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Looking at a portfolio of growth stocks which traded at high multiples until end of last year.
Stocks have been underperforming (no surprise there) but I'm trying to find ways to determine, quantitatively to what extent it is due to inflation / risk free rates, or fears of recession (meaning the market anticipates l... |
Looking at a portfolio of growth stocks which traded at high multiples until end of last year.
Stocks have been underperforming (no surprise there) but I'm trying to find ways to determine, quantitatively to what extent it is due to inflation / risk free rates, or fears of recession (meaning the market anticipates l... |
I would like to replicate a portfolio of stocks $S_1, \cdots, S_n$ using other instruments, $X_1,
\cdots, X_m$. Using the letters above with a subscript $t$ to denote the forward returns over some horizon of the portfolio at time $t$, the return of the portfolio (and the variable I am targeting) is:
$$
P_t = \fra... |
Constructing a Replicating Portfolio : Regression on Individual Stocks or their Average? |
Constructing a Replicating Portfolio : Regression on Individual Constituents or their Average? |
I would like to replicate a portfolio of stocks $S_1, \cdots, S_n$ using other instruments, $X_1,
\cdots, X_m$. Using the letters above with a subscript $t$ to denote the forward returns over some horizon of the portfolio at time $t$, the return of the portfolio (and the variable I am targeting) is:
$$
P_t = \fra... |
Are there optimal portfolio theories than instead of the expected value they were based on the **[Mode](https://en.m.wikipedia.org/wiki/Mode_(statistics))** of distributions?
During my engineer student days I saw the Markowitz theory for portfolio selection and there is something that always bothers me, and it is th... |
> Why are monthly active returns averaged? Should they not be
> multiplied?
His returns are **log returns** and assumes that they are normally distributed, hence they are additive. Assuming log returns are normally distributed implies that simple returns are lognormal and, hence not additive but multiplicative.
... |
Now I make research about market making for cryptocurrency. I’m using model like Avellaneda-Stoikov for optimal control inventory, and I can’t understand how to find S(t) price. Of course, taking the mid-price is not a good idea.
I read a lot about Kyle’s model, and the main thing that I found, is that I need to move ... |
I recently read a document posted by a user in QF, who said that "In the past, I have calibrated simple short rate models to the term structure by using maximum likelihood to get the parameters of the Vasicek/CIR sde and then use the ZCB formula and the current yield curve to calibrate the market price of risk."
I c... |
When to analysing historical movement of credit rating, sometime credit rating is put as `Non-rated or NR`.
Is there any industry acceptance definition of `Non rated`? Or is it just non availability of credit rating the cause of which may include Data issue?
Appreciate any insight on this subject. |
Suppose we introduce the following: a token S with an initial supply of a 1000. At $t_0$, a 1000 different parties $P_1,\dots,P_{1000}$ each buy a single token for $1$\$.
Whoever has the most tokens at time $t_N$ (suppose $N$ discrete time steps), receives $950$\$. After $t_N$ the tokens become useless and nothing h... |
How would the following be priced? |
We are currently in the US Treasury roll period when investors are rolling from the previously issued notes and bonds into the currently issued notes and bonds, aka "Rolling from Off-The-Runs to On-The-Runs".
By some measures, such as yield give up, these are quite rich currently when compared to past historical spr... |
Suppose we introduce the following: a token S with an initial supply of a 1000. At $t_0$, a 1000 different parties $P_1,\dots,P_{1000}$ each buy a single token for $1$\$.
Whoever has the most tokens at time $t_N$ (suppose $N$ discrete time steps), receives $950$\$. After $t_N$ the tokens become useless and nothing h... |
I am trying to find a quick and dirty way to estimate fugit for a basket of American options real time. Is there a quick way to provide a proxy? I know one can do binomial tree or monte carlos simulation, but that would just take too long to run for a large universe of options.
Thank you! |
Is there a closed form solution to calculate Fugit for stock options? |
That is a classic F1 F1 question. It's proprietary software and BBG offers a dedicated help desk.
DTK is not available for free via BLPAPI. Connecting DLIB to an API requires a premium service called Mars API (which will work via DAPI, but also BPIPE and the like, depending on your needs). I suggest you reach out t... |
I watched this [video tutorial][1] to learn how to estimate the Hurst Exponent using an Excel spreadsheet and a time series sample of 1025 data.
