16 votes

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

Let me add two points to Quantoisseur's answer. Standard Errors The difference between estimating variances and means is that the standard error of the variance estimator depends on the size of the ...
Kevin's user avatar
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11 votes
Accepted

Returns and logreturns differences

OK, this need have nothing to do with any single sample of data. It's an inherent difference between the behaviour of linear vs logarithmic numbers. Which is what make up your respective simple and ...
demully's user avatar
  • 5,061
6 votes

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

The answer is not statistical. In almost every other area of statistics, estimating the mean is easier (i.e. it can be estimated with higher precision) and estimating higher moments like variance (and ...
kurtosis's user avatar
  • 2,900
4 votes

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

A simpler answer is thus. There are known historical values for the past year for the mean. It's simply the end of year value divided by the beginning value. However, we can't improve the estimate ...
eSurfsnake's user avatar
4 votes

Returns and logreturns differences

It happens because the log function is concave around 1, which means it returns "more negative" numbers for values less than 1 than the positive values it returns for numbers the same distance greater ...
D Stanley's user avatar
  • 1,356
4 votes
Accepted

How to properly calculate the average across multiple correlations?

The problem with sample correlation estimator defined as: $$r_{sample} =\frac{\sum\left(X_i - \bar{X}\right)\left(Y_i - \bar{Y}\right)}{\sqrt{\sum\left(X_i-\bar{X}\right)^2\left(Y_i-\bar{Y}\right)^2}}....
emot's user avatar
  • 876
3 votes

What is better: A negatively skewed return or a positively skewed returns distribution?

The usual answer is that most risk assets tend to exhibit left-skew, with correlations ->1 into the left tail (ie diversification breaks down). And so positively skewed assets have attractive ...
demully's user avatar
  • 5,061
3 votes

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

The sample variance and standard deviation (volatility) formulas are: If your question is why is volatility easier to predict than returns, the intuitive answer is because the numerator is squared ...
Quantoisseur's user avatar
2 votes
Accepted

How to evaluate prediction(s) made of the asset return mean?

The standard error for an estimate of a mean like a mean return - is: $$SE(\bar{r}) = \frac{\sigma}{\sqrt{T}}$$ Now for the stock market, if σ=0.2 and you have 100 years of data, then the confidence ...
phdstudent's user avatar
  • 8,306
2 votes

R code for Ornstein-Uhlenbeck process

The Euler method is simple but it gives an approximate distribution. The method implemented below gives an exact distribution of $X_{t_i}$ and exact conditional distributions $(X_{t_j} \mid X_{t_i})$. ...
Stéphane Laurent's user avatar
2 votes

Why can we neglect the mean in the variance when the time step is very small?

The average return scales linearly with the time period, i.e. $R_N = N R_1$, while the standard deviation scales with the square root, i.e. $\sigma_N = \sqrt{N}\sigma_1$. As the period becomes really ...
fni's user avatar
  • 1,886
2 votes

Verify numerically relation between mean deviation and standard deviation

There's a small typo, Mean absolute deviation, with 0 mean = sum(abs(x))/n Standard deviation, with 0 mean = np.sqrt(sum(x ** 2))/np.sqrt(n) So when you divide MAD over SD you should use: sum(abs(x)) /...
Julie Taylor's user avatar
2 votes

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

This is largely because the variance of stock returns is high relative to their mean. The idea that stock return means are harder to estimate is old and was already known before high frequency data, ...
fes's user avatar
  • 1,727
2 votes

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

I am reading this 2.5 months after the question was asked but I still see some confusion in the answers (or at least I am confused by them). The OP claims that the variance of asset returns is easier ...
Richard Hardy's user avatar
2 votes

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

In fact, a standard way to estimate the volatility does not use the mean at all (the mean is set to zero in the formula), because, as pointed out in @Kevin's answer, it really makes no difference, so ...
Igor Rivin's user avatar
1 vote

Monthly and annual arithmetic mean in valuations?

Returns are usually quoted on annual basis but to arrive at right PV(or FV) you need to know the compounding term. Below are some examples. 12% compounded annually: \$100 now is \$112 in 1 year. [100*...
Tarun Bhasker L's user avatar
1 vote

What is better: A negatively skewed return or a positively skewed returns distribution?

It's a little simplistic to say that positive skew is better, you could for example have a return distribution which is negatively skewed but has a mean of 10%, versus a positively skewed one with a ...
deftfyodor's user avatar
1 vote

Mean estimate in portfolio optimization (Markowitz)

Hi and welcome MathStat2718, The "other standard methods" you ask about are EXACTLY the cute financial products of the last decade. Assume mu is constant across constituents, this gives you ...
demully's user avatar
  • 5,061
1 vote

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

Similar to what eSurfsnake said: Actually, it is because you can estimate the variance exactly if you increase the sampling frequency enough (given that you use time-series data). This is the idea ...
Thiago's user avatar
  • 11
1 vote

Why is asset volatility easier to estimate than the asset mean if it contains the mean?

I would like to posit a more straightforward answer, it is a mathematical illusion. Although this can be solved through formal theory because the distributions are known, doing so would create a long ...
Dave Harris's user avatar
  • 4,299
1 vote
Accepted

GARCH Model Constant in Regression

When calculating the simple arithmetic mean, each observation has an equal weight: $$ \hat \mu^{simple} = \frac{1}{T}\sum_{t=1}^T x_t.$$ If the observations are $i.i.d.$, $\hat \mu^{simple}$ is an ...
Richard Hardy's user avatar
1 vote

the relationship between VaR(0.05) and mean?

I think first understanding what the mean is and what a quantile is would be helpful. The 0.05 quantile is the value for which for a given distribution only 5% of the values are expected to be lower, ...
Stelios Kounis's user avatar
1 vote

ARMA moments proof

For the first, where $|\beta| < 1.0$, you can write it using the lag operator. $x_t (1 - \beta L) = (1 + \theta L) u_t $ $X_t = \frac{(1 + \theta L) u_t}{(1- \beta L)} $ Since $|\beta| < 1.0 ...
mark leeds's user avatar
  • 1,112
1 vote

What is the correct way to calculate the annualized returns from rolling windows starting from monthly returns?

I think it also depends how you defined your returns in the first place: log-returns or arithmetic returns. The formula for geometric mean is for arithmetic returns only, for log returns you can use a ...
Ana B.'s user avatar
  • 91
1 vote

Portfolio diversification and Sharpe ratio

You should start looking at Merton's Portfolio problem. A lot of papers elaborated on the top of it. The principle is "simple": optimize the allocation between one risky asset (Brownian) and a ...
lehalle's user avatar
  • 12.1k

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