The calculated approximation of a result which is usable even if input data may be incomplete or uncertain.

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18
votes
5answers
3k views

What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework?

One of the main problems when trying to apply mean-variance portfolio optimization in practice is its high input sensitivity. As can be seen in (Chopra, 1993) using historical values to estimate ...
1
vote
1answer
198 views

Basics about the scaling property of volatility

It is a usual practice to calculate realized volatility $\sigma$ using the square root of the usual variance estimator $\hat{{\sigma}²}$. This is done using the stock log returns (practitioners ...
3
votes
0answers
174 views

Should I use Resampling or Expectation Maximization to compute a robust covariance matrix?

I have several assets, each with different return histories. Some of the assets have 75 days of return history, others have 40 or so days. In calculating a robust covariance matrix, should I be using ...
11
votes
1answer
584 views

rugarch: Joint estimation leads to different results

I want to fit an ARMA-GARCH model to my data using rugarch package in R. First of all, I look at the acf and pacf: ...
2
votes
1answer
701 views

How does the CME set margin requirements on commodity Futures

I am trying to model margin requirements on various commodity futures, however it doesn't seem that the CME has released the formula they use to set these performance bonds. I am sure that they use ...
2
votes
1answer
337 views

Which prices to use to compute realized volatility?

For computation of realized volatility, especially range based volatility, deal prices are commonly used. If Level I data available should the deals data still be used or another measures of spot ...
4
votes
2answers
1k views

Fitting distributions to financial data using volatility model to estimate VaR

I want to fit a distribution to my financial data using a volatility model to estimate the VaR. So in case of a normal distribution, this would be very easy, I assume the returns to follow a normal ...
3
votes
1answer
531 views

How to calculate tracking error given mismatches in available data

Apologies if this is an overly simple question. I have a series of stock returns, and I would like to estimate my portfolio's ex-ante tracking error versus the benchmark (S&P 500) given the ...
4
votes
0answers
221 views

Estimation of ranks of log-returns via copula

I have successfully chosen and estimate a copula for the ranks of the log-returns of my actions. My question is, since I have worked with the ranks instead of directly the log-returns (in order to be ...
11
votes
3answers
2k views

How to detect regime change when estimating asset correlation from historical time series?

Suppose I have two asset time series, $X_t$ and $Y_t$, and I'm estimating their correlation from historical data. I'd like to apply some systematic criterion to estimate what time window I should use ...
8
votes
2answers
772 views

Fitting a generalized logistic distribution

I have a process that estimates the parameters for the following function using the NL2SOL algorithm. $C-[\alpha+\frac{\beta-\alpha}{1+e^-\theta(y_t-\delta)} \vartriangle y_t]$ The process currently ...
2
votes
2answers
975 views

Should I use GARCH volatility or standard deviation in cross-sectional regression?

I want to do a cross-sectional study where the historical, medium-long run volatility of some return series (call it $R_t$) is included as a regressor. Which of the following two estimates of ...
4
votes
1answer
2k views

How do I estimate the parameters of an MA(q) process?

It is relatively easy to estimate the parameters of an autoregressive $AR(p)$ process. How do I do with a moving average $MA(q)$ process?
7
votes
1answer
399 views

What distribution should I apply to estimate the likelihood of extreme returns?

Say I have a limited sample, a month of daily returns, and I want to estimate the 99.5th percentile of the distribution of absolute daily returns. Because the estimate will require extrapolation, I ...
9
votes
1answer
841 views

Musiela parameterization

I have a question regarding the proof of the Musiela parametrization for the dynamics of the forward rate curve. If $T$ is the maturity, $\tau=T-t$ is the time to maturity, and $dF(t,T)$ defines the ...
7
votes
1answer
191 views

What tradeoff is there to using an accurate estimate with a large confidence interval?

I am working on calibrating a Heston model from simulated historical stock data. After obtaining an accurate estimate of the model parameters I found very large 95% confidence intervals for these ...
2
votes
1answer
139 views

How to reconstruct a discontinued economic time series such as the Fed's CP rate?

The old 3-Month Commercial Paper Rate (CP3M) on FRED was discontinued in 1997. I would like to reconstruct this series in a reasonable fashion, so I can use it to analyze more recent events. I was ...
6
votes
2answers
4k views

How can I estimate the degrees of freedom for a Student's T distribution?

I am doing research estimating the value at risk for non-normally distributed assets. I need help in the process of estimating the parameters of Student's t distribution and which method to use. I ...
16
votes
5answers
2k views

How to estimate the probability of drawdown / ruin?

A fairly naive approach to estimate the probability of drawdown / ruin is to calculate the probabilities of all the permutations of your sample returns, keeping track of those that hit your drawdown / ...