I decided to use futures 1H markPriceKlines data from Binance Market Data to play around with those. I set:
* The **Start Date** as: `January 2nd 2022` and the **End Dat... |
How to correctly explain the current price action in a trading chart with the Hurst Exponent found? |
I watched this [video tutorial][1] to learn how to estimate the Hurst Exponent using an Excel spreadsheet and a time series sample of 1025 data.
I decided to use futures 1H markPriceKlines data from Binance Market Data to play around with those. I set:
* The **Start Date** as: `January 2nd 2022` and the **End Dat... |
I watched this [video tutorial][1] to learn how to estimate the Hurst Exponent using an Excel spreadsheet and a time series sample of 1025 data.
I decided to use futures 1H markPriceKlines data from Binance Market Data to play around with those. I set:
* The **Start Date** as: `January 2nd 2022` and the **End Dat... |
> Why are monthly active returns averaged? Should they not be
> multiplied?
His returns are **log returns** and assumes that they are normally distributed, hence they are additive. Assuming log returns are normally distributed implies that simple returns are lognormal and, hence not additive but multiplicative.
... |
I'm new to volatility modeling, I'm struggling to understand when to use a Local Vol model and when to use Stochastic Vol Model, Also now we use a hybrid model combining the two models ? Can someone please provide some explanation ? |
When to use a Local Vol model vs Stochastic Vol Model? |
I just found out about the term revenue leakage in the paper linked below. However, this paper and other resources mentioning it do not provide a definition of the term.
However, for my thesis I require such a definition.
Hence my question: Is revenue leakage a well-known term in finance? What's its formal defin... |
What exactly is revenue leakage? |
First, what is the [SLV](https://quant.stackexchange.com/questions/26/local-volatility-vs-stochastic-volatility/63561#63561)? It combines LV (not really a model, just uses vanilla surface to get a grid) with SV (in a nutshell, BSM with a separate stochastic process for vol, hence multiple dynamic factors).
Shortcomi... |
That is a classic F1 F1 question. It's proprietary software and BBG offers a dedicated help desk.
DTK is not available for free via BLPAPI. Connecting DLIB to an API requires a premium service called Mars API (which will work via DAPI, but also BPIPE and the like, depending on your needs). I suggest you reach out t... |
First, what is the [SLV](https://quant.stackexchange.com/questions/26/local-volatility-vs-stochastic-volatility/63561#63561)? It combines LV (not really a model, just uses vanilla surface to get a grid) with SV (in a nutshell, BSM with a separate stochastic process for vol, hence multiple dynamic factors).
Shortcomi... |
First, what is the [SLV](https://quant.stackexchange.com/questions/26/local-volatility-vs-stochastic-volatility/63561#63561)? It combines LV (not really a model, just uses vanilla surface to get a grid) with SV (in a nutshell, BSM with a separate stochastic process for vol, hence multiple dynamic factors).
Shortcomi... |
That is a classic F1 F1 question. It's proprietary software and BBG offers a dedicated help desk.
DTK is not available for free via BLPAPI. Connecting DLIB to an API requires a premium service called Mars API (which will work via DAPI, but also BPIPE and the like, depending on your needs). I suggest you reach out t... |
> Does the above mean that I should consider opening short positions for
> these trading pairs when I get a Hurst Exponent greater than 0.5 and
> also its prices come from top to the bottom?
No.
Hurst gives you information about the past. It is not predictive. If you want to open up a trading position, you shou... |
I'm reading through [Active Portfolio Management][1], and I can't get my head around the APT.
As far as I can tell, the statement in equation 7.2 translates into:
"If you can get better than consensus estimates on what *qualities* will outperform, and if you can get an intentional excess exposure to these qualiti... |
What is the APT trying to say? |
For time to maturity greater than zero, has it been proved somewhere that the Black-Scholes greeks
$$
\frac{\partial^n BS}{\partial x^n}
$$
are bounded, where $x := \log S$ and $S$ is the current spot price.
