'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (67.9%) in the period of the last 5 years, the total return, or increase in value of 157.1% of T-Mobile US is larger, thus better.
- During the last 3 years, the total return is 48%, which is higher, thus better than the value of 38.6% from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (10.9%) in the period of the last 5 years, the annual return (CAGR) of 20.8% of T-Mobile US is greater, thus better.
- Compared with SPY (11.5%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 13.9% 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the volatility of 28.7% of T-Mobile US is greater, thus worse.
- Compared with SPY (21.5%) in the period of the last 3 years, the 30 days standard deviation of 29.7% is greater, thus worse.

'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.'

Which means for our asset as example:- The downside volatility over 5 years of T-Mobile US is 19.3%, which is greater, thus worse compared to the benchmark SPY (13.6%) in the same period.
- Looking at downside deviation in of 19.8% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (15.7%).

'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 0.64 in the last 5 years of T-Mobile US, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.45)
- Looking at ratio of return and volatility (Sharpe) in of 0.39 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.42).

'The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk.'

Which means for our asset as example:- Looking at the ratio of annual return and downside deviation of 0.95 in the last 5 years of T-Mobile US, we see it is relatively higher, thus better in comparison to the benchmark SPY (0.62)
- Looking at ratio of annual return and downside deviation in of 0.58 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.57).

'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 7.93 , which is higher, thus worse compared to the benchmark SPY (5.82 ) in the same period.
- Looking at Downside risk index in of 8.62 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (6.87 ).

'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:- The maximum reduction from previous high over 5 years of T-Mobile US is -26 days, which is larger, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum reduction from previous high is -26 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 below previous high over 5 years of T-Mobile US is 322 days, which is greater, thus worse compared to the benchmark SPY (187 days) in the same period.
- During the last 3 years, the maximum days under water is 322 days, which is higher, thus worse than the value of 139 days from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (43 days) in the period of the last 5 years, the average time in days below previous high water mark of 74 days of T-Mobile US is higher, thus worse.
- Compared with SPY (39 days) in the period of the last 3 years, the average days below previous high of 94 days is higher, thus worse.

Historical returns have been extended using synthetic data.
[Show Details]

- Note that yearly returns do not equal 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.