'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.'

Using this definition on our asset we see for example:- Looking at the total return, or increase in value of 33.9% in the last 5 years of Express Scripts, we see it is relatively lower, thus worse in comparison to the benchmark SPY (111.3%)
- Looking at total return, or performance in of 7.8% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (39.3%).

'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:- The annual performance (CAGR) over 5 years of Express Scripts is 6%, which is lower, thus worse compared to the benchmark SPY (16.2%) in the same period.
- During the last 3 years, the compounded annual growth rate (CAGR) is 2.5%, which is lower, thus worse than the value of 11.7% 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.'

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 30 days standard deviation of 22.9% of Express Scripts is larger, thus worse.
- During the last 3 years, the historical 30 days volatility is 24.8%, which is greater, thus worse than the value of 17.5% 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.'

Which means for our asset as example:- The downside deviation over 5 years of Express Scripts is 16.4%, which is higher, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Looking at downside deviation in of 17.9% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.2%).

'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.'

Which means for our asset as example:- Looking at the ratio of return and volatility (Sharpe) of 0.15 in the last 5 years of Express Scripts, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.66)
- Compared with SPY (0.53) in the period of the last 3 years, the Sharpe Ratio of 0 is smaller, thus worse.

'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:- Compared with the benchmark SPY (0.92) in the period of the last 5 years, the excess return divided by the downside deviation of 0.21 of Express Scripts is smaller, thus worse.
- Looking at downside risk / excess return profile in of 0 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.75).

'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.'

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 Downside risk index of 19 of Express Scripts is higher, thus worse.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Ratio of 20 is greater, 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.'

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 drop from peak to valley of -39.6 days of Express Scripts is lower, thus worse.
- During the last 3 years, the maximum drop from peak to valley is -35.6 days, which is lower, thus worse than the value of -24.5 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:- The maximum days below previous high over 5 years of Express Scripts is 794 days, which is higher, thus worse compared to the benchmark SPY (488 days) in the same period.
- Looking at maximum days under water in of 673 days in the period of the last 3 years, we see it is relatively larger, 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:- Looking at the average days below previous high of 279 days in the last 5 years of Express Scripts, we see it is relatively greater, thus worse in comparison to the benchmark SPY (124 days)
- Compared with SPY (179 days) in the period of the last 3 years, the average days below previous high of 310 days is larger, thus worse.

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 Express Scripts are hypothetical and do not account for slippage, fees or taxes.