'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:- Compared with the benchmark SPY (66.2%) in the period of the last 5 years, the total return, or increase in value of 121.1% of T-Mobile US is greater, thus better.
- Looking at total return, or increase in value in of 95.4% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (45.7%).

'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.'

Applying this definition to our asset in some examples:- Looking at the annual return (CAGR) of 17.2% in the last 5 years of T-Mobile US, we see it is relatively larger, thus better in comparison to the benchmark SPY (10.7%)
- Compared with SPY (13.4%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 25.1% is larger, thus better.

'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.'

Applying this definition to our asset in some examples:- The 30 days standard deviation over 5 years of T-Mobile US is 26.3%, which is higher, thus worse compared to the benchmark SPY (13.3%) in the same period.
- Compared with SPY (12.5%) in the period of the last 3 years, the historical 30 days volatility of 23.8% is higher, thus worse.

'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:- Compared with the benchmark SPY (14.6%) in the period of the last 5 years, the downside deviation of 27.1% of T-Mobile US is larger, thus worse.
- Compared with SPY (14.1%) in the period of the last 3 years, the downside deviation of 23.6% is greater, thus worse.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Which means for our asset as example:- The Sharpe Ratio over 5 years of T-Mobile US is 0.56, which is lower, thus worse compared to the benchmark SPY (0.62) in the same period.
- Looking at risk / return profile (Sharpe) in of 0.95 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.87).

'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:- The ratio of annual return and downside deviation over 5 years of T-Mobile US is 0.54, which is lower, thus worse compared to the benchmark SPY (0.56) in the same period.
- Looking at ratio of annual return and downside deviation in of 0.96 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.77).

'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 Index over 5 years of T-Mobile US is 9.35 , which is larger, thus better compared to the benchmark SPY (3.96 ) in the same period.
- During the last 3 years, the Ulcer Index is 7.18 , which is larger, thus better than the value of 4.01 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:- Looking at the maximum DrawDown of -29.5 days in the last 5 years of T-Mobile US, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-19.3 days)
- Compared with SPY (-19.3 days) in the period of the last 3 years, the maximum reduction from previous high of -19 days is larger, thus better.

'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'

Which means for our asset as example:- Compared with the benchmark SPY (187 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 322 days of T-Mobile US is larger, thus worse.
- Looking at maximum time in days below previous high water mark in of 322 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (131 days).

'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:- Looking at the average time in days below previous high water mark of 90 days in the last 5 years of T-Mobile US, we see it is relatively higher, thus worse in comparison to the benchmark SPY (39 days)
- Looking at average days under water in of 88 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (34 days).

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.