'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:- Compared with the benchmark SPY (102%) in the period of the last 5 years, the total return of 162.7% of Linde plc - Ordinary is greater, thus better.
- During the last 3 years, the total return is 55.9%, which is greater, thus better than the value of 31.5% 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:- Looking at the annual performance (CAGR) of 21.3% in the last 5 years of Linde plc - Ordinary, we see it is relatively greater, thus better in comparison to the benchmark SPY (15.1%)
- During the last 3 years, the compounded annual growth rate (CAGR) is 16%, which is greater, thus better than the value of 9.6% 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:- Looking at the volatility of 26% in the last 5 years of Linde plc - Ordinary, we see it is relatively higher, thus worse in comparison to the benchmark SPY (20.9%)
- Looking at historical 30 days volatility in of 22.3% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (17.6%).

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside volatility of 17.7% of Linde plc - Ordinary is larger, thus worse.
- Looking at downside volatility in of 15.3% in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (12.4%).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.6) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.73 of Linde plc - Ordinary is greater, thus better.
- Compared with SPY (0.4) in the period of the last 3 years, the risk / return profile (Sharpe) of 0.6 is higher, thus better.

'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:- Compared with the benchmark SPY (0.84) in the period of the last 5 years, the downside risk / excess return profile of 1.06 of Linde plc - Ordinary is larger, thus better.
- During the last 3 years, the downside risk / excess return profile is 0.88, which is greater, thus better than the value of 0.57 from the benchmark.

'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 8.13 of Linde plc - Ordinary is smaller, thus better.
- Compared with SPY (10 ) in the period of the last 3 years, the Downside risk index of 8.11 is lower, thus better.

'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:- The maximum drop from peak to valley over 5 years of Linde plc - Ordinary is -32.6 days, which is greater, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -22.8 days is larger, thus better.

'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). Many assume Max DD Duration is the length of time between new highs during which the Max DD (magnitude) occurred. But that isn’t always the case. The Max DD duration is the longest time between peaks, period. So it could be the time when the program also had its biggest peak to valley loss (and usually is, because the program needs a long time to recover from the largest loss), but it doesn’t have to be'

Using this definition on our asset we see for example:- Looking at the maximum days below previous high of 225 days in the last 5 years of Linde plc - Ordinary, we see it is relatively smaller, 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 225 days, which is smaller, thus better 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.'

Using this definition on our asset we see for example:- The average days below previous high over 5 years of Linde plc - Ordinary is 42 days, which is lower, thus better compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (177 days) in the period of the last 3 years, the average days under water of 55 days is lower, 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 Linde plc - Ordinary are hypothetical and do not account for slippage, fees or taxes.