(The slope also equals
ratio of the standard deviations.)
There are any number of other statistics one can also use —
the ratio of the standard deviation to the mean, the range, and so on.
At right, the model diversity, defined
a the ratio of the standard deviation of all models from their corresponding mean values.
Not exact matches
If we take a look at the numbers another way, by price to sales, the average 2017 forward
ratio is around 5.95 with a
standard deviation of around 3.5.
Key performance metrics are annualized average gross return, annualized
standard deviation of returns, annualized gross Sharpe
ratio (assuming risk - free rate 0 %) and maximum drawdown.
For each decile, we've subtracted the 1986 - 2016 average price / revenue
ratio for that decile, dividing the result by the
standard deviation of valuations in that decile (again from 1986 - 2016).
These conditions comprise the following: S&P 500 overvalued with the Shiller P / E (the
ratio of the S&P 500 to the 10 - year average
of inflation - adjusted earnings) greater than 18; overbought with the S&P 500 within 3 %
of its upper Bollinger band (2
standard deviations above the 20 - period average) at daily, weekly, and monthly resolutions, more than 7 % above its 52 - week smoothing, and more than 50 % above its 4 - year low; overbullish with the 2 - week average
of advisory bullishness (Investors Intelligence) greater than 52 % and bearishness below 28 %; and yields rising with the 10 - year Treasury bond yield higher than 6 - months earlier.
The product writ large is designed to reduce a diversified portfolio's correlation to the market, lower
standard deviation (thus increasing a portfolio's Sharpe
ratio) and ultimately deliver long - term returns in excess
of the market.
The Sharpe
ratio is calculated by subtracting the risk - free rate - such as that
of the 3 - month U.S. Treasury Bill - from the rate
of return for a portfolio and dividing the result by the
standard deviation of the portfolio returns.
We focus on gross compound annual growth rate (CAGR), gross maximum drawdown (MaxDD) and rough gross annual Sharpe
ratio (average annual return divided by
standard deviation of annual returns) as key performance statistics for the Top 1, equally weighted (EW) Top 2 and EW Top 3 portfolios
of monthly winners.
One
standard deviation increase
of CSF ApoA1 was associated with a 30 % increased risk
of clinical progression (hazard
ratio (HR)(95 % CI) = 1.3 (1.0 — 1.6)-RRB-.
Association
of Genetically - Elevated Waist - to - Hip
Ratio Adjusted for Body Mass Index (One
Standard Deviation Increase) With Type 2 Diabetes Using Three Instruments
Association
of Genetically - Elevated Waist - to - Hip
Ratio Adjusted for Body Mass Index (One
Standard Deviation Increase) With Type 2 Diabetes Using Three Instruments With Additional Adjustment for Body Mass Index
Association
of Genetically - Elevated Waist - to - Hip
Ratio Adjusted for Body Mass Index (One
Standard Deviation Increase) With Coronary Heart Disease Using Three Instruments With Additional Adjustment for Body Mass Index
Association
of Genetically - Elevated Waist - to - Hip
Ratio Adjusted for Body Mass Index (One
Standard Deviation Increase) With Type 2 Diabetes and Coronary Heart Disease, Overall and by Quintile
of WHRadjBMI
Although Gaetz's bill does not include fiscal expenditures, as noted in the main text (§ IV, supra), in reviewing the start time / academic achievement studies undertaken by fellow economists, Columbia University Assistant Professor
of Finance and Economics Jonah Rockoff and the Walter H. Annenberg Professor
of Education Policy, Professor
of Economics, and Professor
of Education at the University
of Michigan, Brian Jacob, concluded that delaying middle and high school start times «from roughly 8 a.m. to 9 a.m. -LSB-,]» will increase academic achievement by 0.175
standard deviations on average, with effects for disadvantaged students roughly twice as large as advantaged students, at little or no cost to schools; i.e., a 9 to 1 benefits to costs
ratio when utilizing single - tier busing, the most expensive transportation method available.
The above historical performance figures from Morningstar indicate that the fund had a higher volatility (expressed as a
standard deviation of returns) and underperformed the S&P 500 ® index, its best - fit benchmark, on a risk - adjusted basis (Sharpe
Ratio) in both the three - and five - year trailing periods.
Using filters
of Expense
ratio, Sharpe
ratio and
Standard Deviation, I now have just 29 debt mutual fund schemes spread across the 4 categories mentioned above.
Metrics such as the
standard deviation of returns and value at risk are more absolute - risk measures, while beta and the Sharpe
ratio give a sense
of risk / return versus a given benchmark.
Each
of the table above lists the equity mutual fund name along with the Expense
Ratio,
Standard Deviation and the Sharpe
Ratio of the respective fund.
Information
ratio = (Mutual fund returns — benchmark returns) / (
Standard deviation of mutual fund —
Standard deviation of benchmark)
Specifically, it is the
ratio of the fund's annualized excess return divided its
standard deviation.
While IJR outperformed MDY in terms
of the annualized return, alpha and Sharpe
ratio (just slightly), it also had the highest
standard deviation (volatility), maximum drawdown and beta
of all three ETFs.
Both
standard deviation and Sharpe
ratio define risk in terms
of volatility.
Other statistical measures such as calculation
of standard deviation and shape
ratios are important to calculate or estimate the risk.
Risk, when measured by
standard deviation, is minimized with a 50 % allocation to the DRS.. The Sharpe
ratio, which is the most commonly used measure
of risk / return trade - off, is maximized at around a 70 % allocation to the DRS.
