'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.'

Which means for our asset as example:- Looking at the total return, or performance of -10.5% in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (63%)
- Compared with SPY (33.5%) in the period of the last 3 years, the total return, or performance of -24.9% is smaller, thus worse.

'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 return (CAGR) of -2.2% in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (10.3%)
- Looking at compounded annual growth rate (CAGR) in of -9.1% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (10.1%).

'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.'

Applying this definition to our asset in some examples:- The 30 days standard deviation over 5 years of Sirius XM is 29.5%, which is larger, thus worse compared to the benchmark SPY (21.6%) in the same period.
- Compared with SPY (25.1%) in the period of the last 3 years, the historical 30 days volatility of 33.1% is larger, thus worse.

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

Using this definition on our asset we see for example:- Compared with the benchmark SPY (15.6%) in the period of the last 5 years, the downside volatility of 21.9% of Sirius XM is larger, thus worse.
- Compared with SPY (18.1%) in the period of the last 3 years, the downside deviation of 24.4% 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.'

Using this definition on our asset we see for example:- The Sharpe Ratio over 5 years of Sirius XM is -0.16, which is smaller, thus worse compared to the benchmark SPY (0.36) in the same period.
- Looking at Sharpe Ratio in of -0.35 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.3).

'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:- Looking at the downside risk / excess return profile of -0.21 in the last 5 years of Sirius XM, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.5)
- Compared with SPY (0.42) in the period of the last 3 years, the excess return divided by the downside deviation of -0.47 is lower, thus worse.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (8.88 ) in the period of the last 5 years, the Downside risk index of 18 of Sirius XM is larger, thus worse.
- During the last 3 years, the Downside risk index is 17 , which is greater, thus worse than the value of 11 from the benchmark.

'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.'

Which means for our asset as example:- 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 smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum drop from peak to valley in of -39.5 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-33.7 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.'

Using this definition on our asset we see for example:- Looking at the maximum days under water of 1166 days in the last 5 years of Sirius XM, we see it is relatively higher, thus worse in comparison to the benchmark SPY (273 days)
- Looking at maximum days under water in of 745 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (273 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.'

Applying this definition to our asset in some examples:- The average days under water over 5 years of Sirius XM is 552 days, which is larger, thus worse compared to the benchmark SPY (57 days) in the same period.
- Looking at average days below previous high in of 370 days in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (73 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.