'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 over 5 years of T-Mobile is 119.8%, which is higher, thus better compared to the benchmark SPY (100.7%) in the same period.
- During the last 3 years, the total return is 18%, which is smaller, thus worse than the value of 33.2% 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:- Looking at the annual performance (CAGR) of 17.1% in the last 5 years of T-Mobile, we see it is relatively larger, thus better in comparison to the benchmark SPY (15%)
- Looking at annual performance (CAGR) in of 5.7% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (10%).

'Volatility is a rate at which the price of a security increases or decreases for a given set of returns. Volatility is measured by calculating the standard deviation of the annualized returns over a given period of time. It shows the range to which the price of a security may increase or decrease. Volatility measures the risk of a security. It is used in option pricing formula to gauge the fluctuations in the returns of the underlying assets. Volatility indicates the pricing behavior of the security and helps estimate the fluctuations that may happen in a short period of time.'

Using this definition on our asset we see for example:- The historical 30 days volatility over 5 years of T-Mobile is 27.4%, which is larger, thus worse compared to the benchmark SPY (20.9%) in the same period.
- During the last 3 years, the volatility is 22.5%, which is higher, thus worse than the value of 17.3% from the benchmark.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- Looking at the downside risk of 18.2% in the last 5 years of T-Mobile, we see it is relatively higher, thus worse in comparison to the benchmark SPY (15%)
- During the last 3 years, the downside volatility is 15.3%, which is higher, thus worse than the value of 12% from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of 0.53 of T-Mobile is smaller, thus worse.
- Compared with SPY (0.44) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.14 is smaller, thus worse.

'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.'

Which means for our asset as example:- The downside risk / excess return profile over 5 years of T-Mobile is 0.8, which is smaller, thus worse compared to the benchmark SPY (0.83) in the same period.
- Looking at excess return divided by the downside deviation in of 0.21 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.62).

'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 is 9.6 , which is larger, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Downside risk index in of 11 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (10 ).

'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 drop from peak to valley over 5 years of T-Mobile is -32 days, which is larger, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum drop from peak to valley is -32 days, which is lower, 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) in days.'

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 smaller, thus better in comparison to the benchmark SPY (488 days)
- Looking at maximum days below previous high in of 324 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (488 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:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average time in days below previous high water mark of 86 days of T-Mobile is lower, thus better.
- Looking at average days below previous high in of 119 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (180 days).

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.