'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.'

Which means for our asset as example:- Compared with the benchmark SPY (100.7%) in the period of the last 5 years, the total return, or increase in value of -29.3% of Charter Communications is lower, thus worse.
- During the last 3 years, the total return, or performance is -60.3%, which is smaller, thus worse than the value of 33.2% 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.'

Which means for our asset as example:- Looking at the annual return (CAGR) of -6.7% in the last 5 years of Charter Communications, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (15%)
- Looking at annual performance (CAGR) in of -26.5% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (10%).

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Which means for our asset as example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the 30 days standard deviation of 32.5% of Charter Communications is greater, thus worse.
- During the last 3 years, the historical 30 days volatility is 34.5%, which is greater, thus worse than the value of 17.3% from the benchmark.

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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 deviation over 5 years of Charter Communications is 24.5%, which is larger, thus worse compared to the benchmark SPY (15%) in the same period.
- Looking at downside volatility in of 27% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12%).

'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:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the risk / return profile (Sharpe) of -0.28 of Charter Communications is lower, thus worse.
- Looking at risk / return profile (Sharpe) in of -0.84 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.44).

'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 excess return divided by the downside deviation of -0.38 in the last 5 years of Charter Communications, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.83)
- During the last 3 years, the ratio of annual return and downside deviation is -1.07, which is lower, thus worse than the value of 0.62 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:- The Ulcer Ratio over 5 years of Charter Communications is 36 , which is greater, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- During the last 3 years, the Ulcer Index is 46 , which is larger, 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.'

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 -69 days of Charter Communications is smaller, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -69 days, which is lower, thus worse than the value of -24.5 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) in days.'

Applying this definition to our asset in some examples:- Looking at the maximum days under water of 680 days in the last 5 years of Charter Communications, we see it is relatively larger, thus worse in comparison to the benchmark SPY (488 days)
- During the last 3 years, the maximum time in days below previous high water mark is 680 days, which is greater, thus worse than the value of 488 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:- The average time in days below previous high water mark over 5 years of Charter Communications is 210 days, which is greater, thus worse compared to the benchmark SPY (123 days) in the same period.
- Looking at average days under water in of 317 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (180 days).

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 and do not account for slippage, fees or taxes.