In other words, is there an expression and corresponding proof that
$$
\left| \frac{\partial^n BS}{\p... |
Are Black-Scholes Greeks bounded? |
I am trying to price a convertible bond by using a binomial tree. For this, I wrote a binomial tree for the stock price. I noticed that changing the step size (timesteps), changes the final value of my stock prices significantly. Intuitively this is wrong as the up and down movements should be scaled accordingly. I can... |
Why does changing the step size in my Binomial Tree changes the final stock prices so much? |
From Derivatives Markets (McDonald) it is stated that we may price a financial forward and, equivalently, get an implied spot price from a given futures price:
$$
F_{0, T}=S_0e^{(r-\delta)T} \implies S_0=\frac{F_{0,T}}{e^{(r-\delta)T}}
$$
Applying this to S&P500 mini-futures however, I observed a deviation in the a... |
> Is the reason that μ>r because by definition r is the rate of return
> least risky investment, and therefore to entice investors to invest in
> something more risky (a stock index), u must be strictly greater?
Strictly greater because **humans are risk averse** by nature, they don't like uncertainty. They would ... |
Sorry if this is too obvious to you. The marginal risk contribution mentioned here is the same as in this post https://quant.stackexchange.com/questions/37878/marginal-risk-contribution-formula .
I understand the concepts and derivation on the formula. But I got some questions from some legacy codes I'm working on a... |
Whenever analyzing a particular company through CAPM, I used to take the Equity Risk Premium (ERP) of the country where the company was listed/headquartered. However, recently I came to know that some practitioners don't consider it a good choice. The reason that they give is that assume that you have an Israeli softwa... |
I have an linear optimisation problem and I'd like to impose a constraint of the following form:
sum(x(i),y(i))<=C, where 0<i<N and x is the decision variable and C is the constraint value
how can I linearize it ? |
how can I linearize a constraint of the form sum(min(x(i),y(i))) for a linear optimisation problem? |
Sorry if this is too obvious to you. The marginal risk contribution mentioned here is the same as in this post https://quant.stackexchange.com/questions/37878/marginal-risk-contribution-formula .
I understand the concepts and derivation on the formula. But I got some questions from some legacy codes I'm working on. ... |
I have an linear optimisation problem with the objective :
$ max PortfolioSpread(x_1,x_2,....x_N) = ∑_{i=0}^N(x_i*s_i)/budget$
s.t.
1. $∑_{i=0}^N x_i = budget$ (+ other constraints)
2. $∑_{i=0}^N min(x_i,y_i)≥C$
where decision variables $x_i$ represent market values, $y_i$ represent current holdings expr... |
I am new to Quantitative Finance so please bear with me. I have the following data set:
> head(df, 20)
# A tibble: 20 × 15
deal_id book counterparty commodity_name commodity_code executed_date first_delivery_date last_delivery_date last_trading_date volume buy_sell trading_unit tenor d... |
I am new to Quantitative Finance so please bear with me. I have the following data set:
> head(df, 20)
# A tibble: 20 × 15
deal_id book counterparty commodity_name commodity_code executed_date first_delivery_date last_delivery_date last_trading_date volume buy_sell trading_unit tenor d... |
Suppose we introduce the following: a token S with an initial supply of a 1000. At $t_0$, a 1000 different parties $P_1,\dots,P_{1000}$ each buy a single token for $1$\$.
Whoever has the most tokens at time $t_N$ (suppose $N$ discrete time steps), receives $950$\$. After $t_N$ the tokens become useless and nothing h... |
Suppose we introduce the following: a token S with an initial supply of a 1000. At $t_0$, a 1000 different parties $P_1,\dots,P_{1000}$ each buy a single token for $1$\$.
Whoever has the most tokens at time $t_N$ (suppose $N$ discrete time steps), receives $950$\$. After $t_N$ the tokens become useless and nothing h... |
Let's assume a stock at time $t$ is worth $X(t)$. If the returns of $X(t)$ are i.i.d. and normally distributed,the probability of $X(t)$ hitting a value $H>X(t)$ before $L<X(t)$ is $\frac{H-X(t)}{H-L}$ (not considering exchange fees and the cost of shorting).
Now, I ran a python simulation on a stochastic process wi... |
How to import **Growth Estimates: Next 5 years(per annum)** from yahoo finance to microsoft excel?
