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Given an expected returns vector and a covariance matrix, one can perform a joint draw and measure the average *cross-sectional* variation across returns for a particular draw.
What is the analytical relationship between a given covariance matrix and expected returns vector (e.g., a multivariate normal distribution)... |
Given an expected returns vector and a covariance matrix, one can perform a joint draw and measure the average *cross-sectional* variation as the standard deviation across returns for a particular joint draw. Or using empirical data, it would be the standard deviation across returns at a point in time.
What is the a... |
I need to estimate the daily VaR of a portfolio of various exposures in $n$ risky assets (say equity futures).
The simplest approach, I think, would be to just estimate VaR from a multivariate normal distribution using historical daily return covariances. Would this approach significantly underestimate the risk beca... |
Do I need a copula to accurately estimate the VaR of a portfolio of risky assets? |
can some one kindly go over some of the applications and use of lie groups in finance? The math is very rigerous and I don't fully understand it or the potential it could have. |
I would start by studying the distribution of the returns. Normal or not? (probably not). <p>
Then, study the behavior of your stocks one against the others.
Other actors to take into account are your data, and your requirements in terms computational time.<p>
All that will allow you to decide whether VaR or copula,... |
I'm trying to understand how to combine two strategies dynamically in trading - 1 mean reversion and the other momentum.
One way(also the simplest one) of doing this is by scaling/normalizing values from both strategies and simply adding them. However, this doesn't seem to be a very smart way of doing things.
Is... |
How are momentum and reversion long/short strategies dynamically combined in trading? |
Given an expected returns vector and a covariance matrix, one can perform a joint draw and measure the average *cross-sectional* variation as the standard deviation across returns for a particular joint draw.
Demonstrating the same idea using empirical/historical data, the cross-sectional variation is simply the st... |
If you arrived at the weights via a mean-variance utility optimization you can back-out the implied expected returns based on these weights and a risk aversion parameter. (Indeed, this is the approach Black-Litterman took to back-out the implied expected returns from a set of benchmark weights, and Jay Walters shows th... |
I've been experimenting with bond pricing using easily available data (treasury auction prices and treasury yield curves on treasury direct).
At first I assumed that I could use the components yield curve to price any (risk free) series of cash flows, but that doesn't work because the curve is of the yield-to-maturi... |
Given an expected returns vector and a covariance matrix, one can perform a joint draw and measure the average *cross-sectional* variation as the standard deviation across returns for a particular joint draw.
Demonstrating the same idea using empirical/historical data, the cross-sectional variation is simply the st... |
I'm trying to understand how to combine two strategies dynamically in trading: one mean-reversion and the other momentum.
One way (also the simplest one) of doing this is by scaling/normalizing values from both strategies and simply adding them. However, this doesn't seem to be a very smart way of doing things.
... |
First step is to decide what instruments you want to include in process for estimating the spot curve.
You want to look at the following instruments for inclusion - treasury coupon strips, on-the-run treasury issues, and some off-the-run treasury issues (those not trading at liquidity discounts), or all treasury co... |
First step is to decide what instruments you want to include in your process for estimating the spot curve.
You want to look at the following instruments for inclusion - treasury coupon strips, on-the-run treasury issues, and some off-the-run treasury issues (those not trading at liquidity discounts), or all treasu... |
Given a set of monthly alpha forecasts (i.e. standardized z-scores from a multi-factor return model) and a non-linear market impact model (or more specifically, its piecewise-linear approximation), is there a generally accepted "standard" method of setting their objective weights in an optimization so they are scaled a... |
Is there a standard method of scaling alpha forecasts to t-cost estimates? |
Given a set of monthly alpha forecasts (i.e. standardized z-scores from a multi-factor return model) and a non-linear market impact model (or more specifically, its piecewise-linear approximation), is there a generally accepted "standard" method of setting their objective weights in an optimization so they are scaled a... |
Two aspects of statistical learning are useful for trading
1. First the ones mentionned earlier: some **statistical methods** focussed on working on *live* datasets. It means that you know you are observing only a sample of data and you want to **extrapollate**. You thus have to deal with *in sample* and *out of sa... |
Two aspects of statistical learning are useful for trading
1. First the ones mentionned earlier: some **statistical methods** focussed on working on *live* datasets. It means that you know you are observing only a sample of data and you want to **extrapollate**. You thus have to deal with *in sample* and *out of sa... |
I would like to write a program that takes as input a list of cik/year/quarter entries. The program should iterate through the list and, for each entry, grab xbrl financial data from the SEC website for the given cik/year/quarter combination.
