'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:- The total return, or performance over 5 years of T-Mobile US is 131.8%, which is greater, thus better compared to the benchmark SPY (66.2%) in the same period.
- Compared with SPY (47.5%) in the period of the last 3 years, the total return of 91.8% is higher, thus better.

'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.'

Which means for our asset as example:- The annual performance (CAGR) over 5 years of T-Mobile US is 18.3%, which is greater, thus better compared to the benchmark SPY (10.7%) in the same period.
- Compared with SPY (13.9%) in the period of the last 3 years, the annual return (CAGR) of 24.3% is greater, thus better.

'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:- Compared with the benchmark SPY (13.3%) in the period of the last 5 years, the 30 days standard deviation of 25.8% of T-Mobile US is greater, thus worse.
- During the last 3 years, the volatility is 23.9%, which is higher, thus worse than the value of 12.5% 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.'

Applying this definition to our asset in some examples:- The downside volatility over 5 years of T-Mobile US is 26.7%, which is larger, thus worse compared to the benchmark SPY (14.6%) in the same period.
- Looking at downside risk in of 23.9% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (14.2%).

'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.'

Using this definition on our asset we see for example:- The Sharpe Ratio over 5 years of T-Mobile US is 0.61, which is smaller, thus worse compared to the benchmark SPY (0.62) in the same period.
- During the last 3 years, the risk / return profile (Sharpe) is 0.91, which is greater, thus better than the value of 0.91 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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.56) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.59 of T-Mobile US is larger, thus better.
- Compared with SPY (0.8) in the period of the last 3 years, the downside risk / excess return profile of 0.92 is higher, thus better.

'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.'

Using this definition on our asset we see for example:- The Downside risk index over 5 years of T-Mobile US is 9.27 , which is larger, thus better compared to the benchmark SPY (3.96 ) in the same period.
- Compared with SPY (4.01 ) in the period of the last 3 years, the Ulcer Ratio of 7.19 is higher, 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.'

Using this definition on our asset we see for example:- The maximum DrawDown over 5 years of T-Mobile US is -29.5 days, which is lower, thus worse compared to the benchmark SPY (-19.3 days) in the same period.
- Looking at maximum reduction from previous high in of -19 days in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (-19.3 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'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum days under water of 322 days of T-Mobile US is larger, thus worse.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 322 days is higher, 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.'

Which means for our asset as example:- The average days under water over 5 years of T-Mobile US is 90 days, which is larger, thus worse compared to the benchmark SPY (41 days) in the same period.
- During the last 3 years, the average time in days below previous high water mark is 87 days, which is larger, thus worse than the value of 36 days from the benchmark.

Historical returns have been extended using synthetic data.
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- "Year" returns in the table above are not equal to the sum of monthly returns due to compounding.
- Performance results of T-Mobile US 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.