Questions tagged [standard-deviation]
The standard-deviation tag has no usage guidance.
86
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Standard Deviation and Monotonicity property
I just read that standard deviation is a coherent risk measure, and therefore it should satisfy the monotonicity property:
$X_1 \geq X_2 \implies \rho(X_1) \leq \rho(X_2)$ where $X_1,X_2$ are asset ...
1
vote
1
answer
206
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Figuring out how TradingView calculates the Sharpe ratio [closed]
This is the simplest backtest I've come up with, yet I can't figure out how TradingView has calculated the Sharpe ratio to be 0.577. I've set the risk_free_rate=0. Is it possible to extract the ...
4
votes
1
answer
160
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Deriving an Analytical Expression for Standard Deviation of Log Returns
I am looking to find an expression for the standard deviation log returns of a stock price process.
I have a stock price which follows the following dynamics:
$dY(t) = Y(t)(r(t)dt + η(t)dW(t))$
Here,...
1
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1
answer
157
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Standard deviation of annual returns formulas return all different values
I am trying to build a monte-carlo simulator for predicting the possible future values of a portfolio. I have daily historical prices for several assets but I don't know how to correctly estimate ...
2
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0
answers
243
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Does a portfolio on efficient frontier also lie on CML(capital market line)?
I am trying to solve this question:
Assume that CAPM is true. The risk-free rate is 3%, the expected return on the market portfolio is 10% and the standard deviation of the return on the market ...
2
votes
1
answer
555
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How does autocorrelation bias annualizing variance?
I read somewhere that autocorrelation prevents someone from annualizing variance. But how does it bias it? Let's say you have daily returns. If autocorrelation is high, should that overstate or ...
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1
answer
906
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Daily vs Monthly vs. other return for volatility calculation?
I thought I read/heard somewhere that annualized volatility, using monthly returns vs daily returns is usually lower. With that said, I can't seem to find any papers on this.
Does anyone have any ...
0
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0
answers
238
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What are the advantages and disadvantages of converting standard deviation of higher-frequency returns to a lower sampling frequency?
I have a minute-by-minute price series of a stock. I would like to calculate the daily volatility or standard deviation of the stock's returns.
One way to do so is to get the end-of-day prices (i.e. ...
1
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0
answers
94
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Combine standard error in finite difference with Monte Carlo
I'm using Montecarlo to estimate the value of an option,
$$\overline V(S_T, r, \sigma, T;N)=\mathbb{E} \left[V(S_T, r, \sigma, T)\right]$$
which comes with a standard error $SE$.
I'm using "bump-...
2
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2
answers
729
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How to annualize Sharpe Ratio if monthly returns are serially correlated? Calculation of autocorrelations
I am looking at a data set of 60 monthly returns (last 5 years) and want to calculate an annualized Sharpe Ratio.
The usual way of doing this is to calculate the monthly Sharpe Ratio first, and then ...
2
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1
answer
3k
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Correlation Matrix to Variance Covariance Matrix Portfolio STDEV
I have a correlation matrix that I wanted to convert into a variance covariance matrix. I also have the weights in a column in excel along with each assets standard deviation. What excel function can ...
0
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1
answer
93
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Verify numerically relation between mean deviation and standard deviation
I was reading "We Don’t Quite Know What We Are Talking About When We Talk About Volatility" by Goldstein and Taleb, and I was trying to quickly verify numerically the relation between mean ...
4
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5
answers
3k
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Why is the price of an ATM straddle not the same as the "dollar move" from implied volatility?
Knowing that implied volatility represents an annualized +/-1 Standard Deviation range of the stock price, why does the price of an ATM straddle differ from this? Also for simplicity, no rates, no ...
3
votes
1
answer
365
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Estimating volatility of a geometric Brownian motion at different sample rates
I have troubles estimating volatility (= standard deviation of log returns) when the data is re-sampled at different sample frequencies.
Problem
I have generated a time series data using a geometric ...
1
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0
answers
187
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returns, standard deviation and mean absolute deviation
I'm trying to understand the relationships between return, standard deviation and mean absolute deviation.
I saw someone mention:
$daily return * 16 \approx annualized volatility$
$weekly return * 7.2 ...
1
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0
answers
57
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Why standard errors in macro-level variables are normally higher than that in firm-level variables?