[![screenshot from analysis section in yahoo finance regarding importing the value 21.44% from yahoo finance to excel ][1]][1]
[1]: https://i.stack.imgur.com/zW0k9.png |
There is no direct connection for excel.
[These steps](https://smallbusiness.chron.com/import-yahoo-finance-financial-statements-excel-28682.html) work though.
[![enter image description here][1]][1]
Still tedious but Yahoo Finance is what it is. You can use https://finance.yahoo.com/quote/GOOG/analysis?p=... |
If you know about Microsoft Power BI, you can use it and pick which columns of which tables you want to import.
[![1.Import from web][1]][1]
[![2.Import from web URL][2]][2]
[![3.Add Table Using Example][3]][3]
[![4.Import][4]][4]
[1]: https://i.stack.imgur.com/NNtU8.png
[2]: https://i.stack.i... |
If you know about Microsoft Power BI, you can use it and pick which columns of which tables you want to import.
**add tables using examples** button at the bottom as in the attached images.
[![1.Import from web][1]][1]
[![2.Import from web URL][2]][2]
[![3.Add Table Using Example][3]][3]
[![4.Import][4... |
If you know about Microsoft Power BI, you can use it and pick which columns of which tables you want to import.
**add tables using examples** button at the bottom as in the attached images.
[![1.Import from web][1]][1]
[![2.Import from web URL][2]][2]
[![3.Add Table Using Example][3]][3]
[![4.Import][4... |
If you know about Microsoft Power BI, you can use it and pick which columns of which tables you want to import.
**add tables using examples** button at the bottom as in the attached images.
[![1.Import from web][1]][1]
[![2.Import from web URL][2]][2]
[![3.Add Table Using Example][3]][3]
[![4.Import][4... |
In most (all?) practical cases, Delta is a model-dependent measure; you need a model to compute it. Black-Scholes, Heston, ... each model has a formula for the (call) option price $C$ and its Delta $\Delta$ , and each model depends on a set of contractually fixed parameters (strike, maturity date $T$), quasi-observable... |
Le us assume that depo and repo rates are zero. And let us assume I can read the ATM implied volatility of 1y option from the volatility surface. I now have some algorithm to reprice this option (let's say, using local volatility Monte Carlo). Having the PV inferred via Blacck-Scholes from the ATM implied vol on the vo... |
Suppose that we have five trades each day with these returns ($R_{day,trade}$) and we have 300 days in total:
$R_{1,1}$, $R_{1,2}$, $R_{1,3}$, $R_{1,4}$, $R_{1,5}$
$R_{2,1}$, $R_{2,2}$, $R_{2,3}$, $R_{2,4}$, $R_{2,5}$
For each day, we calculate the return of that day by weighting these returns (these weights ... |
How to calculate the log return of portfolio? |
Suppose that we have five trades each day with these returns ($R_{day,trade}$) and we have 300 days in total:
$R_{1,1}$, $R_{1,2}$, $R_{1,3}$, $R_{1,4}$, $R_{1,5}$
$R_{2,1}$, $R_{2,2}$, $R_{2,3}$, $R_{2,4}$, $R_{2,5}$
For each day, we calculate the return of that day by weighting these returns (these weights ... |
Suppose that we have five trades each day with these returns ($R_{day,trade}$) and we have 300 days in total:
$R_{1,1}$, $R_{1,2}$, $R_{1,3}$, $R_{1,4}$, $R_{1,5}$
$R_{2,1}$, $R_{2,2}$, $R_{2,3}$, $R_{2,4}$, $R_{2,5}$
For each day, we calculate the return of that day by weighting these returns (these weights ... |
How to calculate the gaussian VaR for a portfolio with 3 corporate bonds and 1 IRS payer? |
Suppose that we have five trades each day with these returns ($R_{day,trade}$) and we have 300 days in total:
$R_{1,1}$, $R_{1,2}$, $R_{1,3}$, $R_{1,4}$, $R_{1,5}$
$R_{2,1}$, $R_{2,2}$, $R_{2,3}$, $R_{2,4}$, $R_{2,5}$
For each day, we calculate the return of that day by weighting these returns (these weights ... |
Suppose that we have five trades each day with these returns ($R_{day,trade}$) and we have 300 days in total:
$R_{1,1}$, $R_{1,2}$, $R_{1,3}$, $R_{1,4}$, $R_{1,5}$
$R_{2,1}$, $R_{2,2}$, $R_{2,3}$, $R_{2,4}$, $R_{2,5}$
For each day, we calculate the return of that day by weighting these returns (these weights ... |
If we assume the estimator for a sample mean is biased and if the optimal portfolio weights vary with the estimated mean, is there a way (similar to the zero beta portfolio approach wrt the risk free rate) to construct the Markowitz efficient frontier only from the covariance matrix? |
Is it possible to construct an efficient frontier without the mean? |
Assuming B&S world, is it possible to price an (European) option on a general transformation $f(\cdot)$ of $X$? What kind of assumptions should we make on $f$? Is convexity sufficient to find some meaningful results?
