Let's begin with the generally understood percentages for a bell curve (Gaussian probability distribution) in
terms of standard deviations (sigmas):
It's harder to quantify the gains on the local level, which the CREDO report frames in
terms of standard deviations (s.d.'s) rather than days of learning.
The impact of each intervention component is shown in
terms of standard deviations on the horizontal axis.
And researchers do not help, tending to talk in
terms of standard deviations of achievement and effect sizes, phrases that simply have no meaning outside of the rarefied world of research.
We report our results in
terms of standard deviations of student test scores.
Raddr's precise definition in
terms of the standard deviation after a selected number of years makes sense.
How do the 60/40 vs. 40/60 compare in
terms of standard deviation, downside capture, and risk to return (Sharpe)?
Not exact matches
Bollinger Bands ® are a Simple Moving Average with
standard deviations of that moving average acting as the outer «bands,» or short -
term support and resistance zones.
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.
«Identifying VXX / XIV Tendencies» finds that the Volatility Risk Premium (VRP), estimated as the difference between the current level
of the S&P 500 implied volatility index (VIX) and the annualized
standard deviation of S&P 500 Index daily returns over the previous 21 trading days (multiplying by the square root
of 250 to annualize), may be a useful predictor
of iPath S&P 500 VIX Short -
term Futures ETN (VXX) and VelocityShares Daily Inverse VIX Short -
term ETN (XIV) returns.
And while with more voters the
standard deviation becomes larger in absolute
terms, it becomes smaller as a percentage
of the vote.
Z - scores standardize the data to represent the number
of standard deviations above or below the long -
term average.
Their peers» average test scores are about 0.15
standard deviations higher, and the new schools have higher - quality teachers, measured in
terms of the fraction
of teachers with less than three years» experience, the fraction that are new to the school that year, the percentage
of teachers with an advanced degree, and the share
of teachers who attended a «highly competitive» college as defined by the Barron's rankings.
Examining longer -
term effects, however, the study's authors found that double - dosed students» scores on the math portion
of the ACT (taken in the spring
of 11th grade) were 0.15
standard deviations higher, the equivalent
of closing roughly 15 %
of the black - white achievement gap.
For instance, the median finding across 10 studies
of teacher effectiveness estimates that a teacher who is one
standard deviation above the average in
terms of quality produces additional learning gains for students
of 0.12
standard deviations in reading and 0.14
standard deviations in math.
In
terms of academic performance, KIPP students» achievement in grade 4 (before entering KIPP) is lower than the district average by 0.09
standard deviations in reading and by 0.08
standard deviations in math, or roughly one - quarter
of a grade level in each subject.
To estimate benefits
of the policy, we converted our best estimate
of the program's impact on reading scores (2.63 percentiles) to its equivalent in
standard deviation terms, calculated as 0.09.
A study by the RAND Corporation
of students from Louisiana districts affected by the hurricane suggests that these two factors had a short -
term net negative effect on evacuees» performance
of 0.03 to 0.06
standard deviations.
(In technical
terms, the relationships presented for these variables reflect the effect
of an increase
of one
standard deviation in the value
of the characteristic in question.)
«So that [they] can more validly and meaningfully describe school - and state - level progress... [they also endorse] reporting performance in
terms of scale scores and
standard deviations rather than percent proficient» indicators.
As per the full report as well, researchers more specifically found that students who were enrolled in the REACH program gained between 0.13 and 0.17
standard deviations greater gains in mathematics, and (although not as evident or highlighted in the text
of the actual report, but within a related table) students who were enrolled in the REACH program gained between 0.10 and 0.05
standard deviations greater gains in reading, although these gains were also less significant in statistical
terms.
A
Standard deviation of say 20 means that fund will generate plus or minus 20 % from its long
term average returns.
In fact, at a 75 % discount to growth on price - to - tangible book value — two
standard deviations below the average long -
term level — value hasn't been this cheap relative to growth since the peak
of the» dotcom» bubble.2 But, is this unpopularity permanent?
We track short -
term pain by looking at a fund's maximum drawdown, its Ulcer index which measures the depth and duration
of a drawdown, its
standard deviation and downside
deviation.
