15 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 ...
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  • 13.9k
7 votes

What is the preferred GARCH method in practice?

I personally use the simple Garch(1,1) for volatility filtering in the risk management area. In fact in most cases I don't even estimate the parameters, I stick 0.94 for mean reversion, 0.04 for the ...
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  • 4,227
7 votes

What good papers of short term (<30 seconds) volatility estimation

Very interesting question. I am not an expert on the subject, however, I was able to find a collection of papers on the subject that should get you started. Here is a good and very informative paper ...
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  • 1,335
6 votes
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Estimating implied volatility of an index component with no vanilla options market

There is no standard approach to this problem to the best of my knowledge. Different approaches exist and each has its own pros and cons as usual. To mention a few: Information-based methods: these ...
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  • 14k
6 votes
Accepted

Are asset return means difficult to predict because they have no lower bound?

To answer, the assertion that volatility is easier to predict than expected return requires clarification. The phrase "easier to predict" is particularly ambiguous. To me this means that the ...
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  • 3,365
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 ...
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  • 2,760
5 votes

Unsmoothing of returns

Did you try solving for $w_k$? $$\bar{r}_t = \sum_{k=0}^p w_k r_{t-k}$$ $$\bar R = W R$$ Since you probably have $t>>k$, you can solve for $W$ using OLS $$\bar R = W R +\varepsilon$$ -- ...
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5 votes
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Change of measure

You can't have a precise argument without a precise definition. In general, the appropriate notion of integral here is the Lebesgue-Stieltjes integral. In a fairly general setup, let $F: \mathbb R \to ...
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  • 186
4 votes

2-step estimation of DCC GARCH model in Python

If $\log{(|R_t|)}$ is your first term, I'm not sure why this is a matrix. Modulus (determinant herein) applied to a matrix $R_t$ gives a scalar. If your implementation in python produces a matrix, ...
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4 votes
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Estimating correlation using EWMA

The $\lambda$ value used in the original paper is arbitrary, but you can estimate that by assuming (in the simplest case) 2 assets and running the following model: $\sigma^2_{12,t+1}$ $=$ $\lambda$$*$...
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  • 2,446
4 votes
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How to estimate today's closing price?

Since you're asking on a quant finance forum, the mathematical approach would be Decide on a model that the stock price follows, and Compute the expected value of the price, conditional on the most ...
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  • 2,748
4 votes
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Unsmoothing of returns

Thanks @Aksakal for suggesting Kalman Filter. Here I provide more details. We will view it as a state-space model: $$ \begin{split} z_t &= A_t z_{t-1} + B_t u_t + \epsilon_t, \\ y_t &= C_t ...
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  • 273
4 votes

Bond yield to maturity vs current interest yield

Not really. For infinite maturity bonds we have $Price = coupon/yield$ so your approximation is actually correct. However for short dated bonds it is not a good approximation. For example , a 1 ...
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  • 14.1k
4 votes
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Neural Networks for Estimation of Unmarked Private Asset Returns from Market Data

Based on an my updated understanding of your problem you have a portfolio consisting of $N$ illiquid assets. Valuations are not real time and usually lagged, by say, upto 3 months (or slightly longer),...
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  • 8,079
4 votes
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Methods for superior estimates of returns in m.v. portfolio optimization

Expected returns are very difficult to estimate reliably without incurring estimation error as found out by Merton (1980) "On estimating the expected return on the market". This is why estimating ...
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  • 2,835
4 votes

Arithmetic Brownian Motion in Market Making papers

The time step typically depends on the context. Due to the self-similarity of Brownian motion the mathematics should work similarly on any time scale, although the resultant estimates might vary ...
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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 ...
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4 votes
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Question on the use of a limit in a proof

It makes no sense to write $C^h \to e^{\delta C}$ as $T \to \infty$ when $C = I_K +\Lambda/T$ since $e^{\delta C}$ on the right-hand side depends on $T$. What can be confirmed is $(C^h)_{k,k} \to e^{\...
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  • 3,365
3 votes

GJR-GARCH with $\alpha = 0$ as parameter estimate

$\alpha=0$ does not imply constant volatility. Consider just a simple Garch(1,1): $$\sigma^2_t = \omega + \alpha \eta_t^2 + \beta \sigma^2_{t-1}$$ Note that: $$\sigma^2_t = \omega + (\alpha + \...
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  • 6,810
3 votes

What is the preferred GARCH method in practice?

Interesting question, as All the answers (including mine) could not be generalized unfortunately. As far as I am concerned, I use a univariate EGARCH for risk modelling purposes (Filtered Historical ...
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  • 315
3 votes
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Streaming update of the GARCH(1,1) model

If you estimate your model via Maximum Likelihood method, you are forced to re-estimate the full model. This is due to the fact that estimates are values which maximize the full likelihood, the latter ...
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  • 2,514
3 votes
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What volatility estimator for continuous data and small time window?

First, you should use an exponential moving average, since the amount of state you need to keep is much smaller than for a simple moving average. Second the well known estimator of volatility, $$ \...
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  • 5,628
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 ...
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3 votes

Do EWMA weights remove autocorrelation in asset returns?

EWMA (and other sort of moving averages) introduces positive autocorrelation into otherwise uncorrelated returns. The fitted values of EWMA are linear combinations of past returns, and the constituent ...
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3 votes
Accepted

A simple question about VaR estimation

I think there is a mistake in your definition. It should be between "50th and 51st" sorted numbers. 95% VAR means 5% is in the tail. 5% * 1000 = 50. The 95% VAR will be the 50th worst ...
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  • 5,325
3 votes

Do portfolio mean and portfolio variance have probability distributions?

Yes, they can/do. But you have to drink the proverbial Kool-Aid(or taking the blue pill is probably the more relevant metaphor these days ;-), and approach this as a Bayesian inference problem. So ...
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  • 4,926
3 votes

How does yahoo calculate Growth Estimates

5 year forward estimates comes from Refinitiv IBES (Institutional Broker Estimate System). It will be the mean estimate from all the analyst that cover the stock that report into IBES. It’s used ...
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2 votes

Predicting stock returns - in a panel data specification or by using portfolio formation strategies?

Both approaches can be useful. For stocks, sorting into quantiles is popular because it's easy to understand and explain it's a simple matter to build factor portfolios and track or backtest their ...
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  • 876
2 votes

What is Estimation Risk - VAR Backtest

Even in calculating VAR, you have certain assumptions / constants / random numbers being used. Hence, even your VAR calculation is not 100% correct. So, you are estimating VAR and you hedge similar ...
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2 votes
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How to approximate the Carr-Madan decomposition formula?

Carr-Madan formula tells you that the European-style payoff $f(F_T)$ can be decomposed as: $$f(F_T)=f(\kappa) + f'(\kappa) [(F_T - \kappa)^+ - (\kappa - F_T)^+] + \int_0^{\kappa} f''(K) (K-F_T)^+ \ d ...
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