If you believe as we do that risk can not be adequately explained by a single number such
as standard deviation of return, but is rather the potential for the respective portfolios to face future capital impairment, it becomes important to compare the fundamental character of the manager's portfolio to that of the benchmark.
The theory is that, using relationships between risk and return such as alpha and beta, and defining risk
as the standard deviation of return, an «efficient frontier» for investing can be identified and exploited for maximum gain at a given amount of risk.
Ideally, investors want to take three factors into account in portfolio construction: the expected return for each asset, the expected risk (normally expressed
as the standard deviations of return) and the co-movement of each asset.
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.
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.
Ideally, investors want to take three factors into account in portfolio construction: the expected return for each asset, the expected risk (normally expressed
as the standard deviations of return) and the co-movement of each asset.
Not exact matches
Volatility profiles based on trailing - three - year calculations
of the
standard deviation of service investment
returns as of February 28, 2017.
As long as the returns of the assets within the portfolio are not perfectly correlated, the standard deviation of the portfolio must be less than the average standard deviation of the asset
As long
as the returns of the assets within the portfolio are not perfectly correlated, the standard deviation of the portfolio must be less than the average standard deviation of the asset
as the
returns of the assets within the portfolio are not perfectly correlated, the
standard deviation of the portfolio must be less than the average
standard deviation of the assets.
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.
Calculate daily realized volatility
of IEF
as the
standard deviation of daily total
returns over the past 21 trading days, multiplied by the square root
of 252 to annualize.
«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.
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.
Similarly to its predecessors, the fund failed to outperform its reference ETF portfolio which had a slightly smaller volatility, measured
as the
standard deviation of monthly
returns.
For this comparison, Sharpe is defined
as fund annualized percentage
return (APR) minus 90 - day TBill APR divided by fund annualized
standard deviation STDEV, all over the same period, which is lifetime
of fund (or back to January 1962).
I also have had a lower amount
of volatility (
as measured by
standard deviation of day - over-day
returns) then my benchmark index (the S&P / TSX Composite Index).
Its cumulative
return was lower and the volatility (measured
as a
standard deviation of monthly
returns) higher than those
of its reference ETF portfolio.
The efficient frontier is a curve which represents all the points where for a given level
of risk (
as measured by
standard deviation)
of a portfolio you are achieving the optimal rate
of return.
That's because the
standard deviation of returns changes over time,
as does the correlation between asset classes.
The fund's volatility, measured
as a
standard deviation of monthly
returns, was comparable to that
of the reference ETF portfolio.
The following chart shows rolling volatility (measured
as a
standard deviation of two years
of monthly
returns) and accompanying statistics for the portfolio:
It beat its Russell 2000 ® index benchmark in one -, three -, five - and ten - year periods
as well
as since inception through 2013, at a comparable risk level measured by a
standard deviation of returns.
If one compares the market timer's
return to that
of a portfolio
of stocks and cash weighted to have the same
standard deviation as the market timer's portfolio, the result is that the market timer must be correct 74 %
of the time in order to perform better than the passive portfolio
of the same risk.
During the 1978 - 2017 time frame, the S&P 500 Index
returned 11.81 % with a risk factor
of 15.20 %,
as measured by
standard deviation, whereas the Barclays Bond Index
returned 6.99 % with a
standard deviation of only 4.19 %.
This often serves
as the benchmark in most portfolio discussions and has been around for ages
as the go - to portfolio.The average rate
of return on this portfolio since 1972 has been
of 5.8 % with a low
standard of deviation of 11.6 %.
The volatility
of the reference portfolio, measured
as the
standard deviation of monthly
returns, was slightly below that
of the fund.
Tracking error is reported
as a
standard deviation percentage difference, which reports the difference between the
return an investor receives and that
of the benchmark he was attempting to imitate.
*
As measured by the
Standard Deviation (volatility)
of our monthly
returns versus the TSX Composite.
For implied volatility it is okey to use Black and scholes but what to do with the historical volatility which carry the effect
of past prices
as a predictor
of future prices.And then precisely the conditional historical volatility.i suggest that you must go with the process like, for stock
returns 1) first download stock prices into excel sheet 2) take the natural log
of (P1 / po) 3) calculate average
of the sample 4) calculate square
of (X-Xbar) 5) take square root
of this and you will get the
standard deviation of your required data.
Since the
standard deviation of returns is commonly used
as a measure
of portfolio risk, a High volatility measurement indicates that holding the motif in the past subjected the holder to higher fluctuations.
However, the fund's volatility (measured
as standard deviation of monthly
returns) was higher than that
of the reference ETF portfolio.
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.
The fund subtracted value compared to its reference ETF portfolio that had a similar volatility, measured
as the
standard deviation of monthly
returns.
The fund's volatility, measured
as an annualized
standard deviation of monthly
returns, was about 10 % above that
of the reference portfolio.
To investigate, we consider two measures
of U.S. stock market volatility: (1) realized volatility, calculated
as the
standard deviation of daily S&P 500 Index
return over the last 21 trading days (annualized); and, (2) implied volatility
as measured by the Chicago Board Options Exchange Market Volatility Index (VIX).
She defines idiosyncratic volatility
as the
standard deviation of daily residuals from monthly regressions
of returns (in excess
of the risk - free rate) for each stock versus Fama - French model factors.
For both, we calculate VoV
as the
standard deviation of volatility over the past 21 trading days and test the ability
of VoV to predict SPDR S&P 500 (SPY)
returns.
Calculated by annualizing the
standard deviation of the fund's daily
returns over the 1 - year period ended
as of the date
of the calculation.
Tracking error Tracking error is defined
as the
standard deviation of the difference between the fund's
returns and the
returns on the index.
The volatility
of the reference portfolio, measured
as the annualized
standard deviation of monthly
returns, was slightly higher than that
of the fund.
Risk adjusted
returns would favor municipal bonds
as equities have done it the hard way with a
standard deviation (a measure
of volatility)
of over 2.6 % while munis have seen a
standard deviation of under 1 %.
Low Volatility: This is the ultimate risk measurement
as gauged by the
standard deviation of returns.
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).
Volatility profiles based on trailing - three - year calculations
of the
standard deviation of service investment
returns as of February 28, 2017.
As per data of the past 3 years, the fund's standard deviation, i.e., the volatility of the returns of the fund vis - à - vis its average, is 13.43 % as of 31st July 201
As per data
of the past 3 years, the fund's
standard deviation, i.e., the volatility
of the
returns of the fund vis - à - vis its average, is 13.43 %
as of 31st July 201
as of 31st July 2017.
As per data of the past 3 years, the fund's standard deviation, i.e., the volatility of the returns of the fund vis - à - vis its average, is 10.72 % as of 31st May 201
As per data
of the past 3 years, the fund's
standard deviation, i.e., the volatility
of the
returns of the fund vis - à - vis its average, is 10.72 %
as of 31st May 201
as of 31st May 2017.
When talking about «low volatility products,» Yasenchak is referring to portfolios that «specifically seek benchmark - like
returns, over the full market cycle, with a total volatility, measured
as the
standard deviation, falling considerably below that
of the index.»
Risk: The variability
of returns, often expressed
as Standard Deviation, associated with a given asset.
Risk means trying to avoid loss on every name in my portfolio, not avoiding loss on the portfolio
as a whole, and certainly not
standard deviation of returns, or even worse, beta.
The Levy - Gunthorpe
standard deviation is superior to calculating the annualized
standard deviation of returns as the product
of the
standard deviation of the monthly
returns multiplied by the square root
of 12.