From this dicussion, the commentor said
Lastly, firm fixed effects may absorb more variation and likely
reduced the size of their standard errors.
In practice, I also mainly see that the standard ...
0
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0
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115
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Intraday volatility pattern of Emini
I have the series of 1-min logarithmic returns of Emini future from 2007 to 2020
I calculated the standard deviation of each return at a fixed time of day and then I plotted the results (see image).
I ...
4
votes
1
answer
195
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Reconciling Two Claims About Volatility Under Fat Tails
I have read the Wikipedia article on volatility, and Nassim N. Taleb's Incerto, and found two statements attributed to Mandelbrot's views, which appear to be in contradiction.
Taleb (who was mentored ...
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1
answer
302
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Equivalence of Standard Deviation and Variance as a risk measure - WRONG?
In Modern Portfolio Theory, I often see that people seem to view Standard Deviation and Variance as equivalent. Example from Markowitz himself:
"Thus far I have used the standard deviation ...
1
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0
answers
532
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How to annualise hourly returns?
I have hourly open,high,low,close candles data for a particular asset. I wrote my own algo and some back testing code that replays the data from the past hourly candles to calculate the total return ...
0
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1
answer
198
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Why are these two methods to calculate standard deviation gives very different answers? [closed]
Values=[100, 101, 102.01, 103.03]
Method 1: Sum of the squared differences from the mean
Mean = 101.51
std = sqrt(((100 - 101.51)^2 + (101 - 101.51)^2 + (102 - 101.51)^2 + (103 - 101.51)^2) / 4) = 1....
2
votes
1
answer
805
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T-statistics on monthly returns vs annualized monthly returns
eqI am very confused about a very basic question. This is probably more statistics than quantitative finance, but still, should be useful for this stackexchange board as well.
Let's assume I have ...
1
vote
2
answers
870
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Standard deviation formula with Short selling- Markowitz model
I have 2 fast quastions.
Before I begin I want to show you that I found minus before SD of bills in the book Principles of corporate finance(1.screen). I know SD of bills is zero and minus in this ...
0
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2
answers
160
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Empirical equivalent for implied vol
Implied volatility is supposed to show volatility of the underlying over next k days where k - maturity of the option. Say our stock price is $S_t$ and percentage return is $r_t$. Then which empirical ...
2
votes
2
answers
192
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Industry or academic standard frequency to report the return, standard deviation, and Sharpe ratio?
Everyone (funds, banks, academics, financial information sites etc.) reports the annualized return, standard deviation, and Sharpe ratio. Yet we never get to know what the basis of their computation ...
0
votes
1
answer
531
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Beta and standard deviation
IS beta of a stock formula equals to correlation coefficient multiply with annualized standard deviation of stock A divide annualized standard deviation of market . i am not sure whether to use ...
1
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0
answers
92
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Get the weights of porfolio variance given standard deviation
I am trying to create a Simulated Portfolio Optimization based on Efficient Frontier on 50 stocks, which you can find the csv here. Yet it already takes me several minutes to get a suboptimal solution:...
0
votes
0
answers
254
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Calculation of portfolio beta (CAPM)
Let the market risk be $\sigma_m=28\%$. A portfolio consists of four stocks, all with the same weight ($w_i=0.25$ for all $i$). We also know that $\sigma_a=18\%,\sigma_b=36\%,\sigma_c=22\%,\sigma_d=17\...
0
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0
answers
43
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how to calculate yearly volatility from weekly obersvations over 179 weeks?
I am working right now at something and I want to get sure that I am not doing any mistakes - maybe you can help me:
I collected weekly returns from a stock over 179 weeks and know I want to ...
1
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1
answer
926
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What is the difference between standard deviation, volatility and quadratic variation?
What is the difference between standard deviation, volatility and quadratic variation?
As I know, volatility is the standard deviation of the log returns, so they are basically the same. (One of ...
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0
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106
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Selecting strike prices for put-writing strategy based on Z-scores
I'm trying to replicate the put-writing strategy of Jurek and Stafford from 2015 (The Cost of Capital for Alternative Investments, Jrl. Fin. SSRN). Their strategy writes index put options on the SP500,...
1
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0
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65
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Where do some numbers in finance papers which seem to appear out of nowhere come from?
On p. 1671 in the paper Kempf/Manconi/Spalt (2017, RfS), Distracted shareholders and corporate actions it says (I think it is in the context of a log regression):
Those effects are economically ...
