'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:- The total return over 5 years of Merck is 103.4%, which is greater, thus better compared to the benchmark SPY (100.7%) in the same period.
- Compared with SPY (33.2%) in the period of the last 3 years, the total return, or performance of 88.8% is higher, thus better.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (15%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 15.3% of Merck is higher, thus better.
- During the last 3 years, the annual performance (CAGR) is 23.6%, which is higher, thus better than the value of 10% from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the 30 days standard deviation of 23% of Merck is higher, thus worse.
- During the last 3 years, the 30 days standard deviation is 20.6%, which is higher, thus worse than the value of 17.3% from the benchmark.

'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:- The downside deviation over 5 years of Merck is 15.8%, which is greater, thus worse compared to the benchmark SPY (15%) in the same period.
- Looking at downside risk in of 13.7% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12%).

'The Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance of an investment by adjusting for its risk. The ratio measures the excess return (or risk premium) per unit of deviation in an investment asset or a trading strategy, typically referred to as risk, named after William F. Sharpe.'

Which means for our asset as example:- Looking at the ratio of return and volatility (Sharpe) of 0.56 in the last 5 years of Merck, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.6)
- Looking at risk / return profile (Sharpe) in of 1.02 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.44).

'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.'

Using this definition on our asset we see for example:- Looking at the downside risk / excess return profile of 0.81 in the last 5 years of Merck, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.83)
- Looking at excess return divided by the downside deviation in of 1.55 in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (0.62).

'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.'

Applying this definition to our asset in some examples:- The Downside risk index over 5 years of Merck is 8.93 , which is smaller, thus better compared to the benchmark SPY (9.32 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 7.21 is smaller, thus better.

'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.'

Which means for our asset as example:- Looking at the maximum DrawDown of -27.3 days in the last 5 years of Merck, we see it is relatively higher, thus better in comparison to the benchmark SPY (-33.7 days)
- Looking at maximum reduction from previous high in of -20.2 days in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (-24.5 days).

'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.'

Using this definition on our asset we see for example:- Looking at the maximum days below previous high of 441 days in the last 5 years of Merck, we see it is relatively lower, thus better in comparison to the benchmark SPY (488 days)
- During the last 3 years, the maximum time in days below previous high water mark is 165 days, which is lower, thus better than the value of 488 days from the benchmark.

'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:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days under water of 110 days of Merck is lower, thus better.
- Compared with SPY (180 days) in the period of the last 3 years, the average days under water of 43 days is smaller, thus better.

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