One last note: the
standard deviation of the error
term was 6.3383 %, which helps show that in the short run, the volatility
of implied volatility is a larger effect than mean - reversion.
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.
And historically the value style has produced slightly higher returns for about the same risk — let's say 14 % to 15 %
standard deviation, similar to the index in
terms of risk, with slightly higher returns.
Both
standard deviation and Sharpe ratio define risk in
terms of volatility.
Standard deviation, a statistical
term that provides a good indication
of volatility, ensures the bands will react to price movements and reflect periods
of high and low volatility.
Grouped funds are plotted in
terms of 3 year annualized
standard deviation versus 3 year compound return
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.
It is much more than a measure
of correlation — it's regression analysis, and it gives you a better long -
term picture than
standard deviation.
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).
Also, note the observation that the long -
term Treasury fund, with no credit risk but large
term risk, has a higher
standard deviation of annual returns than does the high - yield corporate bond fund, which has significant credit risk but much less
term risk.
The first is
standard deviation, a statistical measure
of how much annual returns vary around their long -
term average.
For instance, an U.S. investor in Canadian stocks would have experienced real returns with a
standard deviation of 16.8 % in local currency, 4.6 % in exchange rate and 18.4 % in U.S. dollar
terms.
If each year's stock return were totally independent
of the past, the
standard deviation would fall in accordance with the square root
of N. Even if we were to allow for a short -
term memory
of two or three years (i.e., momentum), independence would still imply this square root
of N behavior.
Yes greater risk profile leads to greater return profile, but not necessarily at reduced risk (if we're talking risk in
terms of volatility or
standard deviation).
And to quantify that volatility in a mutual fund ETF or portfolio
of investments, investors typically turn to
standard deviation, a measure that calculates how much an investment's annual return fluctuates around its long -
term average annual return.
(3) Black - Scholes calculation based upon certain assumptions for Convertible Security including: MNOV stock price
of $ 1.59 as
of March 13, 2009; convertible security exercise price
of $ 4.00; assumed risk - free interest rate
of 0.44 %; one - year
term for convertible security; and
standard deviation volatility assumption
of 69 % based upon MediciNova's 10 - K filed March 17, 2008.
It maintains an approximate normal distribution that accumulates to an average 1.14 % monthly fair return over 600 months, but with a
standard deviation of 4.67 %, which is a high level
of short -
term volatility.
The
standard deviation of the residuals from a linear regression to annual averages 1975 - 2007 is 0.472, so we expect a range
of variation
of roughly + / - 0.94 deg.C from the long -
term trend.
Before we proceed, it may be useful to define the
term «statistically stationary», the meaning here being that statistical aspects
of the weather (means,
standard deviation etc.) aren't changing.
For much
of the season, the sea ice was tracking close to long -
term norms, though it had a precipitous decline in July, and is now almost two
standard deviations away from the long -
term average.
The MSLP anomaly difference
of Tahiti minus Darwin, normalised by the long -
term mean and
standard deviation of the MSLP difference (Troup, 1965; Können et al., 1998).
You mention»
standard deviation of a set
of non-random numbers» The numbers were generated on a spreadsheet using Excel's random number generator so they the net result was what, in electronic
terms, I would say was real data (signal) and unwanted randomness (noise).
(Top) Time series
of the NPI (sea level pressure during December through March averaged over the North Pacific, 30 ° N to 65 ° N, 160 ° E to 140 ° W) from 1900 to 2005 expressed as normalised departures from the long -
term mean (each tick mark on the ordinate represents two
standard deviations, or 5.5 hPa).
It should be noted that the formula can be used for any level
of uncertainty, not just one
standard deviation (1 sigma), provided the same level
of uncertainty is used for each
term.
The mean
of all the 8 year trends is close to the long
term trend (0.19 ºC / decade), but the
standard deviation is almost as large (0.17 ºC / decade), implying that a trend would have to be either > 0.5 ºC / decade or much more negative (< -0.2 ºC / decade) for it to obviously fall outside the distribution.
In
terms of model error, Y12 investigated only the relationship between the errors
of ensemble mean and
standard deviation of model ensemble members.