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can anyone tell me where can I find derivation of formula for portfolio skewness and kurtosis? I can find formulas everywhere, but how did they get like that?
for example, portfolio variance formula is well known and i can find the derivation of that formula in a lot of books, but i can't find anything on portfolio ... |
What are some of the best ways to effectively measure headwinds for an open ended fund? Headwinds in this case refers to the amount of volatility contributed by a factor or a set of factors to a portfolio.
|
What is the data basis that you start from? If you just have the covariance matrix, then you can only calculate portfolio variance or volatility by $$ w^T \Sigma w$$ where $w$ are the portfolio weights and $\Sigma$ is the covariance matrix. If you have the individual asset returns $r^j_t$ where $j$ indexes assets, $j=1... |
Any thoughts on how Warren Buffet's B of A warrants might be "marked-to-market" by either counterparty? |
I developed an optimization algorithm that uses returns (among other parameters) as input and basically output an allocation.
As I'm pretty happy with the results, I am in the process of putting the algorithm in production. As a matter of fact, I have to embed some checks into the algorithm to make sure that the inp... |
How do I statistically differentiate a series of prices from a series of returns? |
I need to backfill the price of bonds for testing a startegy.
The method employed is:
1. Regressing the YTM of the bond against a benchmark.
2. Using the regression estimates to calculate the YTM for the period in which the bond data is not available.
3. Using the "price" function in excel to calculate the bond... |
How do I backfill the price of bonds for backtesting? |
Returns possess non-zero skewness and excess kurtosis. If these assets are temporally aggregated both will disappear due to the law of large numbers. To be exact, if we assume IID returns skewness scales with $\frac{1}{\sqrt{n}}$ and kurtosis with $\frac{1}{n}$.
I'm interested in a concise, clear and openly accessi... |
I developed an optimization algorithm that uses returns (among other parameters) as input and basically output an allocation.
As I'm pretty happy with the results, I am in the process of putting the algorithm in production. As a matter of fact, I have to embed some checks into the algorithm to make sure that the inp... |
I developed an optimization algorithm that uses returns (among other parameters) as input and basically output an allocation.
As I'm pretty happy with the results, I am in the process of putting the algorithm in production. As a matter of fact, I have to embed some checks into the algorithm to make sure that the inp... |
I developed an optimization algorithm that uses returns (among other parameters) as input and basically output an allocation.
As I'm pretty happy with the results, I am in the process of putting the algorithm in production. As a matter of fact, I have to embed some checks into the algorithm to make sure that the inp... |
I have a limited financial background but I'm trying to figure out the usefulness of buying size-n arbitrages (n > 3), and I wonder the kind of risks - if any - associated with such a strategy.
Say that I simultaneously detect :
- a triangular arbitrage with currencies A, B and C (one intermediate currency) ;
... |
I have a basic question about annualized Sharpe Ratio Calculation: if I know the daily return of my portfolio, the thing I need to do is multiply the Sharpe Ratio by $\sqrt{252}$ to have it annualized.
I don't know why is that, can any body explain? |
How to annualize Sharpe Ratio? |
Can you recommend a good tutorial for working with tick data for the purpose of algorithmic trading?
Is the data normally stored in a database and only bits are read into memory at a time?
Is there some useful software that's easy to get?
|
Tutorial for working with tick data? |
A concrete example of negative forward rates is provided by the 3M CHF LIBOR futures. They're all trading above a price of 100, which implies negative forward rates.
See the prices [here][1]. Despite the prices of the forwards, CHF libor hasn't actually fixed negative yet. But the forwards are certainly.
Also, yo... |
A concrete example of negative forward rates is provided by the 3M CHF LIBOR futures. They're all trading above a price of 100, which implies negative forward rates.
See the prices [here][1]. Despite the prices of the forwards, CHF libor hasn't actually fixed negative yet. But the forwards are certainly all below ze... |
Do you know how to decompose the risk of index linked bonds?
To value a inflation linked bond, one plugs the real zero curve into the bond PV calculation, the real interest rate is as the fisher equation tells us: $r_{real}=r_{nom}-r_{be}$, where $r_{be}$ is the break even inflation rate.
