'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (103.4%) in the period of the last 5 years, the total return of 184.2% of Caterpillar is greater, thus better.
- During the last 3 years, the total return, or performance is 56.3%, which is larger, thus better than the value of 33.4% from the benchmark.

'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 return (CAGR) over 5 years of Caterpillar is 23.3%, which is larger, thus better compared to the benchmark SPY (15.3%) in the same period.
- Looking at annual return (CAGR) in of 16% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (10.1%).

'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.'

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 historical 30 days volatility of 32.3% of Caterpillar is greater, thus worse.
- Compared with SPY (17.3%) in the period of the last 3 years, the volatility of 29.1% is greater, 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:- Looking at the downside deviation of 22.2% in the last 5 years of Caterpillar, we see it is relatively larger, thus worse in comparison to the benchmark SPY (14.9%)
- Looking at downside risk in of 19.8% in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (12.1%).

'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.'

Applying this definition to our asset in some examples:- The risk / return profile (Sharpe) over 5 years of Caterpillar is 0.64, which is higher, thus better compared to the benchmark SPY (0.61) in the same period.
- Looking at risk / return profile (Sharpe) in of 0.47 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.44).

'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.'

Which means for our asset as example:- Looking at the downside risk / excess return profile of 0.93 in the last 5 years of Caterpillar, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.85)
- During the last 3 years, the ratio of annual return and downside deviation is 0.69, which is larger, thus better than the value of 0.63 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 13 of Caterpillar is larger, thus worse.
- During the last 3 years, the Ulcer Ratio is 11 , which is larger, 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:- The maximum DrawDown over 5 years of Caterpillar is -38.6 days, which is smaller, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- Looking at maximum reduction from previous high in of -30.1 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 383 days of Caterpillar is lower, thus better.
- Looking at maximum time in days below previous high water mark in of 141 days in the period of the last 3 years, we see it is relatively lower, thus better in comparison to SPY (488 days).

'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:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days below previous high of 91 days of Caterpillar is lower, thus better.
- During the last 3 years, the average days below previous high is 45 days, which is lower, thus better than the value of 180 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 Caterpillar are hypothetical and do not account for slippage, fees or taxes.