'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.'

Which means for our asset as example:- The total return, or performance over 5 years of The Trade Desk is 486.9%, which is larger, thus better compared to the benchmark SPY (101.5%) in the same period.
- During the last 3 years, the total return, or increase in value is 55.8%, which is larger, thus better than the value of 29.7% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The compounded annual growth rate (CAGR) over 5 years of The Trade Desk is 42.5%, which is higher, thus better compared to the benchmark SPY (15.1%) in the same period.
- During the last 3 years, the annual performance (CAGR) is 16%, which is higher, thus better than the value of 9.1% from the benchmark.

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 68.8% of The Trade Desk is greater, thus worse.
- During the last 3 years, the historical 30 days volatility is 68%, which is higher, thus worse than the value of 17.6% 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.'

Using this definition on our asset we see for example:- The downside volatility over 5 years of The Trade Desk is 44.2%, which is greater, thus worse compared to the benchmark SPY (14.9%) in the same period.
- During the last 3 years, the downside deviation is 41.4%, which is larger, thus worse than the value of 12.3% 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.'

Applying this definition to our asset in some examples:- The risk / return profile (Sharpe) over 5 years of The Trade Desk is 0.58, which is lower, thus worse compared to the benchmark SPY (0.6) in the same period.
- Compared with SPY (0.37) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of 0.2 is smaller, 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 excess return divided by the downside deviation of 0.91 in the last 5 years of The Trade Desk, we see it is relatively larger, thus better in comparison to the benchmark SPY (0.84)
- During the last 3 years, the downside risk / excess return profile is 0.32, which is lower, thus worse than the value of 0.53 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Index of 32 of The Trade Desk is larger, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Index of 38 is larger, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the maximum drop from peak to valley of -64.3 days in the last 5 years of The Trade Desk, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum drop from peak to valley of -64.3 days is lower, thus worse.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 723 days of The Trade Desk is greater, thus worse.
- During the last 3 years, the maximum time in days below previous high water mark is 723 days, which is greater, thus worse than the value of 488 days from the benchmark.

'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 time in days below previous high water mark over 5 years of The Trade Desk is 247 days, which is higher, thus worse compared to the benchmark SPY (123 days) in the same period.
- Looking at average time in days below previous high water mark in of 355 days in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (177 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 The Trade Desk are hypothetical and do not account for slippage, fees or taxes.