Let's say we hava a po... |
What I'm writing is based on the methodology in http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1565134
You observe the nominal and real bond prices/YTMs. Transform them to zero or forward curves. Estimate the multivariate dynamics and project them to your horizon, let's call this $X$. Use the distribution of zer... |
I have written a simulation that matches buy and sell orders, keeps track of an order book and simulates trades. My first pass at order submission was to generate random orders around the bid/ask spread. This does not produce a random walk in trade prices. What happens is the orders are distributed evenly but around... |
What sort of order submission strategy would result in a random walk of trade prices? |
Can someone shed light on optimal ways to execute medium sized orders ~ 2000 shares in the market?
Unfortunately the execution algo I have access to is very dumb. It follows the top of book price and hence I can see that the algo I am using is getting gamed by some predatory algo ( for example, if the spread is 2 c... |
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 dynamics of the forward rate curve, then the Musiela parametrization defines the forward rate dynamics $d\bar{F}(t,\tau)... |
While triangular arbitrages exists, they are a rare, short lived, and shallow. In several academic datasets they are very rarely seen, mainly for two reasons, market efficiency aside: (1) the time resolution of the data is not tick by tick but aggregated at some level (for example at 1 second intervals), (2) the datase... |
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 dynamics of the forward rate curve, then the Musiela parametrization defines the forward rate dynamics $$d\bar{F}(t,\tau... |
Can someone shed some light on optimal ways to execute medium sized orders ~2000 shares in the market?
Unfortunately the execution algo I have access to is very dumb. It follows the top-of-book price and hence I can see that the algo I am using is getting gamed by some predatory algo. For example, if the spread is ... |
It is well known that the standard estimator of the covariance matrix can lose the property of being positive-semidefinite if the number of variables (e.g. number of stocks) exceeds the number of observations (e.g. trading days). I think the matrix can become singular. I have a clear idea why (inspired by the geometry ... |
Can someone explain what "Exotics Trade Capture" capture means in layman's terms? |
I am trying to find out what *Exotics Trade Capture* entails. I can't find anything on Google that isn't a job posting.
Say you did this for a living, how would you explain it to someone that didn't know anything about it?
What references on the internet would you point them to find out more information about it?... |
From [Wilmott][1]:
> Trade capture is the process of booking (or capturing) the trade into
> the systems used within a financial organisation. This may sometimes have to happen multiple times
> depending on the complexity of the trades and the ability of the
> systems to be able to capture the economic, non-econo... |
Assume we have two instruments `A` and `B`. Also time is increasing from 1 to n. Let's say that `A1` is price of instrument `A` at time `1`. Let's assume that `A` and `B` are highly correlated instruments. Then we can try to compute `TruePrice` of stock `B` from stock `A`.
Then if `Bn` is more enough than `TruePrice... |
What does *Exotics Trade Capture* exactly entail?
|
While triangular arbitrages exists, they are a rare, short lived, and shallow. In several academic datasets they are very rarely seen, mainly for two reasons, market efficiency aside: (1) the time resolution of the data is not tick by tick but aggregated at some level (for example at 1 second intervals), (2) the datase... |
I'm trying to adapt tools from portfolio theory for another use, and I have a question about how I might do so.
Suppose that instead of having normally distributed returns, the return $R_i$ is either, say, 3 or 0. So, $E(R_i)=3P(R_i=3)$.
On the wiki page for Modern Portfolio, it says
> Note that the theory ... |
I'm trying to adapt tools from portfolio theory for another use, and I have a question about how I might do so.
Suppose that instead of having normally distributed returns, the return $R_i$ is either, say, 3 or 0. So, $E(R_i)=3P(R_i=3)$.
On the wiki page for Modern Portfolio, it says
> Note that the theory ... |
I'm trying to adapt tools from portfolio theory for another use, and I have a question about how I might do so.
Suppose that instead of having normally distributed returns, the return $R_i$ is either, say, 3 or 0. So, $E(R_i)=3P(R_i=3)$.
On the wiki page for Modern Portfolio, it says
> Note that the theory ... |
I'm trying to adapt tools from portfolio theory for another use, and I have a question about how I might do so.
Suppose that instead of having normally distributed returns, the return $R_i$ is either, say, 3 or 0. So, $E(R_i)=3P(R_i=3)$.
On the wiki page for Modern Portfolio, it says
> Note that the theory ... |
Here is an example where using standard deviation as a measure of risk does not make sense:
Let's say that
Case 1:
Probability of getting 3 is 0.5, and probability of getting 0 is 0.5. Your expected return is `1.5`, and you expected standard deviation is `1.5` (I hope my calculation is right).
Case 2:
Probab... |
I'm trying to adapt tools from portfolio theory for another use, and I have a question about how I might do so.
