'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:- The total return, or increase in value over 5 years of Broadcom is 224.1%, which is greater, thus better compared to the benchmark SPY (84.3%) in the same period.
- Looking at total return, or performance in of 64.9% in the period of the last 3 years, we see it is relatively larger, thus better in comparison to SPY (37.3%).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (13%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of 26.6% of Broadcom is larger, thus better.
- Compared with SPY (11.1%) in the period of the last 3 years, the annual performance (CAGR) of 18.1% is higher, 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.'

Which means for our asset as example:- The 30 days standard deviation over 5 years of Broadcom is 36.3%, which is higher, thus worse compared to the benchmark SPY (18.8%) in the same period.
- During the last 3 years, the historical 30 days volatility is 39.7%, which is greater, thus worse than the value of 22.3% from the benchmark.

'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.'

Using this definition on our asset we see for example:- Looking at the downside risk of 25.8% in the last 5 years of Broadcom, we see it is relatively larger, thus worse in comparison to the benchmark SPY (13.7%)
- During the last 3 years, the downside volatility is 28.9%, which is larger, thus worse than the value of 16.5% from the benchmark.

'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:- Looking at the ratio of return and volatility (Sharpe) of 0.66 in the last 5 years of Broadcom, we see it is relatively greater, thus better in comparison to the benchmark SPY (0.56)
- Looking at ratio of return and volatility (Sharpe) in of 0.39 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.39).

'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (0.77) in the period of the last 5 years, the ratio of annual return and downside deviation of 0.93 of Broadcom is greater, thus better.
- During the last 3 years, the excess return divided by the downside deviation is 0.54, which is higher, thus better than the value of 0.52 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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (5.78 ) in the period of the last 5 years, the Ulcer Ratio of 10 of Broadcom is higher, thus worse.
- During the last 3 years, the Ulcer Index is 12 , which is greater, thus worse than the value of 7.08 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.'

Using this definition on our asset we see for example:- The maximum DrawDown over 5 years of Broadcom is -48.3 days, which is lower, thus worse compared to the benchmark SPY (-33.7 days) in the same period.
- During the last 3 years, the maximum DrawDown is -48.3 days, which is smaller, thus worse than the value of -33.7 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) in days.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (139 days) in the period of the last 5 years, the maximum time in days below previous high water mark of 298 days of Broadcom is greater, thus worse.
- During the last 3 years, the maximum time in days below previous high water mark is 298 days, which is larger, thus worse than the value of 139 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:- Looking at the average days below previous high of 61 days in the last 5 years of Broadcom, we see it is relatively higher, thus worse in comparison to the benchmark SPY (37 days)
- Looking at average time in days below previous high water mark in of 87 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (45 days).

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, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.