'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 performance over 5 years of Vanguard Long Term Treasury Fund is 6.5%, which is lower, thus worse compared to the benchmark SPY (81.9%) in the same period.
- During the last 3 years, the total return, or performance is -1.8%, which is smaller, thus worse than the value of 46.1% 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:- Looking at the annual return (CAGR) of 1.3% in the last 5 years of Vanguard Long Term Treasury Fund, we see it is relatively lower, thus worse in comparison to the benchmark SPY (12.7%)
- During the last 3 years, the compounded annual growth rate (CAGR) is -0.6%, which is lower, thus worse than the value of 13.5% from the benchmark.

'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:- The 30 days standard deviation over 5 years of Vanguard Long Term Treasury Fund is 13.6%, which is lower, thus better compared to the benchmark SPY (19.8%) in the same period.
- Compared with SPY (23%) in the period of the last 3 years, the volatility of 15.9% is lower, thus better.

'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:- Looking at the downside risk of 9.4% 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 (14.5%)
- During the last 3 years, the downside volatility is 11.1%, which is lower, thus better than the value of 16.8% 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.'

Applying this definition to our asset in some examples:- Looking at the ratio of return and volatility (Sharpe) of -0.09 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 (0.52)
- Compared with SPY (0.48) in the period of the last 3 years, the ratio of return and volatility (Sharpe) of -0.2 is smaller, 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:- Compared with the benchmark SPY (0.7) in the period of the last 5 years, the downside risk / excess return profile of -0.13 of Vanguard Long Term Treasury Fund is smaller, thus worse.
- Looking at excess return divided by the downside deviation in of -0.28 in the period of the last 3 years, we see it is relatively lower, thus worse in comparison to SPY (0.65).

'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.'

Applying this definition to our asset in some examples:- Looking at the Ulcer Index of 9.35 in the last 5 years of Vanguard Long Term Treasury Fund, we see it is relatively higher, thus worse in comparison to the benchmark SPY (6.08 )
- Looking at Downside risk index in of 11 in the period of the last 3 years, we see it is relatively higher, thus worse in comparison to SPY (6.77 ).

'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 Vanguard Long Term Treasury Fund is -30.7 days, which is higher, thus better compared to the benchmark SPY (-33.7 days) in the same period.
- Compared with SPY (-33.7 days) in the period of the last 3 years, the maximum DrawDown of -30.7 days is higher, thus better.

'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.'

Applying this definition to our asset in some examples:- The maximum days under water over 5 years of Vanguard Long Term Treasury Fund is 449 days, which is higher, thus worse compared to the benchmark SPY (139 days) in the same period.
- During the last 3 years, the maximum days under water is 449 days, which is higher, thus worse than the value of 119 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.'

Applying this definition to our asset in some examples:- Looking at the average days below previous high of 156 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 (35 days)
- Compared with SPY (27 days) in the period of the last 3 years, the average days under water of 156 days is greater, 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 Vanguard Long Term Treasury Fund 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.