I can decipher some parts of the sec file structure, but not all. For ex... |
can some one kindly go over some of the applications and use of lie groups in finance? The math is very rigerous and I don't fully understand it or the potential it could have.
let me share some examples with you all, i'm sure there are many more, there's even a financial math graduate program in europe where there ... |
I would like to write a program that takes as input a list of cik/year/quarter entries. The program should iterate through the list and, for each entry, grab xbrl financial data from the SEC website for the given cik/year/quarter combination.
I can decipher some parts of the sec file structure, but not all. For exa... |
I would like to write a program that takes as input a list of CIK/year/quarter entries. The program should iterate through the list and, for each entry, grab XBRL financial data from the SEC website for the given CIK/year/quarter combination.
I can decipher some parts of the SEC file structure, but not all. For exa... |
I'm currently doing a course in derivatives pricing and I'm having some trouble wrapping my head around the sweet spot where theory meets reality in terms of Risk Neutral Pricing.
I know that the first and second fundamental theorems of asset pricing lays the foundation for the normal risk neutral pricing argument,... |
What mathematical characteristics are required from the asset price process in order to stay within the RNP framework? |
as I am preparing for the CFA level 2 exam, I got confused by the concept Z-spread and OAS. When a call option is added to a bond, since it is not favorable to the bond buyer, they would require more spread (which is the OAS) for this instrument in order to get more discount on the bond price. So to me, Z spread should... |
Can some one kindly go over some of the applications and use of Lie groups in finance? The math is very rigorous and I don't fully understand it or the potential it could have.
Let me share some examples with you, I'm sure there are many more. There even is a financial math graduate program in Europe where there is ... |
I am preparing for the CFA level 2 exam, I got confused by the concept Z-spread and OAS.
When a call option is added to a bond, since it is not favorable to the bond buyer, they would require more spread (which is the OAS) for this instrument in order to get more discount on the bond price.
So to me, Z spread sho... |
What is the difference between Option Adjusted Spread (OAS) and Z-spread? |
How to value non-libor swaps (not basis swaps)? |
Assume $X_t$ is multivariate Ornstein-Uhlenbeck process, i.e.
$$dX_t=\sigma dB_t-AX_tdt$$
and the spot interest rate evolves by the following equation:
$$r_t=a+b\cdot X_t$$
After solving for $X_t$ using $e^{tA}X_t$ and Ito and looking at $\int_0^T{r_s\;ds}$, it turns out that
$$\int_0^T{r_s\;ds} \sim \mathcal{N}(... |
Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e.
$$dX_t=\sigma dB_t-AX_tdt$$
and the spot interest rate evolves by the following equation:
$$r_t=a+b\cdot X_t.$$
After solving for $X_t$ using $e^{tA}X_t$ and Ito and looking at $\int_0^T{r_s\;ds}$, it turns out that
$$\int_0^T{r_s\;ds} \sim \mathcal{... |
I am reading this paper, www.jds-online.com/file_download/353/JDS-746.pdf
Basically, it is about estimating parameters using Bayesian inference.
It estimates this stochastic differential equation:
$$dy(t)=\{ \alpha-\beta y(t)\}dt+ \sigma \sqrt{y(t)}dB(t)$$
where $B(t)$ is standard Brownian motion.
by using... |
What is augmented data when simulating stochastic differential equations using Gibbs Sampler? |
I am reading [this paper][1] on Bayesian Estimation of CIR Model.
Basically, it is about estimating parameters using Bayesian inference.
It estimates this stochastic differential equation:
$$dy(t)=\{ \alpha-\beta y(t)\}dt+ \sigma \sqrt{y(t)}dB(t)$$
where $B(t)$ is standard Brownian motion.
by using this ap... |
I assume that by "this machinery breaks down" you mean that when it breaks down as theory, but not as a practical tool.
