# Tag Info

### 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 ...
• 15.9k
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 ...
• 5,061

### 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 ...
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### 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 ...
• 435

### 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 ...
• 1,356
Accepted

• 3,136
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, ...
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 ...
• 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 ...
• 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 ...
• 12.1k

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