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I've come across a research paper where for a specific period of time, the portfolio has negative returns (or roughly flat returns). During this same period of time, the portfolio's Fama-French 3-factor alpha is fairly positive.
[Here][1] is a photo of the returns from the paper, I'm looking at the 2000-2007ish time... |
Could someone describe how risk-neutral probability measures are linked to arbitrage opportunities and also to whether or not a market is complete? I've been asked this question and am unsure how to answer it. It also asks me to 'state any results I make use of in my answer'. Not really too sure what this is getting at... |
if i have some utility function say $U(p)=p^{1/2}$
and i am betting on a basketball game.
I have my initial investment, payouts and probabilities of winning, how can I determine the maximum I need to bet on each basketball team to maximize my utility function? I have been looking through the theory for this and im no... |
how do i maximize my expected utility of wealth? |
Suppose I have a utility function say $U(p)=p^{1/2}$
and I bet on a basketball game.
I have my initial investment, payouts and probabilities of winning, how can I determine the maximum I need to bet on each basketball team to maximize my utility function? I have been looking through the theory for this and im not sur... |
How do I maximize my expected utility of wealth? |
Traditionally, retail traders have leveraged on price patterns discovered by applying graphical tools such as flags, fractals, pennants, heads, shoulders, etc.
However, while this method has been very profitable for many, it is often based on the individual's capability of empirically detecting/visualizing trends.
... |
How can I combine traditional trading patterns and machine learning algorithms to produce a trading system? |
if my discrete random variable had a poisson distribution
with both moments say = 10, how would i find the Value at Risk for a 95 percent confidence interval? I have seen that I need to integrate the pdf from the lower limit up until L so I am trying to integrate that from 0 to L then equating it to 0.5 but its an a... |
So I understand that the minimum variance hedge ratio minimizes the second moment of the portfolios. My question is how is it related to the size of the risk capital (which is calculated as the Value at Risk - Expected Value). Is the Risk capital also minimized at the optimal hedge ratio? Since the Value at Risk is not... |
I am very new with python, and I am used to work with bloomberg formulas for excel. I am starting to use a lot more python in my analysis, is there any library that performs same functions as bdp, bdh or bcurve?
Thanks!
Juan |
Python libraries for bloomberg? |
Let's stick to a discrete market for simplicity. So, you have a finite number of states in this type of model.
The **first fundamental theorem of asset pricing** says that the absence of arbitrage in such markets imply the existence of (not necessarily unique) risk-neutral measure and vice-versa.
The reason it wo... |
If my discrete random variable had a poisson distribution with both moments say equal to 10, how can I find the Value at Risk for a 95 percent confidence interval?
I have seen that I need to integrate the PDF from the lower limit up until $L$ so I am trying to integrate that from $0$ to $L$ then equating it to 0.5 ... |
Bounded random variables are sub-Gaussian, yet I, intuitively, assume financial returns are bounded random variables; however, they are not sub-Gaussian. **Am I wrong to assume financial returns are bounded random variables? How could that be so?**
For a proof of bounded RV $\implies$ sub-Gaussian, see Example 2.4 o... |
Bounded random variables are sub-Gaussian, yet I, intuitively, assume financial returns are bounded random variables; however, they are not sub-Gaussian. **Am I wrong to assume financial returns are bounded random variables? How could that be so?**
For a proof of bounded RV $\implies$ sub-Gaussian, see Example 2.4 o... |
A bounded random variable is sub-Gaussian, thus financial returns are not bounded? |
How does SABR model capture volatility smile? |
While reading [How does implied volatility affect option pricing by Investopedia][1], it states the following in key takeaways
> - When options markets experience a downtrend, implied volatility generally increases.
> - Implied volatility falls when the options market shows an upward trend.
> - Higher implied... |
Why does Implied volatility fall when the options market shows an upward trend? |
It is poorly worded. **Replace "options markets" with "stock markets" and it becomes clear that they're just noting typical spot vol correlation.** When stock markets trade up volatility tends to fall and when stock markets trade down volatility tends to rise. This has been the case, on average, historically. For mor... |
I have a list of factors (and their returns) as well as a set of
mutual fund returns. What are some techniques I could use to select
relevant factors for the funds. For example, fixed income factors to be
selected for fixed income funds. I have tried stepwise regressions and
then filtering on the $p$-value, but I w... |
I am looking for a free real time tick by tick data for training and analyzing and plotting forex charts, but I am searching a lot and I couldn't find any good data feed provider.