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1
answer
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Custom normalisation from 0 to 20
I want to normalise from 0 to 20
For example right now I do normalisation with dynamic outlier exclusion , using median.
So it works fine for some values like below
...
1
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1
answer
319
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Normalization of volume
suppose we have volumes every minute like below
100, 200 , 19, 0 , 200 , 12 , 100
I want to convert all these numbers to less than 10 , where 10 is max and 1 is ...
0
votes
2
answers
353
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Estimation of volatility into Black-76 formula
I am trying to estimate the (annualized) volatility that should go into an European Swaption (such as 2y5y).
Given we take the black76-formula, where the discounting is the term outside the ...
3
votes
1
answer
2k
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Calculating "annualized" standard deviation from monthly returns and the different month lengths
I have the monthly returns and want to estimate an "annualized" standard deviation.
An industry-standard way seems to be the following:
$$
\sigma_a = \sqrt{12} \sigma_m,
$$
where $\sigma_m$ is "...
1
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0
answers
101
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One day standard deviation of a portfolio (long/short, different scalars)
I am attempting to calculate the expected one-day standard deviation of a portfolio in dollars. In other words, I am looking for the following: "I expect my portfolio to move _______ dollars on ...
2
votes
1
answer
638
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annualized volatility formula is an approximation?
suddenly having troubles with the annualized volatility formula... is it really an approximation?
one usually writes the standard deviation of the yearly percentage change in the stock price as $$\...
1
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1
answer
2k
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How to calculate standard deviation cone around expected returns?
I would like to evaluate the returns of an investment manager who has given me their return and volatility expectations for their fund. I would like to calculate both 1 and 2 standard deviations from ...
0
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0
answers
64
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Labeling Returns in 5 categories based on BL view approach
I have to label a time series of returns into 5 categories based on the Black Litterman view approach.
The categories should look as follows:
very bullish: + 2 std. dev.
bullish: + 1 std. dev.
...
3
votes
1
answer
172
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Dorfleitner's Standard Deviation
Can someone please advise how to compute the following (as my results go into thousands):
E.g. I have used
and the result (for T=12) = 580103.7261
Thanks
2
votes
1
answer
376
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In-sample volatility measurement
I would like to know what is the most reasonable way to measure volatility in a sample of past observations. Aside from standard deviation, are more complex models like GARCH used for (historical) ...
1
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1
answer
109
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Efficient Frontier Graph
I'm writing some C code to create different portfolios using a few stocks that are given as inputs. I am having some trouble trying to find if these results are correct. My biggest hesitation is that ...
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1
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3k
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Annualising standard deviation (monthly, quarterly data)
The question I have refers to annualised standard deviation.
For example, I have various funds monthly returns data for the period 1980-2019. Some of them report data for e.g. 13, 19, 43, 56 months ...
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2
answers
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Annualisation of Downside Deviation
Is it possible to annualise the downside deviation? If so, on the basis of what theory?
The downside deviation (DD) of a series of daily returns is computed according to the formula:
$\text{DD} = \...
0
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0
answers
71
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Disalignment between global standard deviation and mean of rolling standard deviation
Ciao,
I am working on proprerties of time series. I was trying to deduce an estimate of standard deviation of a process from the series of rolling standard deviation but I've got some issues when I ...
1
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1
answer
237
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Markowitz expected return time
This is perhaps a rather silly question for the more experienced people in the community but it has been puzzling my mind for a while.
Let's say we have a portfolio of 10.000 dollar.
We will apply ...
3
votes
1
answer
236
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Interpretation of IV and its use in stock movement prediction
I would like to validate my understanding of IV as a prediction tool.
Black-Scholes model is based on the assumption that rate of return of a stock is a Wiener process:
$$ \frac{dS_t}{S_t} =\mu \,...
1
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0
answers
646
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Overlapping Data
I have a daily time series data spanning over 22 years. I need to compute some meaningful yearly standard deviation statistics / generate probability distribution and estimate tail risk. 22 years ...
3
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1
answer
716
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How to have an unbiased estimation of the standard deviation when using rolling returns?
I want to estimate the weekly standard deviation of a lognormal process in a usual setup.
$$
\frac{dS}{S} = (\dots) dt + \sigma dW
$$
where $\sigma$ is a constant and $W$ a brownian motion.
The ...