'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (66.2%) in the period of the last 5 years, the total return, or performance of 79.8% of Sirius XM is greater, thus better.
- During the last 3 years, the total return, or increase in value is 51.5%, which is higher, thus better than the value of 45.7% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the compounded annual growth rate (CAGR) of 12.5% in the last 5 years of Sirius XM, we see it is relatively higher, thus better in comparison to the benchmark SPY (10.7%)
- Looking at annual performance (CAGR) in of 14.9% in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (13.4%).

'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.'

Which means for our asset as example:- The volatility over 5 years of Sirius XM is 21.4%, which is higher, thus worse compared to the benchmark SPY (13.3%) in the same period.
- During the last 3 years, the 30 days standard deviation is 22.6%, which is larger, thus worse than the value of 12.5% from the benchmark.

'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 risk over 5 years of Sirius XM is 23.5%, which is greater, thus worse compared to the benchmark SPY (14.6%) in the same period.
- Looking at downside volatility in of 25% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (14.1%).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (0.62) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.47 of Sirius XM is smaller, thus worse.
- Looking at risk / return profile (Sharpe) in of 0.55 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.87).

'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.'

Applying this definition to our asset in some examples:- Looking at the excess return divided by the downside deviation of 0.42 in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.56)
- Compared with SPY (0.77) in the period of the last 3 years, the downside risk / excess return profile of 0.5 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.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Index of 8.32 in the last 5 years of Sirius XM, we see it is relatively greater, thus better in comparison to the benchmark SPY (3.96 )
- Looking at Ulcer Ratio in of 9.62 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (4.01 ).

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (-19.3 days) in the period of the last 5 years, the maximum reduction from previous high of -27.6 days of Sirius XM is lower, thus worse.
- Looking at maximum reduction from previous high in of -27.6 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-19.3 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). 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 (187 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 192 days of Sirius XM is larger, thus worse.
- During the last 3 years, the maximum time in days below previous high water mark is 192 days, which is higher, thus worse than the value of 131 days from the benchmark.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (39 days) in the period of the last 5 years, the average days under water of 56 days of Sirius XM is higher, thus worse.
- During the last 3 years, the average time in days below previous high water mark is 49 days, which is larger, thus worse than the value of 34 days from the benchmark.

Historical returns have been extended using synthetic data.
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- "Year" returns in the table above are not equal to 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.