Sharpe
Ratio uses a fund's
standard deviation and its excess return (the difference between the fund's return and the risk ‐ free return
of 90 ‐ day Treasury Bills) to determine reward per unit
of risk.
(
Ratios to measure risk
of a mutual fund: A good Mutual Fund ideally should have Low
Standard Deviation, High Alpha, Low Beta and High Sharpe
Ratio)
Since 1996, the US CAPE
ratio has been above its long - term simple average (16.6) 96 %
of the time, and above 24, roughly one
standard deviation above its historical norm, more than two - thirds
of the time.
Additionally, these impressive Sharpe
ratios come with low risk when measured by other means than
standard deviation of returns.
Since its July 2013 inception, AQR Long - Short Equity Fund I QLEIX has returned 14.4 % above its benchmark (a 50 - 50 blend
of the MSCI World Index and cash) with a
standard deviation of 5.8 %, for a Sharpe
ratio of 2.46.
Since its October 2014 inception, AQR Equity Market Neutral Fund I QMNIX has returned 18.6 % annualized with a
standard deviation of 7.0 %, for a Sharpe
ratio of 2.66.
The Pain
Ratio - A Better Risk / Return Measure Download PDF Pain
Ratio vs.
Standard Deviation In a previous post, we discussed the pain index as a better measure
of risk.
I would expect long - term stock returns to be in a range
of 5.25 % real (15 %
standard deviation * 0.35 Sharpe
ratio) to 4 % real (2.2 % yield + 1.8 % real payout growth).
A
ratio used to test this reward to risk ratio is the Sharpe Ratio: Portfolio Return — Risk - Free Rate / Standard Deviation of the Port
ratio used to test this reward to risk
ratio is the Sharpe Ratio: Portfolio Return — Risk - Free Rate / Standard Deviation of the Port
ratio is the Sharpe
Ratio: Portfolio Return — Risk - Free Rate / Standard Deviation of the Port
Ratio: Portfolio Return — Risk - Free Rate /
Standard Deviation of the Portfolio
I determined the mean, mean plus and minus one
standard deviation, probability
of exceeding the Minimum Acceptable Return (MAR) for levels
of 0 % and 2 % (approximately), below target
deviation, upside potential and upside
ratio for all individual segments.
For reference, in the same time frame a portfolio consisting
of just the SPY would have an annualized return
of 8.52 % with a
standard deviation of 14.25 %, Sharpe
ratio of 0.55 and maximum drawdown
of 50.8 %.
Data pertaining to «Portfolio allocation», portfolio holdings, Risk stats (
Standard deviation, Alpha, Beta, Downside & Upside capture
ratios etc), returns data etc
of the listed funds and other competing peers have been duly considered.
Stocks were then ranked based on their 1 year sharpe
ratio, or the annualized return
of a stock divided by its annualized
standard deviation of the weekly returns.
Over the same analysis interval, the fund had a total cumulative return
of about 130 % (annualized 9.2 %), with a
standard deviation of 15.1 %, Sharpe
ratio of 0.58, and maximum drawdown
of 44 %.
We consider as performance metrics: average annual excess return (relative to the yield on 1 - year U.S. Treasury notes at the beginning
of each year);
standard deviation of annual excess returns; annual Sharpe
ratio; compound annual growth rate (CAGR); and, maximum annual drawdown (annual MaxDD).
• Will display portfolio statistics like correlation coefficients, average / median / minimum / maximum rates
of return over the selected time frame, along with
standard deviation of monthly returns, Beta, Alpha (Jensen), R - squared, Treynor
Ratio, and Sharpe
Ratio, and all
of that.
The other strategies generate lower maximum drawdowns, but do so for lower Sharpe
ratios: The strategy that kicked into cash at the mean had a maximum drawdown
of 69 percent, and the worst Sharpe
ratio at 0.11; the strategy that kicked into cash at one
standard deviation above the mean had a maximum drawdown
of 80 percent, and a Sharpe
ratio of 0.14, and the strategy that kicked into cash at two
standard deviations above the mean had a maximum drawdown
of 84 percent, and a Sharpe
ratio of 0.15.
The strategy that kicked into cash at the mean had lower a maximum drawdown
of 73 percent, but an improved Sharpe
ratio at 0.12; the strategy that kicked into cash at one
standard deviation above the mean remained unchanged with a maximum drawdown
of 80 percent, and a Sharpe
ratio of 0.14, and the strategy that kicked into cash at two
standard deviations above the mean had a maximum drawdown
of 85 percent, and a Sharpe
ratio of 0.15.
The Sharpe
ratio is calculated for a time series by dividing the mean period return (daily, monthly, yearly), in excess
of the risk free rate, by the
standard deviation of such returns.
High returns have the effect
of increasing the value
of the denominator (
standard deviation), and lowering the value
of the
ratio.
In addition to your portfolio return, we also provide the Sharpe
ratio, which represents the real return (return obtained, less the risk - free return)
of each unit
of risk (
standard deviation).
The results include a visualization
of the portfolio growth chart and rolling returns, CAGR,
standard deviation, Sharpe
ratio, Sortino
ratio, annual returns and inflation adjusted returns.
Markowitz mean - variance optimization and the Sharpe
ratio are two such examples under the umbrella
of modern portfolio theory that reference variance or
standard deviation as a proxy for risk in their formulation.
This model could be used as a starting point in the development
of a GCM parameterization
of a the ice mixing -
ratio probability distribution function and cloud amount, if a means
of diagnosing the depth
of the saturated layer and the
standard deviation of cloud depth from basic large - scale meterological parameters could be determined.