# Questions tagged [standard-deviation]

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### Subpar Results of Historical Portfolio Optimization with Few Assets

Probably a simple question to the P-Quants here, but if you performed portfolio optimization using a historically calibrated covariance matrix (a rolling month of daily returns) with very few assets, ...
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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 ...
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### 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 ...
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### 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, $P = \sum_{n=1}^N p_n / N$...
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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 ...
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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 ...
• 141
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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 vote
216 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 ...
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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 ...
776 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 ...
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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 ...
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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. ...
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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-...
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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 ...
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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 ...
95 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 ...
5k 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 ...
433 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 ...
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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 ...
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1k 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 ...
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1 vote
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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,...
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1 vote
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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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### 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 vote
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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 ...
397 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 ...
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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 "...
• 131
1 vote
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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 ...
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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 vote
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 ...
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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. ...
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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
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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) ...
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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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### 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 ...
1 vote
197 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} = \...
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