'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Applying this definition to our asset in some examples:- Looking at the total return of 39.9% in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (88%)
- During the last 3 years, the total return is -5.4%, which is smaller, thus worse than the value of 39.5% 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:- The annual return (CAGR) over 5 years of Sirius XM is 6.9%, which is smaller, thus worse compared to the benchmark SPY (13.5%) in the same period.
- Compared with SPY (11.7%) in the period of the last 3 years, the annual performance (CAGR) of -1.8% is smaller, thus worse.

'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:- Looking at the volatility of 27% in the last 5 years of Sirius XM, we see it is relatively greater, thus worse in comparison to the benchmark SPY (18.8%)
- Compared with SPY (22.3%) in the period of the last 3 years, the historical 30 days volatility of 30.8% is larger, thus worse.

'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 Sirius XM is 20%, which is larger, thus worse compared to the benchmark SPY (13.7%) in the same period.
- Looking at downside risk in of 23.3% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (16.5%).

'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 Sharpe Ratio over 5 years of Sirius XM is 0.16, which is lower, thus worse compared to the benchmark SPY (0.58) in the same period.
- Compared with SPY (0.41) in the period of the last 3 years, the ratio of return and volatility (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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.8) in the period of the last 5 years, the downside risk / excess return profile of 0.22 of Sirius XM is lower, thus worse.
- Looking at downside risk / excess return profile in of -0.19 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.56).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (5.79 ) in the period of the last 5 years, the Ulcer Ratio of 14 of Sirius XM is higher, thus worse.
- Compared with SPY (7.08 ) in the period of the last 3 years, the Downside risk index of 18 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.'

Which means for our asset as example:- The maximum reduction from previous high over 5 years of Sirius XM is -41.1 days, which is smaller, thus worse 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 -41.1 days, which is lower, 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'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum days under water of 573 days of Sirius XM is greater, thus worse.
- During the last 3 years, the maximum days below previous high is 573 days, which is larger, thus worse than the value of 139 days from the benchmark.

'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.'

Which means for our asset as example:- Looking at the average days under water of 162 days in the last 5 years of Sirius XM, we see it is relatively greater, thus worse in comparison to the benchmark SPY (37 days)
- Compared with SPY (45 days) in the period of the last 3 years, the average time in days below previous high water mark of 232 days is greater, thus worse.

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.