# Questions tagged [variance]

Used for questions related to statistical measure "variance", i.e. a second central moment of a random variable. The variance is a risk measure.

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### Multiplicative Metric Variance

I come from a math/statistics background and as learned some stuff as a data analyst I learned a certain technique to calculate period to period variances between some metrics. I was wondering if ...
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1 vote
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### Single outsized daily return value creates substantive discrepancy between annualized variance calculated from daily vs monthly returns

I am new here, and to the field. I hope my clunkiness in expressing myself can be forgiven. My situation is as follows: I have around three years of daily return data for some financial asset. Out of ...
103 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 ...
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### Bessel Correction and Geometric Brownian Motion

Does it make sense to use bessel's correction for standard deviation and variance when fitting the drift and volatility parameters of geometric brownian motion to historical return data for a security....
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### What is the intuition behind the VIX formula offset term [duplicate]

In the formula for the VIX we have that the spot value for the VIX is: The first part of this equation is exactly the formula for the price of a variance swap which is the present value of realized ...
196 views

### constant dollar Gamma for variance swap

Here is the result of Gamma for Variance swap. I think $S_t$ is the only variable in $\sigma^2_{Exected,t}.$ Then how could we get the presentation of Gamma: $$\dfrac{1}{S_t^2},$$ there should be some ...
94 views

### Does the expected return increase with variance for stocks? [duplicate]

I took a historical dataset of ~2600 stocks and computed the 30-day returns for non-overlapping windows, for a 9 year period. For the returns, I computed the mean and variance. Then I plotted the mean ...
262 views

### What is the Fair Strike in a Var/Vol Swap and how does it relate to its price? [closed]

I am a student trying to price volatility and variance swaps. People who price those two products usually try to get the "fair strike", and don't seem to care about the price. However, I ...
175 views

### How to derive numeric option VaR with delta-vega normal approach?

For an option with price C, the ΔC, with respect to changes of the underlying asset price S and volatility σ (first-order approximation), is given by $\Delta C=\delta \Delta S+\nu\Delta\sigma$, where ...
53 views

### Bias-Variance tradeoff for Covariance Estimation w/ Different Frequencies

In general, what does the bias-variance tradeoff look like when estimating covariance matrices with varying return frequencies (i.e. daily, weekly, monthly returns)? From my observations I've noticed ...
1 vote
384 views

### Calculating variance of long/short portfolio

Say I have a portfolio of stocks, stock A, stock B and stock C, with the below positions: stock A: long 100 USD stock B: long 50 USD stock C: short 200 USD How do I calculate the portfolio variance ...
208 views

### Smile wings and varswap pricing

Is it true that far wings of the volatility smile have an outsized influence on the price of a variance swap? Is there a mathematical argument demonstrating this idea? What do we generally refer as ...
107 views

### Compute monthly realized variance for Fama-French factor

I need to compute monthly realized variance from daily data for Fama-French factors. Knowing that Fama-French factors is the difference of return between different type of stocks, for example SMB ...
1 vote
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### Minimizing variance of a long short equity portfolio in practice

I understand the finance 101 explanation of how to minimize variance of a long-short portfolio using a covariance matrix. I also know that it doesn't really work because the covariance matrix is ...
1 vote
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### Calculating monthly UST3M returns

I am trying compute a variance/covariance matrix for 5 stocks using monthly returns. I plan to use CAPM (using monthly log returns) as the expected return and the US 3-month Treasury Bill (UST3M) ...
1 vote
349 views

### Compute monthly realized variance from daily data

I am confused about the correct formula to compute monthly realized variance from daily data. What is the first sigma in the picture: sum or average? I mean, after subtracting each observation from ...
1 vote
416 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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### Variation of the trading range

Example: The trading range (in points) for each of the last 5 trading days for asset A is: 5,21,2,15,32 and for asset B is: 5,6,5,5,5. Is there an indicator that ranks assets based on variation of ... 471 views

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### Covariance Shrinkage - Am I getting the right variances?

I am looking into a quite simple task: shrinking the sample covariance matrix of a minor sample of monthly returns data on 5 different assets. I am using Python to process my data and have been using ...
1 vote
329 views

### looking for recommendation for a var/vol swap trading book

I am aware this book - volatility trading by Euan Sinclair, and it's nice book. But I am looking for book focus on var/vol swap trading, i.e., introduce about trading strategy/ideas by using var/vol ...
37 views

### Statistical Inference of Variance Risk Premia

Good afternoon, I am currently following Carr and Wu (2009) to compute variance risk premia from options written as (RV-EV)*100 for the payoff of a long var swap position. Now I want to see whether my ...
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### Is scaling the standard deviations in the VaR formula (parametric) equivalent to scaling the VaR figure at the end?

I have come across people calculating parametric VaR who scaled the standard deviations by say square root of 10 to scale up to a 10 day horizon. Elsewhere I have seen textbooks suggesting that it is ...
340 views

### Variance of Log Returns

Consider an asset held for $n$ time periods with weakly stationary log-returns $r_t$, $1≤t≤n$. Show that $var(r_1 +r_2 +r_3 +r_4)=var(r_1 +r_2 +r_3)+var(r_1)(1+2ρ_3 +2ρ_2 +2ρ_1)$, where $ρ_k$ is the ...
1 vote
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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 ...
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### Estimating the variance of returns with aggregated data

Say I have an asset return time series: Jan2020: -5% Feb2020: +5% Mar2020: -5% Apr2020: +5% May2020: -5% Jun2020: +5% Q3 2020: +20% Oct2020: +5 Nov2020: -5 Dec2020: +5 Note that 3 months of data is an ...
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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 ...