawdown Duration is the length of any peak to peak period, or the time between new equity highs. 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.'

Using this definition on our asset we see for example:- Looking at the average time in days below previous high water mark of 478 days in the last 5 years of Liberty Global, we see it is relatively larger, thus worse in comparison to the benchmark SPY (35 days)
- During the last 3 years, the average days under water is 156 days, which is greater, thus worse than the value of 27 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.