'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.'

Which means for our asset as example:- The total return, or increase in value over 5 years of Broadcom is 666.4%, which is larger, thus better compared to the benchmark SPY (103.4%) in the same period.
- During the last 3 years, the total return is 294.9%, which is higher, 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.'

Which means for our asset as example:- Compared with the benchmark SPY (15.3%) in the period of the last 5 years, the annual performance (CAGR) of 50.3% of Broadcom is greater, thus better.
- Compared with SPY (10.1%) in the period of the last 3 years, the compounded annual growth rate (CAGR) of 58.1% is greater, 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.'

Which means for our asset as example:- The 30 days standard deviation over 5 years of Broadcom is 37.6%, which is higher, thus worse compared to the benchmark SPY (20.9%) in the same period.
- Compared with SPY (17.3%) in the period of the last 3 years, the historical 30 days volatility of 34.2% is larger, thus worse.

'The downside volatility is similar to the volatility, or standard deviation, but only takes losing/negative periods into account.'

Which means for our asset as example:- The downside deviation over 5 years of Broadcom is 25%, which is larger, thus worse compared to the benchmark SPY (14.9%) in the same period.
- During the last 3 years, the downside deviation is 20.6%, which is greater, thus worse than the value of 12.1% from the benchmark.

'The Sharpe ratio is the measure of risk-adjusted return of a financial portfolio. Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation. Normally, the 90-day Treasury bill rate is taken as the proxy for risk-free rate. A portfolio with a higher Sharpe ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and professor of finance, emeritus at Stanford University.'

Using this definition on our asset we see for example:- The ratio of return and volatility (Sharpe) over 5 years of Broadcom is 1.27, which is greater, thus better compared to the benchmark SPY (0.61) in the same period.
- Looking at Sharpe Ratio in of 1.62 in the period of the last 3 years, we see it is relatively higher, 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.'

Using this definition on our asset we see for example:- The excess return divided by the downside deviation over 5 years of Broadcom is 1.92, which is higher, thus better compared to the benchmark SPY (0.85) in the same period.
- Looking at ratio of annual return and downside deviation in of 2.7 in the period of the last 3 years, we see it is relatively greater, thus better in comparison to SPY (0.63).

'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.'

Which means for our asset as example:- Looking at the Downside risk index of 11 in the last 5 years of Broadcom, we see it is relatively higher, thus worse in comparison to the benchmark SPY (9.32 )
- Looking at Ulcer Ratio in of 12 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.'

Which means for our asset as example:- The maximum drop from peak to valley 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.
- Compared with SPY (-24.5 days) in the period of the last 3 years, the maximum DrawDown of -35.2 days is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (488 days) in the period of the last 5 years, the maximum days below previous high of 348 days of Broadcom is lower, thus better.
- Compared with SPY (488 days) in the period of the last 3 years, the maximum days under water of 348 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:- Compared with the benchmark SPY (123 days) in the period of the last 5 years, the average days under water of 69 days of Broadcom is lower, thus better.
- Compared with SPY (180 days) in the period of the last 3 years, the average days under water of 96 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 are hypothetical and do not account for slippage, fees or taxes.