Why there is no support or any solution for this problem? Is it costly for companies to provide?
Is it possible to me to gain my need... |
I have been reading Active Portfolio Management by Grinold and Khan. In the chapter about risk, they mention,
*"The third elementary model relies on historical variances and covariances. This procedure is neither robust nor reasonable. Historical models rely on data from T periods to estimate the $NxN$ covariance ma... |
> Is it possible to me to gain my needed data directly from the markets?
Yes, and no. If you want *executable* quotes from one liquidity provider, talk to them (eg. [JPFX](https://www.jpmorgan.com/country/US/en/markets/execute/fxtrading), [Saxo FX](https://www.home.saxo/products/forex), etc.).
If you want bund... |
How can someone make the Keneth French library data returns quarterly from monthly? Since they are not loq returns, then you need to compound returns rather than summing them up. I want to make the returns of the SML, HML, the industry portfolio and the risk free that he uses, as quarterly returns. Does anybody know ho... |
How can someone make the Kenneth French library data returns quarterly from monthly? Since they are not loq returns, then you need to compound returns rather than summing them up. I want to make the returns of the SML, HML, the industry portfolio and the risk free that he uses, as quarterly returns. Does anybody know h... |
I thought I had a pretty good grasp on how to calculate this but I'm getting questioned on it and just want to be sure I'm not getting it mixed up. In my notation you enter into the repo contract at $t=t_0$ and exchange a cash nominal, C, for bonds where C is determined by $C=B_{t_0} (1-HC)$ where HC is the haircut, e.... |
Would it be possible to design a market neutral strategy without short selling?
How? |
Would it be possible to design a market neutral strategy without short selling?
According to [Investopedia][1]:
> Market-neutral strategies are often attained by taking matching long
> and short positions in different stocks...
According to [here][2]:
> Market Neutral investing is also possible without (..... |
> After a lot of searching I find out maybe it's better to gain my needed data directly from brokers
and
> Can someone show me a solution or a way
Here is a one line command line/terminal script to directly download streaming tick data from Oanda, in this case for the EUR_USD pair.
stdbuf -oL -eL curl -... |
Let's say I'm developing an HFT application and seeking arbitrage in futures markets between MAY contract(M) and JUNE contract(J).
In this strategy, my spread is `J-M`. I did not check with real data but I think this is a mean-reverting series... This spread should be around the interest rate, right? In some short... |
How to detect price anomalies in HFT? |
When I first learn the finance, Bond price is just like that;
in continuous yield,
Z = exp^(-r*t) (r:yield, t:time to maturity)
But, when I learn stochastic interest rate model like HO-LEE and HULL&WHITE, ETC..
the formula is changed;
Z= exp^(A-B*r) (A:sth multiplied B:sth multiplied)
What is the reas... |
Why Bond pricing formula is changed? |
When I first learn the finance, Bond price is just like that;
in continuous yield,
Z = exp^(-r*t) (r:yield, t:time to maturity)
But, when I learn stochastic interest rate model like [HO-LEE][1] and HULL&WHITE, ETC..
the formula is changed;
Z= exp^(A-B*r) (A:sth multiplied B:sth multiplied)
What is the... |
When I first learn the finance, a bond with continuous yield was priced via
$$Z = e^{-rT},$$ where $r$ is the yield, $T$ the time to maturity.
But, when I learned stochastic interest rate model like [Ho-Lee][1] and Hull & White, etc. the formula is changed to
$$Z= e^{A-Br},$$ where $A$, $B$ are functions.
... |
When I first learn about finance, a bond with continuous yield was priced via
$$Z = e^{-rT},$$ where $r$ is the yield, $T$ the time to maturity.
But, when I learned about stochastic interest rate models like [Ho-Lee][1] and Hull & White, etc. the formula changed to
$$Z= e^{A-Br},$$ where $A$, $B$ are function... |
My lecturer has written the slide below. The function B^T(t) is a zero coupon bond. I don't understand how V(t) can be a negative integral from `0` to `t`. Surely, it's a negative integral from `t` to `T`? Her notes are full of mistakes so I cannot figure out if I'm not getting something or if she's made a mistake.
... |
I'm taking an online class on stock valuation. In my class, the instructor calculated stock intrinsic value using XNPV function in Excel. While I understand this part, I don't know why it gives a different result from myself manually discounting each cash flow and summing up everything.
