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 ...
- 16.2k
8
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 ...
- 3,700
6
votes
Accepted
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 ...
- 14.7k
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 ...
- 2,952
5
votes
Accepted
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 ...
- 186
5
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 ...
- 51
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 ...
- 8,561
5
votes
Accepted
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 ...
- 16.2k
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 ...
- 17.5k
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 ...
- 141
4
votes
Accepted
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 ...
- 3,080
4
votes
Accepted
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),...
- 11.2k
4
votes
Accepted
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}...
- 8,561
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 ...
- 435
4
votes
Accepted
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^{\...
- 3,700
3
votes
Accepted
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:
$$f(F_T)=f(\kappa) + f'(\kappa) [(F_T - \kappa)^+ - (\kappa - F_T)^+] + \int_0^{\kappa} f''(K) (K-F_T)^+ \ d ...
- 14.7k
3
votes
Accepted
Streaming update of the GARCH(1,1) model
If you estimate your model via Maximum Likelihood method, you are forced to re-estimate the full model. This is due to the fact that estimates are values which maximize the full likelihood, the latter ...
- 2,582
3
votes
Accepted
What volatility estimator for continuous data and small time window?
First, you should use an exponential moving average, since the amount of state you need to keep is much smaller than for a simple moving average.
Second the well known estimator of volatility,
$$
\...
- 5,931
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 ...
- 760
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 ...
- 3,166
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 ...
- 6,652
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 ...
- 5,101
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/...
- 121
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 ...
- 1,406
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 ...
- 2,946
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.
- 238
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 ...
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 ...
- 151
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-$T$ ...
- 14.9k
2
votes
Accepted
Do the weights of the exponentially weighted moving average (EWMA) have to sum to 1?
The weights generated by EWMA do not have to sum to 1. Page 81 of the RiskMetrics 1996 document where EWMA was introduced shows an example with 22 observations, similar to yours, that uses the same ...
- 3,080
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