'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.'

Using this definition on our asset we see for example:- The total return, or performance over 5 years of Dollar Tree is -44.3%, which is lower, thus worse compared to the benchmark SPY (109.2%) in the same period.
- During the last 3 years, the total return is -44.5%, which is smaller, thus worse than the value of 33.3% 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.'

Which means for our asset as example:- Looking at the annual return (CAGR) of -11.1% in the last 5 years of Dollar Tree, we see it is relatively lower, thus worse in comparison to the benchmark SPY (15.9%)
- Compared with SPY (10.1%) in the period of the last 3 years, the annual performance (CAGR) of -17.8% is lower, 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 40% in the last 5 years of Dollar Tree, we see it is relatively greater, thus worse in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.6%) in the period of the last 3 years, the historical 30 days volatility of 38.8% 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 (14.9%) in the period of the last 5 years, the downside deviation of 29.4% of Dollar Tree is greater, thus worse.
- During the last 3 years, the downside volatility is 29.4%, which is greater, thus worse than the value of 12.3% from the benchmark.

'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.'

Which means for our asset as example:- The risk / return profile (Sharpe) over 5 years of Dollar Tree is -0.34, which is lower, thus worse compared to the benchmark SPY (0.64) in the same period.
- Compared with SPY (0.43) in the period of the last 3 years, the risk / return profile (Sharpe) of -0.52 is smaller, thus worse.

'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:- The ratio of annual return and downside deviation over 5 years of Dollar Tree is -0.46, which is lower, thus worse compared to the benchmark SPY (0.9) in the same period.
- Looking at downside risk / excess return profile in of -0.69 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.62).

'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:- The Downside risk index over 5 years of Dollar Tree is 23 , which is larger, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Ulcer Ratio in of 27 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).

'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 (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -64.7 days of Dollar Tree is lower, thus worse.
- Looking at maximum drop from peak to valley in of -64.7 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-24.5 days).

'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.'

Which means for our asset as example:- Looking at the maximum days under water of 643 days in the last 5 years of Dollar Tree, we see it is relatively higher, thus worse in comparison to the benchmark SPY (488 days)
- Looking at maximum days under water in of 643 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (488 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.'

Using this definition on our asset we see for example:- The average days below previous high over 5 years of Dollar Tree is 209 days, which is higher, thus worse compared to the benchmark SPY (123 days) in the same period.
- Looking at average days under water in of 287 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (176 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 Dollar Tree are hypothetical and do not account for slippage, fees or taxes.