'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Which means for our asset as example:- Compared with the benchmark SPY (66.2%) in the period of the last 5 years, the total return, or performance of 169.7% of Charter Communications is higher, thus better.
- During the last 3 years, the total return, or performance is 53.7%, which is larger, thus better than the value of 36.8% from the benchmark.

'The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.'

Using this definition on our asset we see for example:- Looking at the annual performance (CAGR) of 21.9% in the last 5 years of Charter Communications, we see it is relatively greater, thus better in comparison to the benchmark SPY (10.7%)
- Looking at annual performance (CAGR) in of 15.4% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (11%).

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Using this definition on our asset we see for example:- Looking at the volatility of 28.9% in the last 5 years of Charter Communications, we see it is relatively higher, thus worse in comparison to the benchmark SPY (19%)
- During the last 3 years, the 30 days standard deviation is 30.5%, which is greater, thus worse than the value of 22% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The downside volatility over 5 years of Charter Communications is 19.5%, which is greater, thus worse compared to the benchmark SPY (13.9%) in the same period.
- During the last 3 years, the downside volatility is 20.9%, which is greater, thus worse than the value of 16.1% from the benchmark.

'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.'

Which means for our asset as example:- The risk / return profile (Sharpe) over 5 years of Charter Communications is 0.67, which is larger, thus better compared to the benchmark SPY (0.43) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.42, which is higher, thus better than the value of 0.39 from the benchmark.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Using this definition on our asset we see for example:- Looking at the downside risk / excess return profile of 1 in the last 5 years of Charter Communications, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.59)
- During the last 3 years, the ratio of annual return and downside deviation is 0.62, which is higher, thus better than the value of 0.53 from the benchmark.

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Which means for our asset as example:- Compared with the benchmark SPY (5.9 ) in the period of the last 5 years, the Downside risk index of 13 of Charter Communications is higher, thus worse.
- During the last 3 years, the Downside risk index is 16 , which is higher, thus worse than the value of 6.98 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.'

Which means for our asset as example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -35.1 days of Charter Communications is lower, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -35.1 days, which is smaller, thus worse than the value of -33.7 days from the benchmark.

'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'

Which means for our asset as example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 461 days of Charter Communications is greater, thus worse.
- Looking at maximum days under water in of 461 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (139 days).

'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.'

Using this definition on our asset we see for example:- Looking at the average days under water of 107 days in the last 5 years of Charter Communications, we see it is relatively greater, thus worse in comparison to the benchmark SPY (44 days)
- During the last 3 years, the average time in days below previous high water mark is 157 days, which is larger, thus worse than the value of 41 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 Charter Communications 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.