'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.'

Using this definition on our asset we see for example:- Looking at the total return of 461.8% in the last 5 years of Broadcom, we see it is relatively higher, thus better in comparison to the benchmark SPY (98.3%)
- Looking at total return, or performance in of 207.6% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (27.2%).

'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 (14.7%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 41.3% of Broadcom is greater, thus better.
- Compared with SPY (8.4%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 45.7% is greater, thus better.

'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.'

Applying this definition to our asset in some examples:- Looking at the 30 days standard deviation of 39.2% in the last 5 years of Broadcom, we see it is relatively greater, thus worse in comparison to the benchmark SPY (20.9%)
- During the last 3 years, the volatility is 38%, which is greater, thus worse than the value of 17.7% from the benchmark.

'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:- The downside risk over 5 years of Broadcom is 26.4%, which is greater, thus worse compared to the benchmark SPY (14.9%) in the same period.
- Looking at downside deviation in of 24% in the period of the last 3 years, we see it is relatively greater, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.58) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.99 of Broadcom is greater, thus better.
- During the last 3 years, the Sharpe Ratio is 1.14, which is higher, thus better than the value of 0.33 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.82) in the period of the last 5 years, the ratio of annual return and downside deviation of 1.47 of Broadcom is larger, thus better.
- During the last 3 years, the ratio of annual return and downside deviation is 1.8, which is greater, thus better than the value of 0.47 from the benchmark.

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (9.32 ) in the period of the last 5 years, the Ulcer Index of 11 of Broadcom is larger, thus worse.
- Looking at Ulcer Ratio in of 13 in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (10 ).

'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.'

Using this definition on our asset we see for example:- Looking at the maximum drop from peak to valley of -48.3 days in the last 5 years of Broadcom, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (-33.7 days)
- During the last 3 years, the maximum reduction from previous high is -35.2 days, which is smaller, thus worse than the value of -24.5 days from the benchmark.

'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'

Which means for our asset as example:- Looking at the maximum days below previous high of 348 days in the last 5 years of Broadcom, we see it is relatively lower, thus better in comparison to the benchmark SPY (488 days)
- Compared with SPY (488 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 348 days is smaller, thus better.

'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 below previous high of 68 days of Broadcom is smaller, thus better.
- During the last 3 years, the average time in days below previous high water mark is 97 days, which is lower, thus better than the value of 177 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 Broadcom are hypothetical and do not account for slippage, fees or taxes.