Suppose that instead of having normally distributed returns, the return $R_i$ is either, say, 3 or 0. So, $E(R_i)=3P(R_i=3)$.
On the wiki page for Modern Portfolio, it says
> Note that the theory ... |
I'm trying to adapt tools from portfolio theory for another use, and I have a question about how I might do so.
Suppose that instead of having normally distributed returns, the return $R_i$ is either, say, 3 or 0. So, $E(R_i)=3P(R_i=3)$.
On the wiki page for Modern Portfolio, it says
> Note that the theory ... |
If I understand right, Itô's lemma tells us that for any process $X$ that can be adapted to an underlying standard normal Wiener measure $\mathrm dB_t$, and any twice continuously differentiable function $f$,
$$\mathrm df(X_t) = f'(X_t)\mathrm dX_t + \frac 1 2 f''(X_t)\mathrm d[X_t] ,$$
where $$[X_t]=\lim_{\Delta\Pi\... |
How to measure a non-normal stochastic process? |
The standard method to manage your kind of problem (i.e. dealing with stochastic processes that are note presented or built thanks to a Brownian motion) is to use a measure change.
The power of Brownian motion is that you have a lot of representation theorems (Doob-Meyer theorem, Wold theorem, etc) that allows to (t... |
First you need to define what you need a risk measure for. It is usually to take a decision, so you have an operational criterion that defines your risk. You should go back at this point and see what is the impact of a change of distribution on it.
Just say for instance that you need a risk measure to take decisions... |
There is a wide literature on optimal execution, among others:
* [Rigorous Strategic Trading: Balanced Portfolio and Mean-Reversion, by Lehalle, 2009, Vol. 4, No. 3: pp. 40-46][1]
* [Optimal Control of Trading Algorithms: A General Impulse Control Approach, by Bouchard, Dang, Lehalle, in SIAM J. Finan. Math., 2(1),... |
There is a wide literature on optimal execution, among others:
* [Rigorous Strategic Trading: Balanced Portfolio and Mean-Reversion, by Lehalle, 2009, Vol. 4, No. 3: pp. 40-46][1]
* [Optimal Control of Trading Algorithms: A General Impulse Control Approach, by Bouchard, Dang, Lehalle, in SIAM J. Finan. Math., 2(1),... |
You have intense academic research on orderbook dynamics simulations, just cite:
1. [Econophysics: Empirical facts and agent-based models, by Anirban Chakraborti, Ioane Muni Toke, Marco Patriarca, Frederic Abergel (Arxiv 2010)][1]
2. [High Frequency Simulations of an Order Book: a Two-Scales Approach
by: Charles-A... |
I just saw the question http://quant.stackexchange.com/questions/3210/how-to-calculate-the-most-realistic-historical-option-prices-with-additional-pub and I am interested in the step before that.
How can I calculate historical ATM option prices for the SP500 using VIX prices and other publicly available data? Can I ... |
**Regarding conventions**
One thing to keep in mind in all questions about "what's right and what's not?" is that conventions don't always matter as much as one would think.
When a trader marks his vols by looking up option prices on the market, he is going to mark them using the pricing model which his quants im... |
The standard method to manage your kind of problem (i.e. dealing with stochastic processes that are note presented or built thanks to a Brownian motion) is to use a measure change.
The power of Brownian motion is that you have a lot of representation theorems (Doob-Meyer theorem, Wold theorem, etc) that allows to (t... |
You have intense academic research on orderbook dynamics simulations, just cite:
1. [Econophysics: Empirical facts and agent-based models, by Anirban Chakraborti, Ioane Muni Toke, Marco Patriarca, Frederic Abergel (Arxiv 2010)][1]
2. [High Frequency Simulations of an Order Book: a Two-Scales Approach
by: Charles-A... |
Could anyone explain this to me, please.
For example, if I want to construct a portfolio with five stocks and I have my view on CVaR as a constraint. How can I use this method to manage my portfolio? |
How can I use Entropy-pooling of Atillio Meucci to constuct a portfolio? |
As an example, assume I want to construct a portfolio with five stocks and I have my view on CVaR as a constraint.
How can I use Entropy-Pooling method to manage my portfolio? |
If Libor is found to be fraudulently fixed, are any of the derivative contracts with a floating libor leg still valid? |
Meucci covers this example precisely in his paper "[Fully Flexible Views: Theory & Practice][1]". You can find his code [here][2] for three examples related to the paper.
