'Total return is the amount of value an investor earns from a security over a specific period, typically one year, when all distributions are reinvested. Total return is expressed as a percentage of the amount invested. For example, a total return of 20% means the security increased by 20% of its original value due to a price increase, distribution of dividends (if a stock), coupons (if a bond) or capital gains (if a fund). Total return is a strong measure of an investment’s overall performance.'

Using this definition on our asset we see for example:- The total return, or increase in value over 5 years of T-Mobile is 152%, which is larger, thus better compared to the benchmark SPY (95.5%) in the same period.
- Compared with SPY (25.3%) in the period of the last 3 years, the total return, or performance of 37.8% is higher, 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.'

Which means for our asset as example:- Looking at the compounded annual growth rate (CAGR) of 20.3% in the last 5 years of T-Mobile, we see it is relatively higher, thus better in comparison to the benchmark SPY (14.4%)
- During the last 3 years, the annual performance (CAGR) is 11.3%, which is greater, thus better than the value of 7.8% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The 30 days standard deviation over 5 years of T-Mobile is 27.1%, which is larger, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Looking at volatility in of 22.7% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (17.5%).

'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.'

Which means for our asset as example:- The downside deviation over 5 years of T-Mobile is 18%, which is larger, thus worse compared to the benchmark SPY (15%) in the same period.
- Looking at downside deviation in of 15.2% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (12.3%).

'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 (0.57) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.66 of T-Mobile is larger, thus better.
- Compared with SPY (0.3) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.39 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.'

Applying this definition to our asset in some examples:- Looking at the downside risk / excess return profile of 0.99 in the last 5 years of T-Mobile, we see it is relatively higher, thus better in comparison to the benchmark SPY (0.79)
- Looking at downside risk / excess return profile in of 0.58 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.43).

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Using this definition on our asset we see for example:- Looking at the Downside risk index of 9.45 in the last 5 years of T-Mobile, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.32 )
- During the last 3 years, the Ulcer Index is 9.78 , which is smaller, thus better than the value of 10 from the benchmark.

'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:- Looking at the maximum reduction from previous high of -32 days in the last 5 years of T-Mobile, we see it is relatively larger, thus better in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -29.9 days, which is smaller, thus worse than the value of -24.5 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'

Using this definition on our asset we see for example:- Looking at the maximum days below previous high of 324 days in the last 5 years of T-Mobile, we see it is relatively lower, thus better in comparison to the benchmark SPY (488 days)
- Looking at maximum days below previous high in of 249 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (488 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.'

Which means for our asset as example:- The average days under water over 5 years of T-Mobile is 82 days, which is lower, thus better compared to the benchmark SPY (123 days) in the same period.
- During the last 3 years, the average days under water is 92 days, which is lower, thus better than the value of 179 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 and do not account for slippage, fees or taxes.