'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.'

Using this definition on our asset we see for example:- The total return, or performance over 5 years of Sirius XM is -43.4%, which is lower, thus worse compared to the benchmark SPY (94.9%) in the same period.
- Compared with SPY (22.5%) in the period of the last 3 years, the total return, or performance of -47.8% 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.'

Which means for our asset as example:- The annual performance (CAGR) over 5 years of Sirius XM is -10.8%, which is smaller, thus worse compared to the benchmark SPY (14.3%) in the same period.
- Compared with SPY (7%) in the period of the last 3 years, the annual performance (CAGR) of -19.5% is lower, thus worse.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the 30 days standard deviation of 42.9% of Sirius XM is higher, thus worse.
- Compared with SPY (17.5%) in the period of the last 3 years, the historical 30 days volatility of 47.1% is greater, thus worse.

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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.'

Applying this definition to our asset in some examples:- The downside risk over 5 years of Sirius XM is 28.1%, which is greater, thus worse compared to the benchmark SPY (15%) in the same period.
- Looking at downside volatility in of 29.6% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.3%).

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.56) in the period of the last 5 years, the ratio of return and volatility (Sharpe) of -0.31 of Sirius XM is smaller, thus worse.
- Compared with SPY (0.26) in the period of the last 3 years, the risk / return profile (Sharpe) of -0.47 is lower, thus worse.

'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.'

Which means for our asset as example:- Looking at the ratio of annual return and downside deviation of -0.47 in the last 5 years of Sirius XM, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.79)
- Looking at ratio of annual return and downside deviation in of -0.75 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.37).

'The Ulcer Index is a technical indicator that measures downside risk, in terms of both the depth and duration of price declines. The index increases in value as the price moves farther away from a recent high and falls as the price rises to new highs. The indicator is usually calculated over a 14-day period, with the Ulcer Index showing the percentage drawdown a trader can expect from the high over that period. The greater the value of the Ulcer Index, the longer it takes for a stock to get back to the former high.'

Applying this definition to our asset in some examples:- The Ulcer Index over 5 years of Sirius XM is 28 , which is greater, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 33 is larger, 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:- The maximum DrawDown over 5 years of Sirius XM is -66.8 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum DrawDown is -66.8 days, which is lower, thus worse than the value of -24.5 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) in days.'

Which means for our asset as example:- The maximum time in days below previous high water mark over 5 years of Sirius XM is 858 days, which is higher, thus worse compared to the benchmark SPY (488 days) in the same period.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days below previous high of 264 days is lower, thus better.

'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 under water over 5 years of Sirius XM is 329 days, which is higher, thus worse compared to the benchmark SPY (123 days) in the same period.
- During the last 3 years, the average time in days below previous high water mark is 95 days, which is smaller, thus better than the value of 179 days from the benchmark.

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.