[1]: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1213325
[2]: http://www.mathworks.com/matlabcentral/fileexchange/21307 |
Meucci covers this example precisely in his paper "[Fully Flexible Views: Theory & Practice][1]". You can find his code [here][2] for three examples related to the paper. The Butterfly Trading example covers the CVAR scenario.
[1]: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1213325
[2]: http://www.mat... |
I'm looking at automating the calculation of margin requirements for a portfolio of Eurex markets.
Eurex describe the margin calculations in [this document][1]. However, the only tool I can find is a Windows only, UI driven [application][2].
I can go ahead and implement the algorithm as described, but are there o... |
I have looked at the Variance Swap Papers published by [GS-VarSwap][1] and [JPM-VarSWap][2] where they talk about approximation to VarSwap strike using ATMF vol and Skew(slope of the volatility skew for 90-110 strikes).
But, I have also come across another 'skew measure' which is defined as = sqrt(T)*(sigma1 - sigma... |
Why does Skew measure remain more-or-less constant for Listed Opion Expiries? |
Why does Skew measure remain more-or-less constant for Listed Expiries? |
I am trying to use fundamental factors such as PE, BV, & CFO in a multivariate linear regression with the response variable being the rolling 1 month returns. But this approach seems flawed as the autocorrelation of the residuals is to high and the Durbin Watson test points also to such flaws. What is the best what to ... |
Using rolling returns in a multivariate linear regression? |
I am trying to get my hands on Entropy Pooling which was introduced by Meucci in this [paper][1].
As an example, assume I want to construct a portfolio with five stocks and I have my view on CVaR.
How can I use Entropy-Pooling method to manage my portfolio?
[1]: http://papers.ssrn.com/sol3/papers.cfm?abstr... |
I have looked at the Variance Swap Papers published by [GS-VarSwap][1] and [JPM-VarSWap][2] where they talk about approximation to VarSwap strike using ATMF vol and Skew (slope of the volatility skew for 90-110 strikes).
But, I have also come across another 'skew measure' which is defined as
$$
\mathrm{skew} = \fr... |
Kindly correct me if I am wrong
"Pricing IR Swap doesn't require any stochastic model but calculation of PFE for IR Swap does require Hull White Model or any other stochastic short rate or forward rate model " is this statement correct and if yes why ?
|
In this portfolio optimization utility (and others), mean return, standard deviation and correlation among assets are required inputs.
http://finance.wharton.upenn.edu/~stambaugh/portopt.html
At the same time, I've seen other portfolio optimizers that start with historical price data and a covariance matrix is c... |
I am looking to get a better understanding of an output from a trading strategy. Basically I have a daily equity curve lets call it $Y_t$. I have defined a bunch of independent variables $X_{it}$ that I think can explain the movement in the daily PnL. The independent variables are not used in trading signal generation ... |
How to better understand trading signals? |
In this portfolio optimization utility (and others), mean return, standard deviation and correlation among assets are required inputs.
http://finance.wharton.upenn.edu/~stambaugh/portopt.html
At the same time, I've seen other portfolio optimizers that start with historical price data and a covariance matrix is c... |
What is the difference between these two optimization procedures? |
Does anyone know how to connect IQFeeds with Matlab. It seems the datafeed toolbox only accepts Reuters, Bloomberg, Yahoo and one or two more. I've been looking all over the place for a Matlab toobox or some code because I'm using IQFeeds. It's weird because on here I've read many posts of people talking about their IQ... |
After years of mathematical finance I am still not satisfied with the idea of a risk premium in the case of stocks.
----------
I agree that (often) there is a premium for long dated bonds, illiquid bonds or bonds with credit risk (which in fact they all have). I can explain this to my grandmother. My questio... |
After years of mathematical finance I am still not satisfied with the idea of a risk premium in the case of stocks.
----------
I agree that (often) there is a premium for long dated bonds, illiquid bonds or bonds with credit risk (which in fact they all have). I can explain this to my grandmother. My questio... |
Another observation that the connection between return and risk is not that straightforward (and in contradiction to modern portfolio theory!) is the [low-volatility anomaly][1].
It turns out empirically that stocks that have low-volatility or low-beta show *higher* returns than high-volatility or high-beta stocks. ... |
Since I began thinking about portfolio optimization and option pricing, I've struggled to get an intuition for the risk premium, i.e. that investors are only willing to buy risky instruments when they are compensated by an add-on above $r$ (the risk free interest rate).
