'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Using this definition on our asset we see for example:- Looking at the total return of 250.9% in the last 5 years of Caterpillar, we see it is relatively greater, thus better in comparison to the benchmark SPY (111.3%)
- During the last 3 years, the total return is 121.6%, which is larger, thus better than the value of 39.3% from the benchmark.

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Which means for our asset as example:- Looking at the annual performance (CAGR) of 28.6% in the last 5 years of Caterpillar, we see it is relatively larger, thus better in comparison to the benchmark SPY (16.2%)
- During the last 3 years, the annual performance (CAGR) is 30.4%, which is larger, thus better 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.'

Which means for our asset as example:- The 30 days standard deviation over 5 years of Caterpillar is 32.2%, which is larger, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Compared with SPY (17.5%) in the period of the last 3 years, the historical 30 days volatility of 29.3% is larger, thus worse.

'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:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside volatility of 22.1% of Caterpillar is larger, thus worse.
- Compared with SPY (12.2%) in the period of the last 3 years, the downside risk of 19.6% is higher, 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:- The ratio of return and volatility (Sharpe) over 5 years of Caterpillar is 0.81, which is larger, thus better compared to the benchmark SPY (0.66) in the same period.
- During the last 3 years, the Sharpe Ratio is 0.95, which is greater, thus better than the value of 0.53 from the benchmark.

'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 ratio of annual return and downside deviation of 1.18 in the last 5 years of Caterpillar, we see it is relatively larger, thus better in comparison to the benchmark SPY (0.92)
- Looking at excess return divided by the downside deviation in of 1.42 in the period of the last 3 years, we see it is relatively higher, thus better in comparison to SPY (0.75).

'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.'

Using this definition on our asset we see for example:- The Ulcer Index over 5 years of Caterpillar is 13 , which is larger, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- During the last 3 years, the Ulcer Ratio is 11 , which is greater, thus worse than the value of 10 from the benchmark.

'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:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -38.6 days of Caterpillar is lower, thus worse.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -30.1 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:- Looking at the maximum days under water of 383 days in the last 5 years of Caterpillar, 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 141 days, which is lower, 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.'

Which means for our asset as example:- The average time in days below previous high water mark over 5 years of Caterpillar is 94 days, which is lower, thus better compared to the benchmark SPY (124 days) in the same period.
- Compared with SPY (179 days) in the period of the last 3 years, the average days below previous high of 47 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 Caterpillar are hypothetical and do not account for slippage, fees or taxes.