'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.'

Which means for our asset as example:- The total return, or performance over 5 years of T-Mobile US is 180.9%, which is higher, thus better compared to the benchmark SPY (55.3%) in the same period.
- Compared with SPY (33%) in the period of the last 3 years, the total return of 46.7% is greater, 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (9.2%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 23% of T-Mobile US is larger, thus better.
- Looking at annual performance (CAGR) in of 13.6% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (10%).

'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 25.2%, which is greater, thus worse compared to the benchmark SPY (13.6%) in the same period.
- During the last 3 years, the historical 30 days volatility is 23.4%, which is greater, thus worse than the value of 13.5% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The downside risk over 5 years of T-Mobile US is 16.5%, which is greater, thus worse compared to the benchmark SPY (10%) in the same period.
- Compared with SPY (10.1%) in the period of the last 3 years, the downside deviation of 15.2% is greater, thus worse.

'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:- The ratio of return and volatility (Sharpe) over 5 years of T-Mobile US is 0.81, which is higher, thus better compared to the benchmark SPY (0.49) in the same period.
- During the last 3 years, the ratio of return and volatility (Sharpe) is 0.47, which is smaller, thus worse than the value of 0.55 from the benchmark.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.67) in the period of the last 5 years, the ratio of annual return and downside deviation of 1.24 of T-Mobile US is larger, thus better.
- Compared with SPY (0.74) in the period of the last 3 years, the excess return divided by the downside deviation of 0.73 is smaller, thus worse.

'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.'

Which means for our asset as example:- The Ulcer Index over 5 years of T-Mobile US is 7.31 , which is larger, thus worse compared to the benchmark SPY (4 ) in the same period.
- Looking at Downside risk index in of 7.66 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (4.14 ).

'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:- The maximum DrawDown over 5 years of T-Mobile US is -21.2 days, which is smaller, thus worse compared to the benchmark SPY (-19.3 days) in the same period.
- Compared with SPY (-19.3 days) in the period of the last 3 years, the maximum reduction from previous high of -19 days is greater, thus better.

'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.'

Which means for our asset as example:- The maximum days under water 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.
- Looking at maximum days below previous high in of 322 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (139 days).

'The Average 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. 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:- Looking at the average time in days below previous high water mark of 74 days in the last 5 years of T-Mobile US, we see it is relatively larger, thus worse in comparison to the benchmark SPY (42 days)
- During the last 3 years, the average days below previous high is 94 days, which is greater, thus worse than the value of 36 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 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.