On the one hand this is understandable and bac... |
I'm currently working with historical index data from Yahoo Finance and would like to plot the GARCH(1,1) volatility of these indexes. I'm working with the Datafeed and Finance Tollboxes in Matlab right now, and I'm able to get the data and plot the indexes. However I'm having some difficulty understanding the followin... |
I was asked yesterday by a colleague why we are doing asset allocation using optimizers which target, for a minimum expected return:
- the portfolio with the minimum variance
or
- the portfolio with the minimum expected shortfall
and why nobody uses drawdown optimizations.
I do know that the list above... |
Why is the Drawdown measure not used for portfolio optimization? |
i am new to corporate finance and ask myself why a investor is interested in being *short* on a Option? The only he can win is a premium but he can loose much more. I understand with being a short I can cap the profits on a Stock like this:
![enter image description here][1]
But I think this is a quite theoretical... |
What is the Benefit of holding a short option? |
I'm currently working with historical index data from Yahoo Finance and would like to plot the GARCH(1,1) volatility of these indexes. I'm working with the Datafeed and Finance Tollboxes in Matlab right now, and I'm able to get the data and plot the indexes. However I'm having some difficulty understanding the followin... |
How do I model GARCH(1,1) volatility for historical indexes in Matlab? |
a common repeated belief of options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of a known event. And after the event, volatility drops because more people are selling the contracts.
But I have noticed contracts with ZERO volume ... |
Options volatility, fallacy? |
A common and oft repeated belief about options volatility is that implied volatility increases due to people bidding up a contract, usually related to anticipation of the outcome of an expected event. And that after the event, volatility drops because more people are selling the contracts.
But I have noticed contrac... |
I'd like to calculate portfolio allocation beta on a portfolio that has different asset classes. The portfolio may be made up of:
Short term bond fund (with beta tied to Barclays U.S. Aggregate Bond Index)
Sector fund 1 (with beta tied to DOW)
SP500 fund (with beta tied to SP500 index)
I understand... |
Calculating portfolio allocation beta with different asset classes? |
Let's first restate the formula of the beta of a portfolio $P$ relative to a benchmark $B$:
$$\beta_P=\frac{Cov(r_P,r_B)}{Var(r_B)} $$
As chrisaycock said in his comment, the key thing to understand is that the beta is a statistical measure computed relative to a benchmark. Hence, I believe that the real question... |
Are there any methods/techniques that cover distributing cash into a specific percent of a portfolio asset class while gaining the best average price?
As a simple example, a portfolio starts with 100k cash. It eventually disburses its cash into four asset classes. This means 25k goes to purchase assets in each cla... |
Are there any methods/techniques that cover distributing cash into a specific percent of a portfolio asset class while gaining the best average price?
As a simple example, a portfolio starts with 100k cash. It eventually disburses its cash into four asset classes. This means 25k goes to purchase assets in each cla... |
Are there any methods/techniques that cover distributing cash into a specific percent of a portfolio asset class while gaining the best average price?
As a simple example, a portfolio starts with 100k cash. It eventually disburses its cash into four asset classes. This means 25k goes to purchase assets in each cla... |
It simply points to the fact that your model as stands does not have much explanatory power of monthly returns. One reason could be of a observation period mismatch. I am not a fundamental type of guy, but I imagine that the monthly returns are measured over too short a period (1 month) while most fundamental factors a... |
I am trying to use fundamental factors such as PE, BV, & CFO in a multivariate linear regression with the response variable being the rolling 1 month returns. But this approach seems flawed as the autocorrelation of the residuals is to high and the Durbin Watson test points also to such flaws. What is the best what to ... |
I am developing a market-data engine that receives market-data from different futures exchanges. So I need a general format to deal with sources from different exchanges. Protocols like FIX only specifies the transportation but not the format itself. Like which fields should be included?<br/>
Although I can define a g... |
Is there a general format for various sources of futures market-data? |
I am developing a market-data engine that receives market-data from different futures exchanges. So I need a general format to deal with sources from different exchanges. Protocols like FIX only specifies the transportation but not the format itself. Like which fields should be included, how many fields are there in a ... |
I often hear that [column-oriented databases][1] are the best choice method for storing time series data in finance applications. Especially by people selling expensive column-oriented databases.
Yet, at first glance it seems a poor choice. You want to append new ticks, or new bars, at the end (and you need to do th... |
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