'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.'

Which means for our asset as example:- Looking at the total return, or increase in value of 21.2% in the last 5 years of Broadcom Corp, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (103.3%)
- Compared with SPY (37.7%) in the period of the last 3 years, the total return, or increase in value of 68.5% is greater, 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.'

Using this definition on our asset we see for example:- The annual performance (CAGR) over 5 years of Broadcom Corp is 3.9%, which is lower, thus worse compared to the benchmark SPY (15.3%) in the same period.
- Compared with SPY (11.3%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 19% is larger, thus better.

'In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Commonly, the higher the volatility, the riskier the security.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (20.9%) in the period of the last 5 years, the volatility of 31% of Broadcom Corp is greater, thus worse.
- Compared with SPY (17.3%) in the period of the last 3 years, the historical 30 days volatility of 27.4% is larger, thus worse.

'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.'

Applying this definition to our asset in some examples:- Looking at the downside volatility of 20.7% in the last 5 years of Broadcom Corp, we see it is relatively higher, thus worse in comparison to the benchmark SPY (14.9%)
- During the last 3 years, the downside volatility is 17.4%, which is larger, thus worse than the value of 12% from the benchmark.

'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:- Compared with the benchmark SPY (0.61) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.05 of Broadcom Corp is smaller, thus worse.
- During the last 3 years, the Sharpe Ratio is 0.6, which is higher, thus better than the value of 0.51 from the benchmark.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.85) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.07 of Broadcom Corp is lower, thus worse.
- Looking at downside risk / excess return profile in of 0.95 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.73).

'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:- Looking at the Ulcer Index of 25 in the last 5 years of Broadcom Corp, we see it is relatively greater, thus worse in comparison to the benchmark SPY (9.32 )
- Looking at Ulcer Ratio in of 14 in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (10 ).

'A maximum drawdown is the maximum loss from a peak to a trough of a portfolio, before a new peak is attained. Maximum Drawdown is an indicator of downside risk over a specified time period. It can be used both as a stand-alone measure or as an input into other metrics such as 'Return over Maximum Drawdown' and the Calmar Ratio. Maximum Drawdown is expressed in percentage terms.'

Using this definition on our asset we see for example:- Looking at the maximum drop from peak to valley of -46.4 days in the last 5 years of Broadcom Corp, we see it is relatively lower, thus worse in comparison to the benchmark SPY (-33.7 days)
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -33.8 days is smaller, 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.'

Which means for our asset as example:- The maximum time in days below previous high water mark over 5 years of Broadcom Corp is 1071 days, which is greater, thus worse compared to the benchmark SPY (488 days) in the same period.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days below previous high of 263 days is lower, thus better.

'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 days below previous high over 5 years of Broadcom Corp is 468 days, which is larger, thus worse compared to the benchmark SPY (123 days) in the same period.
- Compared with SPY (181 days) in the period of the last 3 years, the average days below previous high of 69 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 Broadcom Corp are hypothetical and do not account for slippage, fees or taxes.