'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.'

Which means for our asset as example:- Looking at the total return, or performance of 71.2% in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (121.2%)
- Looking at total return, or increase in value in of 4% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (67.5%).

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Which means for our asset as example:- Compared with the benchmark SPY (17.2%) in the period of the last 5 years, the annual performance (CAGR) of 11.4% of Sirius XM is lower, thus worse.
- Compared with SPY (18.7%) in the period of the last 3 years, the annual return (CAGR) of 1.3% is smaller, thus worse.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (18.7%) in the period of the last 5 years, the volatility of 28.2% of Sirius XM is greater, thus worse.
- Looking at 30 days standard deviation in of 32.3% in the period of the last 3 years, we see it is relatively larger, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (13.6%) in the period of the last 5 years, the downside volatility of 20.5% of Sirius XM is greater, thus worse.
- Compared with SPY (16.3%) in the period of the last 3 years, the downside risk of 24.1% is higher, thus worse.

'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:- Looking at the ratio of return and volatility (Sharpe) of 0.31 in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.79)
- During the last 3 years, the ratio of return and volatility (Sharpe) is -0.04, which is smaller, thus worse than the value of 0.72 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:- The excess return divided by the downside deviation over 5 years of Sirius XM is 0.43, which is smaller, thus worse compared to the benchmark SPY (1.08) in the same period.
- Compared with SPY (1) in the period of the last 3 years, the excess return divided by the downside deviation of -0.05 is lower, 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.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Index of 15 in the last 5 years of Sirius XM, we see it is relatively higher, thus worse in comparison to the benchmark SPY (5.59 )
- Compared with SPY (6.83 ) in the period of the last 3 years, the Downside risk index of 19 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.'

Applying this definition to our asset in some examples:- Looking at the maximum reduction from previous high of -41.1 days in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum drop from peak to valley is -41.1 days, which is smaller, thus worse than the value of -33.7 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'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum days below previous high of 707 days of Sirius XM is higher, thus worse.
- Looking at maximum days under water in of 707 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (139 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:- The average days below previous high over 5 years of Sirius XM is 224 days, which is higher, thus worse compared to the benchmark SPY (33 days) in the same period.
- Looking at average time in days below previous high water mark in of 341 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (35 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 Sirius XM 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.