'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.'

Using this definition on our asset we see for example:- The total return over 5 years of Charter Communications is -16.2%, which is smaller, thus worse compared to the benchmark SPY (109.2%) in the same period.
- Looking at total return in of -43.4% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (33.3%).

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Which means for our asset as example:- Looking at the annual performance (CAGR) of -3.5% in the last 5 years of Charter Communications, we see it is relatively lower, thus worse in comparison to the benchmark SPY (15.9%)
- Compared with SPY (10.1%) in the period of the last 3 years, the annual return (CAGR) of -17.3% 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.'

Which means for our asset as example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the historical 30 days volatility of 34.6% of Charter Communications is higher, thus worse.
- Looking at volatility in of 37.6% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (17.6%).

'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 volatility over 5 years of Charter Communications is 25%, which is larger, thus worse compared to the benchmark SPY (14.9%) in the same period.
- During the last 3 years, the downside risk is 27.4%, which is higher, thus worse than the value of 12.3% from the benchmark.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Which means for our asset as example:- Looking at the Sharpe Ratio of -0.17 in the last 5 years of Charter Communications, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.64)
- Compared with SPY (0.43) in the period of the last 3 years, the Sharpe Ratio of -0.53 is lower, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.9) in the period of the last 5 years, the downside risk / excess return profile of -0.24 of Charter Communications is lower, thus worse.
- Compared with SPY (0.62) in the period of the last 3 years, the excess return divided by the downside deviation of -0.72 is lower, 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:- Looking at the Ulcer Ratio of 41 in the last 5 years of Charter Communications, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.32 )
- During the last 3 years, the Downside risk index is 45 , which is larger, thus worse than the value of 10 from the benchmark.

'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.'

Using this definition on our asset we see for example:- The maximum DrawDown over 5 years of Charter Communications is -69 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -63.7 days is smaller, thus worse.

'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.'

Which means for our asset as example:- Looking at the maximum days under water of 801 days in the last 5 years of Charter Communications, we see it is relatively higher, thus worse in comparison to the benchmark SPY (488 days)
- During the last 3 years, the maximum days below previous high is 753 days, which is higher, 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.'

Which means for our asset as example:- Looking at the average time in days below previous high water mark of 281 days in the last 5 years of Charter Communications, we see it is relatively greater, thus worse in comparison to the benchmark SPY (123 days)
- Compared with SPY (176 days) in the period of the last 3 years, the average days below previous high of 377 days is higher, thus worse.

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.