'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (110.3%) in the period of the last 5 years, the total return, or performance of 40.6% of ANSYS is smaller, thus worse.
- During the last 3 years, the total return, or increase in value is -5.7%, which is smaller, thus worse than the value of 39.7% from the benchmark.

'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.'

Using this definition on our asset we see for example:- The annual return (CAGR) over 5 years of ANSYS is 7.1%, which is lower, thus worse compared to the benchmark SPY (16.1%) in the same period.
- Compared with SPY (11.8%) in the period of the last 3 years, the annual performance (CAGR) of -2% is lower, thus worse.

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Applying this definition to our asset in some examples:- Looking at the 30 days standard deviation of 35.7% in the last 5 years of ANSYS, we see it is relatively larger, thus worse in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.5%) in the period of the last 3 years, the historical 30 days volatility of 33.6% is greater, thus worse.

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. 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:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside risk of 24% of ANSYS is higher, thus worse.
- Looking at downside risk in of 21.9% in the period of the last 3 years, we see it is relatively greater, thus worse in comparison to SPY (12.2%).

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (0.65) in the period of the last 5 years, the risk / return profile (Sharpe) of 0.13 of ANSYS is lower, thus worse.
- Compared with SPY (0.53) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.13 is lower, thus worse.

'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.'

Using this definition on our asset we see for example:- The ratio of annual return and downside deviation over 5 years of ANSYS is 0.19, which is lower, thus worse compared to the benchmark SPY (0.91) in the same period.
- Looking at downside risk / excess return profile in of -0.2 in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (0.76).

'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:- The Ulcer Index over 5 years of ANSYS is 23 , which is larger, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Compared with SPY (10 ) in the period of the last 3 years, the Ulcer Ratio of 28 is larger, thus worse.

'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:- The maximum DrawDown over 5 years of ANSYS is -51.3 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 drop from peak to valley is -51.3 days, which is smaller, thus worse than the value of -24.5 days from the benchmark.

'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 time in days below previous high water mark of 697 days of ANSYS is greater, thus worse.
- During the last 3 years, the maximum time in days below previous high water mark is 697 days, which is greater, thus worse than the value of 488 days from the benchmark.

'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.'

Which means for our asset as example:- Compared with the benchmark SPY (124 days) in the period of the last 5 years, the average time in days below previous high water mark of 224 days of ANSYS is larger, thus worse.
- Compared with SPY (179 days) in the period of the last 3 years, the average time in days below previous high water mark of 329 days is higher, thus worse.

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 ANSYS are hypothetical and do not account for slippage, fees or taxes.