'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.'

Applying this definition to our asset in some examples:- Looking at the total return of 203.7% in the last 5 years of Charter Communications, we see it is relatively higher, thus better in comparison to the benchmark SPY (122.1%)
- During the last 3 years, the total return, or performance is 152.3%, which is higher, thus better than the value of 64.6% 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:- Compared with the benchmark SPY (17.3%) in the period of the last 5 years, the annual performance (CAGR) of 24.9% of Charter Communications is higher, thus better.
- During the last 3 years, the compounded annual growth rate (CAGR) is 36.2%, which is larger, thus better than the value of 18.1% from the benchmark.

'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.'

Which means for our asset as example:- The historical 30 days volatility over 5 years of Charter Communications is 28.2%, which is larger, thus worse compared to the benchmark SPY (18.7%) in the same period.
- Looking at 30 days standard deviation in of 28.9% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (22.5%).

'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 18.9%, which is larger, thus worse compared to the benchmark SPY (13.6%) in the same period.
- Compared with SPY (16.4%) in the period of the last 3 years, the downside volatility of 19.1% is higher, thus worse.

'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.'

Using this definition on our asset we see for example:- The ratio of return and volatility (Sharpe) over 5 years of Charter Communications is 0.8, which is larger, thus better compared to the benchmark SPY (0.79) in the same period.
- Compared with SPY (0.69) in the period of the last 3 years, the risk / return profile (Sharpe) of 1.17 is greater, thus better.

'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:- The excess return divided by the downside deviation over 5 years of Charter Communications is 1.19, which is greater, thus better compared to the benchmark SPY (1.09) in the same period.
- Looking at downside risk / excess return profile in of 1.77 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.95).

'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:- Looking at the Ulcer Ratio of 13 in the last 5 years of Charter Communications, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.58 )
- Compared with SPY (6.83 ) in the period of the last 3 years, the Ulcer Ratio of 6.23 is lower, thus better.

'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.'

Applying this definition to our asset in some examples:- Looking at the maximum reduction from previous high of -35.1 days in the last 5 years of Charter Communications, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum DrawDown is -31.5 days, which is greater, thus better 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'

Applying this definition to our asset in some examples:- The maximum days under water over 5 years of Charter Communications is 461 days, which is greater, thus worse compared to the benchmark SPY (139 days) in the same period.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 103 days is smaller, thus better.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (33 days) in the period of the last 5 years, the average days below previous high of 106 days of Charter Communications is higher, thus worse.
- Compared with SPY (35 days) in the period of the last 3 years, the average days below previous high of 24 days is smaller, thus better.

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.