I would say that the exact point where risk neutral pricing approach fails is when the payoff is no more attainable. There exist a precise mathematical characterization for attainable payoffs (see... |
I assume that by "this machinery breaks down" you mean when it breaks down as theory, but not as a practical tool.
I would say that the exact point where risk neutral pricing approach fails is when the payoff is no more attainable. There exist a precise mathematical characterization for attainable payoffs (see the ... |
Let's assume I have an arbitrary option that I can price using Monte-Carlo simulation. What is the general approach (i.e. without relying on specific option type) to calculating the greeks in this case? |
How to get greeks using Monte-Carlo for arbitrary option? |
**Setting the scene**: Assume a multivariate GBM with correlation matrix $\Sigma$. Further, one want to estimate the correlation between two of the assets. Assume one has a suitable estimator of the correlation, the exact estimator might not be directly relevant, so assume e.g. standard, 60 days moving average.
**... |
I'm developing a software to calculate the implied volatility of an option using the Black & Scholes formula and a trial-and-error method. The implied volatility values I get are correct, but I noticed that they are not the only possible ones.
For example, with a given set of parameters, my trial-and-errors lead me ... |
How do I calculate implied volatility? |
The VIX calculation is a weighted average of prices for front-month out-the-money options on the S&P index.
So for VIX futures, this makes sense for the front month vix futures (being based on a front month formula) but what about the months further out? It seems to gets kind of paradoxical, but are back month vix f... |
What are VIX back-month futures based on? |
What precision do I need to calculate implied volatility? |
I have a model specifying a cointegration relationship on a number of transaction-level timeseries.
I would like to specify entry and exit points for trades where these points ideally would be just before the turning points of the time series (bottoms for exit and tops for entry). The issue I am having is that the ... |
Why, in general, variance of volume changes is higher than variance of price changes ? I understand that this two quantities are functions of some very different factors, but I don't understand fully, why volume is changing so much. I've heard that even if account for seasonal changes in volatility (standardize daily s... |
Why generally variance of volume changes is higher than variance of price changes? |
Does correlations between stocks rises when stock declines - any research here ? Which model could account for that effect ? Mayby GARCH-BEKK, or some models using copulas ? |
Does correlations between stocks rises when stock declines? |
Is there any research on whether the correlations among stocks rise when stock indices decline? Which model could account and test for that effect ? Maybe GARCH-BEKK, or some models using copulas? |
Why, in general, is the variance of volume changes higher than variance of price changes?
understand that these two quantities are functions of some very different factors, but I don't understand fully why the variance of volume is changing so much.
I've heard that even if one accounts for seasonal changes in v... |
Why in general is the variance of volume changes higher than variance of price changes? |
Does the correlation amongst stocks rise when stock values decline? |
I'm trying to understand how arbitrage works, but I'm having some difficulties based on some restrictions:
- I have markets A, B and C.
- The currencies that are traded are X <-> Y, and X <-> Z.
- The only thing that can be transferred between markets A, B and C is currency X.
- The time it takes to transfer ... |
I am willing to calculate and monitor the evolution of extreme-viscosity in the financial markets data series.
Wikipedia says "Put simply, the less viscous the fluid is, the greater its **ease of movement** ". So rather than looking for the mighty viscosity should I simply focus on ease-of-movement? Well, the "eas... |
I read in a book that the distance to default of a company is "2.978".
Can anyone please tell me what is the unit implied behind this measure? Are they "years" for instance? |
Why, in general, is the variance of volume changes higher than variance of price changes?
I understand that these two quantities are functions of some very different factors, but I don't understand fully why the variance of volume is changing so much.
I've heard that even if one accounts for seasonal changes in... |
Following on from Tal Fishman's idea of using "some good old-fashioned judgment," you might find the idea of applying a [Tukey chart][1] and its related upper and lower control limits more useful than standard deviation.
[1]: http://gunston.gmu.edu/708/frTukey.asp?E=0 |
Why, in general, is the variance of volume changes higher than variance of price changes?
