'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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (98.3%) in the period of the last 5 years, the total return of -18.6% of Vanguard Long Term Treasury Fund is lower, thus worse.
- Looking at total return in of -24.9% in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (27.2%).

'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 (14.7%) in the period of the last 5 years, the compounded annual growth rate (CAGR) of -4% of Vanguard Long Term Treasury Fund is smaller, thus worse.
- During the last 3 years, the compounded annual growth rate (CAGR) is -9.1%, which is lower, thus worse than the value of 8.4% from the benchmark.

'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 volatility of 16.4% in the last 5 years of Vanguard Long Term Treasury Fund, we see it is relatively lower, thus better in comparison to the benchmark SPY (20.9%)
- Compared with SPY (17.7%) in the period of the last 3 years, the historical 30 days volatility of 16.6% is lower, thus better.

'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:- Compared with the benchmark SPY (14.9%) in the period of the last 5 years, the downside risk of 11.5% of Vanguard Long Term Treasury Fund is lower, thus better.
- During the last 3 years, the downside deviation is 11.9%, which is lower, thus better than the value of 12.4% 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 Vanguard Long Term Treasury Fund is -0.4, which is lower, thus worse compared to the benchmark SPY (0.58) in the same period.
- Compared with SPY (0.33) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.7 is smaller, thus worse.

'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:- Looking at the ratio of annual return and downside deviation of -0.57 in the last 5 years of Vanguard Long Term Treasury Fund, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.82)
- During the last 3 years, the excess return divided by the downside deviation is -0.97, which is smaller, thus worse 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.'

Using this definition on our asset we see for example:- The Downside risk index over 5 years of Vanguard Long Term Treasury Fund is 26 , which is greater, thus worse compared to the benchmark SPY (9.32 ) in the same period.
- Looking at Downside risk index in of 28 in the period of the last 3 years, we see it is relatively higher, 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.'

Applying this definition to our asset in some examples:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum reduction from previous high of -46.2 days of Vanguard Long Term Treasury Fund is smaller, thus worse.
- Looking at maximum drop from peak to valley in of -41.5 days in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (-24.5 days).

'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:- 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 1030 days of Vanguard Long Term Treasury Fund is higher, thus worse.
- During the last 3 years, the maximum time in days below previous high water mark is 693 days, which is larger, 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:- Looking at the average time in days below previous high water mark of 434 days in the last 5 years of Vanguard Long Term Treasury Fund, we see it is relatively greater, thus worse in comparison to the benchmark SPY (123 days)
- Looking at average time in days below previous high water mark in of 323 days in the period of the last 3 years, we see it is relatively larger, thus worse in comparison to SPY (177 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 Vanguard Long Term Treasury Fund are hypothetical and do not account for slippage, fees or taxes.