For example for a call:
$$
\max(0, f({X_T})-K)
$$
|
Are there optimal portfolio theories than instead of the expected value they were based on the **[Mode](https://en.m.wikipedia.org/wiki/Mode_(statistics))** of distributions?
During my engineer student days I saw the Markowitz theory for portfolio selection and there is something that always bothers me, and it is th... |
Le us assume that depo and repo rates are zero. And let us assume I can read the ATM implied volatility of 1y option from the volatility surface. I now have some algorithm to reprice this option (let's say, using local volatility Monte Carlo). Having the PV inferred via Black-Scholes from the ATM implied vol on the vol... |
I was wondering if it's pertinent to use this interpretation of the expected utility function given by the Taylor series expansion,
$${E(U(W)}\approx{U[E(W)}]+\frac{U''[E(W)]\sigma^2_W}{2}\tag{1}$$
to delineate my optimal portfolio from the set of portafolios that lie on the efficient frontier?
So, let's say... |
First, there are a few things I'm not clear about, like what the 'risk free' return is.. is there even such a thing in trading? or how to handle inactive days, etc.
Let's assume I have a period of 30 days.
During these 30 days, I have 5 trades with their duration:
- +5%, 2 days
- -3%, 5 days
- +1%, 3 days
- +2%... |
how to calculate the Sharpe ratio based on a list of trades, with space between them? |
I would like to have a clear picture about lithium investments all over the World.
I like [this website][1] where I can see all companies related to lithium on the Australian Market.
The website also proposes other commodities like nickel, copper, etc...:
[![enter image description here][2]][2]
Nice.
But... |
Looking at some level 1 quotes data (QRM) on the bloomberg terminal for a DAX index option. Why is there always a 1 lot quote for 450 just popping in every other tick? Seems like there is a single MM quoting these elevated prices in hopes that someone will enter a market order and then get a ridiculously bad fill at 45... |
Level 1 NBBO - what is going on? |
I've see a couple of places where a FX rate, denoted $X$, such as EURUSD (quoted as "the number of USD needed to buy 1 EUR") is modeled with a diffusion process / Geometric Brownian Motion as follows through its "rate of change":
$$\frac{dX_t}{X_t} = \left[r_d(t)-r_f(t)\right]dt + \sigma(t,X) dW^Q(t),$$
where $r_... |
I see various levels of detail on different ETF sites. Pouring through the regs is not trivial. If we keep to US ETFs, is there somewhere to find the mandated reporting requirements? Is there any requirement to post calculations somewhere with marks, holdings, fx, net funds, total shares and NAV? Or is it just a requir... |
What is the regulation mandated minimum reporting of calculations and holdings for ETFs? |
I am answering now instead of commenting. The rate of change in FX is naturally forward looking in this case.
What you confuse is what happened to Spot due to changes in interest rate environments relative to what is expected based on no arbitrage arguments. The recent FED hikes ($r_d$ increases) and the EURUSD dec... |
I am answering now instead of commenting. The rate of change in FX is naturally forward looking in this case.
