'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (121.2%) in the period of the last 5 years, the total return of 233.4% of T-Mobile is larger, thus better.
- Compared with SPY (67.5%) in the period of the last 3 years, the total return of 116.3% is larger, thus better.

'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.'

Using this definition on our asset we see for example:- The compounded annual growth rate (CAGR) over 5 years of T-Mobile is 27.3%, which is higher, thus better compared to the benchmark SPY (17.2%) in the same period.
- During the last 3 years, the annual return (CAGR) is 29.3%, which is higher, thus better than the value of 18.7% 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.'

Using this definition on our asset we see for example:- The 30 days standard deviation over 5 years of T-Mobile is 28%, which is higher, thus worse compared to the benchmark SPY (18.7%) in the same period.
- Looking at volatility in of 30.5% in the period of the last 3 years, we see it is relatively greater, 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:- Compared with the benchmark SPY (13.6%) in the period of the last 5 years, the downside volatility of 18.4% of T-Mobile is larger, thus worse.
- Looking at downside volatility in of 20% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (16.3%).

'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:- Compared with the benchmark SPY (0.79) in the period of the last 5 years, the Sharpe Ratio of 0.89 of T-Mobile is greater, thus better.
- During the last 3 years, the risk / return profile (Sharpe) is 0.88, which is higher, thus better than the value of 0.72 from the benchmark.

'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 downside risk / excess return profile of 1.34 in the last 5 years of T-Mobile, we see it is relatively higher, thus better in comparison to the benchmark SPY (1.08)
- During the last 3 years, the downside risk / excess return profile is 1.34, which is higher, thus better than the value of 1 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (5.59 ) in the period of the last 5 years, the Ulcer Index of 7.11 of T-Mobile is higher, thus worse.
- Compared with SPY (6.83 ) in the period of the last 3 years, the Ulcer Ratio of 6.65 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum drop from peak to valley of -26 days of T-Mobile is larger, thus better.
- 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 Maximum Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum days under water of 322 days of T-Mobile is higher, thus worse.
- Compared with SPY (139 days) in the period of the last 3 years, the maximum days under water of 134 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (33 days) in the period of the last 5 years, the average days under water of 65 days of T-Mobile is larger, thus worse.
- Compared with SPY (35 days) in the period of the last 3 years, the average days below previous high of 32 days is lower, 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 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.