I understand that these two quantities are functions of some very different factors, but I don't understand fully why the variance of volume is changing so much.
I've heard that even if one accounts for seasonal changes in... |
Given a bond and a stock issued by the same issuer, what is the appropriate ratio of bond-to-stock one should hold in order to minimize the specific risk to that issuer? Equivalently, what is the expected change in the credit spread for a given change in equity? Knowing this, one could then use the spread duration, o... |
What is an appropriate hedge ratio for hedging a credit instrument with equity of the same issuer? |
In asset allocation, you usually send reports to your clients where you will report the volatility of its portfolio. Assuming you only have monthly returns, you will compute volatility over a considered period of $n$ months with the classic sample volatility estimate:
$$\sigma_s=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i... |
How to measure investors' "experienced" volatility? |
Let's assume I have an arbitrary option that I can price using Monte-Carlo simulation. What is the general approach (i.e. without relying on specific option type) to calculating the greeks in this case?
**Edit:** I woud like to add a few links on the topic that I found useful:
- [Vibrato monte carlo and the calc... |
I'm considering exchange traded options of futures on bonds. Options on bond futures are usually American, thus the Black model is out of question. Which is the most imporatant Greek with respect to update frequency? Delta or Rho or something else? Which model should I use for calculating this? Is CRR79-delta enough, i... |
What is the highest frequency greek for options on futures on bonds? |
Often in a quant process, one will generate a time series of return forecasts and use them in some sort of optimization to generate a portfolio. Generally, there will be a covariance matrix of market returns used in the optimization. I haven't seen any attention ever placed on the covariance of the return forecasts the... |
Is there an optimal covariance one would want forecasts to have? |
Often in a quant process, one will generate a time series of return forecasts and use them in some sort of optimization to generate a portfolio. Generally, there will be a covariance matrix of market returns used in the optimization. I haven't seen any attention ever placed on the covariance of the return forecasts the... |
Often in a quant process, one will generate a time series of return forecasts and use them in some sort of optimization to generate a portfolio. Generally, there will be a covariance matrix of market returns used in the optimization. I haven't seen any attention ever placed on the covariance of the return forecasts the... |
Is there any need for real time weighted volatility on a tick by tick basis for equities?
If you had that access to that, what could you do with it? |
Immediately preceding the worst of the financial crisis, my professors all pointed out to me that the yield curve had inverted -- short-term yields were more risky than 20-year or 30-year Treasury securities. My professors all seemed nervous about this.
Aside from such a situation being generally counter-intuitive,... |
Why is an inverted yield curve a problem? |
To explain why a negative sloping yield curve is bad, you have to start with a theory of the yield curve.
The dominant theories for the term structure of interest rates are the rational expectations, liquidity preference, and market segmentation. (The first two theories are quite compatible with each other and have ... |
Theoretically, a rising yield curve is compensation for the additional duration risk.
An inverted yield-curve is saying that the market thinks that:
Next-year's figures for: growth plus inflation
is less than
Ten years' time's figures for: growth plus inflation
Which means that expectations are **eithe... |
Samuelson once quipped that the yield curve had successfully predicted 9 of the last 5 recessions.
Explanations for why the yield curve inverts have been covered adequately above. But what does it mean for the economy? For the yield curve inversion to predict stock market performance enough to make an actual decis... |
Let me answer your questions in reverse order:
> ...or is fractional reserve banking by individual corporations more to blame?
The majority of money created in the US (and indeed, the world) is created by private banks through fractional reserve lending, not by central banks creating fiat money.
![enter image ... |
I hear a lot of debate over the removal of the U.S. Dollar's precious metal backing and the subsequent inflation rates, but is there any proven relationship between unbacked currency and extreme inflation or is fractional reserve banking by individual corporations more to blame?