What you confuse is what happened to Spot due to changes in interest rate environments relative to what is expected based on no arbitrage arguments. The recent FED hikes ($r_d$ increases) and the EURUSD dec... |
Let $(S_{t}^{1},S_{t}^{2})_{t\geq0}$ be two assets. Define $X_{t}=S^{1}_{t}-S^{2}_{t}$. If $X_{t}$ satisfies the SDE:
\
$dX_{t}=\xi(\zeta-X_{t})dt+\sigma dW_{t}$
\
then what process does $(S_{t}^{1},S^{2}_{t})$ follow (assuming reasonable conditions like nonnegativity)? |
If the spread between two assets is an OU process, what processes do the two assets follow? |
Let $(\Omega,\mathcal{F}, \mathbb{P}, (\mathcal{F}_{t})_{t\geq0})$ be a filtered probability space. Furthemore, let $(S_{t}^{1},S_{t}^{2})_{t\geq0}$ be two assets (adapted to filtration, etc). Define $X_{t}=S^{1}_{t}-S^{2}_{t}$. If $X_{t}$ satisfies the SDE:
\
$dX_{t}=\xi(\zeta-X_{t})dt+\sigma dW_{t}$, ($W_{t}$ is a ... |
Let $(\Omega,\mathcal{F}, \mathbb{P}, (\mathcal{F}_{t})_{t\geq0})$ be a filtered probability space. Furthemore, let $(S_{t}^{1},S_{t}^{2})_{t\geq0}$ be two assets (adapted to filtration, etc). Define $X_{t}=S^{1}_{t}-S^{2}_{t}$. If $X_{t}$ satisfies the SDE:
\
$dX_{t}=\xi(\zeta-X_{t})dt+\sigma dW_{t}$\
($W_{t}$ is ... |
### There is a regulatory framework for the Key Information Document of financial products within the European Union:
*While this is not specifically what you are asking for*, there exists a solid regulatory framework within the European Union on how to provide retail investors with a Key Information Document (KID)$... |
## There is a regulatory framework for the Key Information Document of financial products within the European Union:
*While this is not specifically what you are asking for*, there exists a solid regulatory framework within the European Union on how to provide retail investors with a Key Information Document (KID)$^... |
This month the TerraUSD stablecoin and associated Luna reserve cryptocurrency crashed and [lost most of its value](https://en.wikipedia.org/wiki/Terra_(blockchain)#Collapse). About $45 billion in market capitalization vanished within a week.
Apparently there was some sort of sell-off, but then TerraUSD was supposed ... |
How did the algorithm pegging TerraUSD stablecoins to USD fail? |
Are there optimal portfolio theories than instead of the expected value they were based on the **[Mode](https://en.m.wikipedia.org/wiki/Mode_(statistics))** of distributions?
During my engineer student days I saw the Markowitz theory for portfolio selection and there is something that always bothers me, and it is th... |
Write the Euler discretization of the 1-dimensional stochastic equation
$dXt = b (t, X_t) \space dt + \sigma (t, X_t) \space dW_t$
For this part I would say all right because it is a purely theoretical part that I find on any stochastic calculus book.
The problem arises on the optional part:
Set $b (t, x... |
> How has it failed? How fragile was this pegging of a cryptocurrency to the USD?
> I guess that different currencies can ultimately never be pegged perfectly and a stablecoin is a bit of a misnomer, but still I wonder how easy it might have been to break this pegging.
It depends on the quality of the collateral,... |
There's a huge literature on this topic going back at least 30 years, and I am unfortunately not familiar enough with this literature to give you a great answer to your specific question. However, I will in this answer at least try to point you in some useful directions according to what I've found thus far.
Kurtos... |
> How has it failed? How fragile was this pegging of a cryptocurrency to the USD?
> I guess that different currencies can ultimately never be pegged perfectly and a stablecoin is a bit of a misnomer, but still I wonder how easy it might have been to break this pegging.
It depends on the quality of the collateral,... |
This might be a very broad question, but I would like if someone can please explain to me how a market makers make money in Options market ? Thank you |
How an Option market-makers make money? |
I did some cointegration tests on a 50 stocks sample, whith which I created pairs. I used the Engle-Granger approach and the Johansen approach, both of them gave me a high percentage of cointegrated pairs(45% and 96%). I'm fairly sure about the way I did the Engle-Granger test (OLS->get residual and test for stationnar... |
How rare is cointegration in the case of stocks? |
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