'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.'

Which means for our asset as example:- Compared with the benchmark SPY (78.4%) in the period of the last 5 years, the total return of 89.9% of T-Mobile is higher, thus better.
- During the last 3 years, the total return, or performance is 61%, which is larger, thus better than the value of 44.1% 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.'

Applying this definition to our asset in some examples:- The compounded annual growth rate (CAGR) over 5 years of T-Mobile is 13.7%, which is greater, thus better compared to the benchmark SPY (12.3%) in the same period.
- Compared with SPY (12.9%) in the period of the last 3 years, the annual performance (CAGR) of 17.2% is higher, 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:- The 30 days standard deviation over 5 years of T-Mobile is 28.5%, which is larger, thus worse compared to the benchmark SPY (19.9%) in the same period.
- Compared with SPY (23.1%) in the period of the last 3 years, the historical 30 days volatility of 31.4% is higher, 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.'

Applying this definition to our asset in some examples:- The downside volatility over 5 years of T-Mobile is 19%, which is greater, thus worse compared to the benchmark SPY (14.6%) in the same period.
- Compared with SPY (16.9%) in the period of the last 3 years, the downside risk of 20.8% is higher, 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:- Looking at the risk / return profile (Sharpe) of 0.39 in the last 5 years of T-Mobile, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.49)
- Compared with SPY (0.45) in the period of the last 3 years, the Sharpe Ratio of 0.47 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.'

Using this definition on our asset we see for example:- Looking at the downside risk / excess return profile of 0.59 in the last 5 years of T-Mobile, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.67)
- During the last 3 years, the excess return divided by the downside deviation is 0.71, which is larger, thus better than the value of 0.62 from the benchmark.

'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:- The Ulcer Ratio over 5 years of T-Mobile is 10 , which is higher, thus worse compared to the benchmark SPY (6.16 ) in the same period.
- Compared with SPY (6.87 ) in the period of the last 3 years, the Ulcer Index of 11 is higher, thus worse.

'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.'

Which means for our asset as example:- Looking at the maximum drop from peak to valley of -32 days in the last 5 years of T-Mobile, we see it is relatively higher, thus better in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum reduction from previous high of -32 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) in days.'

Applying this definition to our asset in some examples:- Looking at the maximum time in days below previous high water mark of 322 days in the last 5 years of T-Mobile, we see it is relatively higher, thus worse in comparison to the benchmark SPY (139 days)
- Looking at maximum time in days below previous high water mark in of 214 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (119 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 81 days in the last 5 years of T-Mobile, we see it is relatively larger, thus worse in comparison to the benchmark SPY (35 days)
- During the last 3 years, the average days under water is 56 days, which is higher, thus worse than the value of 27 days from the benchmark.

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 T-Mobile 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.