In short, what are the *real* effects... |
What are the effects of turning a backed currency into a fiat currency? |
Let me give you couple of examples. <br>
You're at a dinner and you order something. You could say:<br>
- "It's OK"
- "It's good"
- "It's great"
- "It's fantastic"
- "I've never ate something this good"
- "Goodlike"
The similar grading can be made for bad food.<br>
The next example would be if you wo... |
Function that best describes intensity of human/(group of humans) emotions? |
One can get some kind of absolute measure of satisfaction by working with [just noticable differences][1]. The idea is that a decision maker is indifferent between very similar choices but not indifferent between dissimilar choices. Here is an example: A decisonmaker likes sugar, and wants as much sugar as possible- wi... |
in my (limited) understanding, the behavior of a stock price can be modeled using Geometric Brownian Motion (GBM). According to the Hull book i'm currently reading, the discrete-time version of this model is as follows: $\triangle S = \mu S \triangle t + \sigma S \epsilon \sqrt{\triangle t}$. My question is this, if i'... |
In my (limited) understanding, the behavior of a stock price can be modeled using Geometric Brownian Motion (GBM). According to the Hull book i'm currently reading, the discrete-time version of this model is as follows:
$$\Delta S = \mu S \Delta t + \sigma S \epsilon \sqrt{\Delta t}, \quad \epsilon \sim N(0,1)$$.
... |
In my (limited) understanding, the behavior of a stock price can be modeled using Geometric Brownian Motion (GBM). According to the Hull book I'm currently reading, the discrete-time version of this model is as follows:
$$\Delta S = \mu S \Delta t + \sigma S \varepsilon \sqrt{\Delta t}, \quad \varepsilon \sim N(0,1)... |
What are some applications of bioinformatics or genetics to generating alpha in U.S. equities? |
There are many disciplines that have contributed to how one model's risk and return. Physics introduced Brownian motion and RMT. Machine learning has helped to solve complex portfolio construction problems, operations research has contributed to market making & risk management, and aerospace engineering has contributed... |
In my (limited) understanding, the behavior of a stock price can be modeled using Geometric Brownian Motion (GBM). According to the Hull book I'm currently reading, the discrete-time version of this model is as follows:
$$\Delta S = \mu S \Delta t + \sigma S \varepsilon \sqrt{\Delta t}, \quad \varepsilon \sim N(0,1)... |
There are many disciplines that have contributed to how one model's risk and return. Physics introduced Brownian motion and RMT. Machine learning has helped to solve complex portfolio construction problems, operations research has contributed to market making & risk management, and aerospace engineering has contributed... |
Using intra-day data, the concept of viscosity is easier to define. At the microstructure scale, you can see the price moves as a diffusion constrained by the quantities in the order books. Viscosity is a mix of pressure of volumes, rounding by the tick size, and bid-ask bounce.
See for instance [A New Approach for ... |
Two aspects of statistical learning are useful for trading
**1.** First the ones mentionned earlier: some **statistical methods** focussed on working on *live* datasets. It means that you know you are observing only a sample of data and you want to **extrapollate**. You thus have to deal with *in sample* and *out of... |
Two aspects of statistical learning are useful for trading
**1.** First the ones mentionned earlier: some **statistical methods** focussed on working on *live* datasets. It means that you know you are observing only a sample of data and you want to **extrapollate**. You thus have to deal with *in sample* and *out of... |
Good reference on sample autocorrelation? |
Is the covariance of the raw return forecasts would a good forecaster of the covariance of market returns?
As you suggest, the covariance of the raw return forecasts is a lousy forecast of the covariance of market returns. Grinold & Kahn explain why quite eloquently in Active Portfolio Management, 2nd edition (pg. ... |
Is the covariance of the raw return forecasts a good forecaster of the covariance of market returns?
As you suggest, the covariance of the raw return forecasts is a lousy forecast of the covariance of market returns. Grinold & Kahn explain why quite eloquently in Active Portfolio Management, 2nd edition (pg. 275). ... |
The World Economic Forum [Global Competitiveness Report][1] offers a comprehensive view of individual country risk/reward. There has been an explosion of these types of indexes over the past few years.
The UN has its [Human Development Index][2], the World Bank has its [Ease of Doing Business][3] report and there... |
What are useful indexes for rapid evaluation of country economic risk? |
There is a paper by [Goldstein and Taleb (2007)][1] which tries to address this question of what number captures investors intuitive feelings of the volatility of series of returns and whether this coincides with the standard deviation of returns.
What they found was that [Median Absolute Deviation][2] does a much ... |
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