'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.'

Which means for our asset as example:- Looking at the total return, or increase in value of -16.4% in the last 5 years of Discovery, we see it is relatively lower, thus worse in comparison to the benchmark SPY (61.3%)
- Looking at total return, or performance in of -15.4% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (31.6%).

'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.'

Using this definition on our asset we see for example:- The annual return (CAGR) over 5 years of Discovery is -3.5%, which is smaller, thus worse compared to the benchmark SPY (10%) in the same period.
- Compared with SPY (9.6%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of -5.4% 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.'

Applying this definition to our asset in some examples:- Looking at the 30 days standard deviation of 43.8% in the last 5 years of Discovery, we see it is relatively larger, thus worse in comparison to the benchmark SPY (20.8%)
- Compared with SPY (24%) in the period of the last 3 years, the volatility of 49.1% 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:- Looking at the downside deviation of 31.5% in the last 5 years of Discovery, we see it is relatively greater, thus worse in comparison to the benchmark SPY (15.3%)
- Compared with SPY (17.6%) in the period of the last 3 years, the downside deviation of 35.5% is larger, thus worse.

'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 Sharpe Ratio of -0.14 in the last 5 years of Discovery, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.36)
- Looking at ratio of return and volatility (Sharpe) in of -0.16 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.3).

'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:- The excess return divided by the downside deviation over 5 years of Discovery is -0.19, which is lower, thus worse compared to the benchmark SPY (0.49) in the same period.
- Looking at ratio of annual return and downside deviation in of -0.22 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.4).

'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.'

Which means for our asset as example:- The Downside risk index over 5 years of Discovery is 35 , which is greater, thus worse compared to the benchmark SPY (7.61 ) in the same period.
- Compared with SPY (8.93 ) in the period of the last 3 years, the Ulcer Index of 41 is higher, thus worse.

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Applying this definition to our asset in some examples:- The maximum drop from peak to valley over 5 years of Discovery is -71.2 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum drop from peak to valley in of -71.2 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-33.7 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:- The maximum time in days below previous high water mark over 5 years of Discovery is 541 days, which is larger, thus worse compared to the benchmark SPY (185 days) in the same period.
- Compared with SPY (185 days) in the period of the last 3 years, the maximum days under water of 278 days is higher, thus worse.

'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.'

Which means for our asset as example:- The average time in days below previous high water mark over 5 years of Discovery is 196 days, which is larger, thus worse compared to the benchmark SPY (46 days) in the same period.
- During the last 3 years, the average time in days below previous high water mark is 111 days, which is greater, thus worse than the value of 44 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 Discovery 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.