'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 increase in value of -58.2% in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (109.2%)
- Compared with SPY (33.3%) in the period of the last 3 years, the total return, or increase in value of -56.2% is lower, thus worse.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Applying this definition to our asset in some examples:- The annual return (CAGR) over 5 years of Sirius XM is -16%, which is lower, thus worse compared to the benchmark SPY (15.9%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is -24.1%, which is lower, thus worse than the value of 10.1% 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.'

Applying this definition to our asset in some examples:- Looking at the historical 30 days volatility of 44.3% in the last 5 years of Sirius XM, we see it is relatively greater, thus worse in comparison to the benchmark SPY (20.9%)
- Looking at historical 30 days volatility in of 49.1% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (17.6%).

'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 Sirius XM is 29.4%, which is higher, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Compared with SPY (12.3%) in the period of the last 3 years, the downside risk of 31.5% is greater, 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:- The ratio of return and volatility (Sharpe) over 5 years of Sirius XM is -0.42, which is lower, thus worse compared to the benchmark SPY (0.64) in the same period.
- Looking at ratio of return and volatility (Sharpe) in of -0.54 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.43).

'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.'

Applying this definition to our asset in some examples:- The excess return divided by the downside deviation over 5 years of Sirius XM is -0.63, which is lower, thus worse compared to the benchmark SPY (0.9) in the same period.
- During the last 3 years, the excess return divided by the downside deviation is -0.84, which is lower, thus worse than the value of 0.62 from the benchmark.

'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:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Downside risk index of 32 of Sirius XM is greater, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 38 is greater, thus worse.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -70.5 days of Sirius XM is lower, thus worse.
- Looking at maximum DrawDown in of -70.5 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 858 days of Sirius XM is larger, thus worse.
- Looking at maximum days under water in of 330 days in the period of the last 3 years, we see it is relatively lower, 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:- The average days under water over 5 years of Sirius XM is 341 days, which is larger, thus worse compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (176 days) in the period of the last 3 years, the average days under water of 118 days is smaller, 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 Sirius XM are hypothetical and do not account for slippage, fees or taxes.