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How do you estimate MC error from a low-discrepancy sequence without using another simulation?

As asked in the question - for a pure random sample, we can estimate standard error by taking the sample standard and divided by square root of n due to IID assumption If I generate $2^n$ samples of N ...
Lost1's user avatar
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1 answer
62 views

How to prove the inequality for the standard deviation of a linear combination of two random variables

The variance of the linear combination V of random variables X₁ and X₂ is given by the following formula: $$ \sigma_{V}^{2} = s^{2} \sigma_{1}^{2}+(1-s)^2 \sigma_{2}^{2}+2 s(1-s) c_{12} $$ where s and ...
bokabokaboka's user avatar
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0 answers
128 views

Time scale of standard deviation of stochastic asset prices

If I run a stochastic interest rate model that is used to price a bond that is a series of cash flows under $N$ scenarios where the price is the average of all the scenarios, $P = \sum_{n=1}^N p_n / N$...
JoeBass's user avatar
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140 views

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 ...
Andrei's user avatar
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1 vote
1 answer
258 views

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 ...
asmani's user avatar
  • 141
4 votes
1 answer
169 views

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,...
user67245's user avatar
1 vote
1 answer
177 views

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 ...
Genfu's user avatar
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273 views

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 ...
TrueWarrior09's user avatar
2 votes
1 answer
666 views

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 ...
confused's user avatar
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1k views

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 ...
confused's user avatar
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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. ...
finstats's user avatar
  • 403
1 vote
0 answers
102 views

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-...
apocalypsis's user avatar
2 votes
2 answers
833 views

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 ...
DavidAJ's user avatar
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2 votes
1 answer
3k views

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 ...
JamieC113's user avatar
0 votes
1 answer
94 views

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 ...
EC_crypto's user avatar
3 votes
5 answers
4k views

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 ...
user avatar
3 votes
1 answer
403 views

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 ...
WolfgangP's user avatar
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1 vote
0 answers
204 views

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 ...
Robbe Van Tillo's user avatar
1 vote
0 answers
57 views

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 ...
Phil Nguyen's user avatar
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115 views

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 ...
AbateFaria's user avatar
4 votes
1 answer
207 views

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 ...
user1337's user avatar
  • 153
1 vote
1 answer
320 views

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 ...
MathStat2718's user avatar
1 vote
0 answers
560 views

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 ...
flojdek's user avatar
  • 21
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1 answer
244 views

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....
lalalal's user avatar
  • 23
2 votes
1 answer
878 views

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 ...
phdstudent's user avatar
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1 vote
2 answers
931 views

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 ...
Miroslav Holub's user avatar
0 votes
2 answers
161 views

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 ...
Kreol's user avatar
  • 117
2 votes
2 answers
196 views

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 ...
Martin's user avatar
  • 273
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1 answer
569 views

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 ...
Renee Fong's user avatar
1 vote
0 answers
93 views

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:...
Revolucion for Monica's user avatar
0 votes
0 answers
258 views

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\...
actuarialboi9's user avatar
0 votes
0 answers
43 views

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 ...
memecon's user avatar
  • 23
1 vote
1 answer
996 views

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 ...
Kapes Mate's user avatar
1 vote
0 answers
108 views

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,...
Mkl's user avatar
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1 vote
0 answers
65 views

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 ...
Aqqqq's user avatar
  • 227
-1 votes
1 answer
40 views

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 ...
Gracie williams's user avatar
1 vote
1 answer
339 views

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 ...
Gracie williams's user avatar
0 votes
2 answers
366 views

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 ...
Kiann's user avatar
  • 622
3 votes
1 answer
2k views

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 "...
Andrey's user avatar
  • 131
1 vote
0 answers
103 views

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 ...
Alex's user avatar
  • 31
2 votes
1 answer
652 views

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 $$\...
SerhiiPoklonskyi's user avatar
1 vote
1 answer
2k views

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 ...
Joe's user avatar
  • 13
0 votes
0 answers
67 views

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. ...
smartquant's user avatar
3 votes
1 answer
173 views

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
Alien_Explorer's user avatar
2 votes
1 answer
384 views

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) ...
Gianluca's user avatar
  • 137
1 vote
1 answer
115 views

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 ...
Matt Bart's user avatar
  • 111
1 vote
1 answer
4k views

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 ...
Alien_Explorer's user avatar
1 vote
2 answers
187 views

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} = \...
Fra_Ve's user avatar
  • 141
0 votes
0 answers
72 views

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 ...
clarkmaio's user avatar
  • 455
1 vote
1 answer
241 views

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 ...
J.W.D's user avatar
  • 23