'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:- Looking at the total return, or increase in value of 132.2% in the last 5 years of Invesco QQQ Trust, we see it is relatively higher, thus better in comparison to the benchmark SPY (81.7%)
- Looking at total return, or increase in value in of 86.1% in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (54.7%).

'Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (12.7%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 18.4% of Invesco QQQ Trust is greater, thus better.
- During the last 3 years, the annual performance (CAGR) is 23%, which is larger, thus better than the value of 15.6% from the benchmark.

'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:- The 30 days standard deviation over 5 years of Invesco QQQ Trust is 17.1%, which is greater, thus worse compared to the benchmark SPY (13.3%) in the same period.
- Compared with SPY (12.8%) in the period of the last 3 years, the historical 30 days volatility of 17.3% is higher, 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (14.8%) in the period of the last 5 years, the downside deviation of 19.3% of Invesco QQQ Trust is greater, thus worse.
- During the last 3 years, the downside risk is 20%, which is greater, thus worse than the value of 14.8% from the benchmark.

'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:- Looking at the risk / return profile (Sharpe) of 0.93 in the last 5 years of Invesco QQQ Trust, we see it is relatively larger, thus better in comparison to the benchmark SPY (0.76)
- Looking at ratio of return and volatility (Sharpe) in of 1.19 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (1.03).

'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.'

Using this definition on our asset we see for example:- The ratio of annual return and downside deviation over 5 years of Invesco QQQ Trust is 0.82, which is greater, thus better compared to the benchmark SPY (0.69) in the same period.
- During the last 3 years, the ratio of annual return and downside deviation is 1.02, which is higher, thus better than the value of 0.89 from the benchmark.

'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.'

Which means for our asset as example:- The Downside risk index over 5 years of Invesco QQQ Trust is 4.98 , which is higher, thus worse compared to the benchmark SPY (3.97 ) in the same period.
- During the last 3 years, the Downside risk index is 4.96 , which is higher, thus worse than the value of 4.09 from the benchmark.

'Maximum drawdown is defined as the peak-to-trough decline of an investment during a specific period. It is usually quoted as a percentage of the peak value. The maximum drawdown can be calculated based on absolute returns, in order to identify strategies that suffer less during market downturns, such as low-volatility strategies. However, the maximum drawdown can also be calculated based on returns relative to a benchmark index, for identifying strategies that show steady outperformance over time.'

Which means for our asset as example:- The maximum DrawDown over 5 years of Invesco QQQ Trust is -22.8 days, which is lower, thus worse compared to the benchmark SPY (-19.3 days) in the same period.
- During the last 3 years, the maximum reduction from previous high is -22.8 days, which is smaller, thus worse than the value of -19.3 days from the benchmark.

'The Maximum 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. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Applying this definition to our asset in some examples:- Looking at the maximum days below previous high of 163 days in the last 5 years of Invesco QQQ Trust, we see it is relatively smaller, thus better in comparison to the benchmark SPY (187 days)
- Looking at maximum days below previous high in of 154 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (139 days).

'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:- Looking at the average days under water of 35 days in the last 5 years of Invesco QQQ Trust, we see it is relatively lower, thus better in comparison to the benchmark SPY (42 days)
- Looking at average days below previous high in of 30 days in the period of the last 3 years, we see it is relatively smaller, thus better in comparison to SPY (37 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 Invesco QQQ Trust 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.