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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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8 votes
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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 ...
RRL's user avatar
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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 ...
Quantuple's user avatar
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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
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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 ...
jacques's user avatar
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5 votes

Incorporating idiosyncratic risk as a pricing factor Fama-MacBeth style

By definition idiosyncratic volatility needs to be computed against a candidate asset pricing model. See for example this paper. So my suggestion is: Run your favorite asset pricing model (e.g. the ...
phdstudent's user avatar
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5 votes
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To estimate the parameters when only the characteristic function is known to us

General remarks A difficult but very interesting problem. Some thoughts: Use GMM instead of MLE. MLE is a special case of the generalised method of moments. The characteristic function gives you the ...
Kevin's user avatar
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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 ...
dm63's user avatar
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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),...
Attack68's user avatar
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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 ...
develarist's user avatar
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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 ...
sfmiller940's user avatar
4 votes
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Implementing Fama-MacBeth cross sectional regression

You first run your FF three factor model. And get an estimate of $\alpha$ and $\beta$ for each factor. Then for each month $t$, you run a cross-section regression: $r_{i,t} = \lambda_0 + \hat{\beta}...
phdstudent's user avatar
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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 ...
eSurfsnake's user avatar
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^{\...
RRL's user avatar
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4 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 ...
user15745325's user avatar
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 ...
Malick's user avatar
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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, $$ \...
Chris Taylor's user avatar
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3 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 ...
Quantuple's user avatar
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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
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 ...
Richard Hardy's user avatar
3 votes
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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 ...
AlRacoon's user avatar
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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 ...
demully's user avatar
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2 votes

How to fit exogenous + GARCH Model In Python?

It is an old thread. Just pointing out that capability is available in ARCH package now for the benefit of future readers. https://pypi.org/project/arch/ Volatility models ARCH GARCH TARCH EGARCH EWMA/...
P RAY's user avatar
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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 ...
kris123456's user avatar
2 votes

Estimate American-style option delta from similar options

I'll summarize my comments into an answer. What you do with missing deltas depends on the purpose of the analysis. If the purpose is to study the market then I'm afraid the best is to drop these ...
Aksakal almost surely binary's user avatar
2 votes

Estimating realised gains given growth rate and churn

Assume we start at $t=0$ with $P_0$, there are $t=1...N$ subsequent periods, and at each period-end $t$ an (entirely arbitrary) portion $c$ of our portfolio $P_t$ is churned and $(1-c)$ remains ...
Ivan's user avatar
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2 votes

How to have an unbiased estimation of the standard deviation when using rolling returns?

Your estimator $\hat{s_i}$ for stock $i$ is an unbiased estimator of its latent standard deviation $\sigma_i$ (which is constant for your model). When applying your "window rolling" for ...
skoestlmeier's user avatar
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2 votes

How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?

With a multivariate normal model, the portfolio has a univariate normal distribution (mean and variance are easy), so it reduces to a scaled univariate quantile.
userid is i's user avatar
2 votes

Is there an issue with estimating future returns from autocorrelated returns?

If you are predicting the return from time "i" to time "i+l" then you cannot use any information beyond time "i" to train your model. As it appears you are getting returns from "i-5" to "i" and ...
wjamdanf1234's user avatar
2 votes

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

The essential difference arises not from the lower bound on volatility, but rather the fact that volatility is mean-reverting and asset values are not. To make this clearer, note that a period-$T$ ...
Brian B's user avatar
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