All XNPV calculation is done ... |
It is well known that Institutional traders (Large trading firms, market makers) most of the time use LIMIT orders or Hidden limit orders. My question is, do they ever use market orders in their trading? |
Do Institutions (large trading firms) use market orders? |
The short answer is yes but the way in which this happens is much more complicated so while eventually a market order is executed, it does not start as a market order. Big institutions often have large trades which cannot just be executed as a market order. Correct me if I'm wrong, but they might even get in trouble wi... |
The short answer is yes but the way in which this happens is much more complicated so while eventually a market order is executed, it does not start as a market order. Big institutions often have large trades which cannot just be executed as a market order. They might even get in trouble with a regulator for moving the... |
We are trying to analyze an algorithm (internal to our company) to calculate currency option pricing using the Garman and Kohlhagen model.
Our internal algorithm calls for CBS (Currency Basis Swaps) rates to be added to interest rates in the following manner.
> Add to the USD interest rate the CBS rate for the n... |
Why is CBS (Currency Basis Swaps) added to Interest Rates? |
(I asked this question on MSE but I think it might have more success here)
Good day,
>I was going over some exercises and I stumbled upon a question that, for its solution, requires me to find/simplify $$ \tilde{\Bbb{E}}[S_T|\mathcal{F}_t] $$ in terms of $S_t$ where
> $$ S_t=S_0Y_t+Y_t\int^t_0\frac{a}{Y_s}ds ... |
I assumed the SEC filings for balance sheet or income statement should follow a standard format across companies. If that is the case, why is some important fields absent for certain companies? For example American Express(AXP) or Goldman Sachs(GS) apparently do not report current liabilities on their balance sheet, th... |
I am trying to understand the butterfly spread. My book (ASM IFM) says one of the ways to write it is:
Long put, strike $=K-c$
Short put, strike $=K$
Short call, strike $=K$
Long call, strike $=K+c$
When I try to calculate it, it doesn't look like a butterfly spread to me. There are four places where the... |
I am trying to understand the butterfly spread. My book (ASM IFM) says one of the ways to write it is:
Long put, strike $=K-c$
Short put, strike $=K$
Short call, strike $=K$
Long call, strike $=K+c$
When I try to calculate it, it doesn't look like a butterfly spread to me. There are four places where the... |
I am trying to understand the butterfly spread. My book (ASM Study Manual for SOA Investment & Financial Markets (IFM) Exam) says one of the ways to write it is:
Long put, strike $=K-c$
Short put, strike $=K$
Short call, strike $=K$
Long call, strike $=K+c$
When I try to calculate it, it doesn't look lik... |
So I'm trying to solve the black scholes equation using a finite difference model, but I'm getting a answer that's off and I'm having trouble understanding why.
This is the result for a option with K = 100.0, r = 0.12, and sigma = 0.10
[![solution][1]][1]
The left side is higher than it should be, and should s... |
I am trying to evaluate the impact of switching an Asset-Swap Package (fixed bond + Swap) into a floating rate bond of the same issuer with the same notional and maturity. My intuition would tell me that both instruments should be equivalent, as with both I am receiving a floating cash flow from the same issuer for the... |
Is the value of an Asset-Swap (Underlying + Swap) the same value as a floating-rate bond with the same issuer, maturity, etc.? |
I am going to try to answer your more general question "Do all SV models generate a smile?" which you put in one of the comments. (Maybe edit also the title of your question if you want, if my answer is satisfactory.)
I will take zero correlation between asset and the volatility process to start with. The generalisa... |
I am going to try to answer your more general question "Do all SV models generate a smile?" which you put in one of the comments. (Maybe edit also the title of your question if you want, if my answer is satisfactory.)
I will take zero correlation between asset and the volatility process to start with. The generalisa... |
Do all stochastic volatility models capture volatility smile? |
My questions relates to this post https://quant.stackexchange.com/questions/36636/implying-risk-free-rates-using-put-call-parity , but I am using a different approach.
Given: ODAX Settlement prices across different maturities and strikes.
$$
PCP: p_{i,t,T} - c_{i,t,T} = (P_{t,T} - S_t) + e^{-r_{t,T}(T-t)}K_i
$$... |
In FIX protocol, how to identify if the trade being submitted to foreign country ?
|
In FIX protocol, how to identify if the trade being submitted to foreign country? |
I'm reading about this three concepts but still can't see the difference between the three of them, can someone please explain the main difference between three of them ? Thanks |
Difference between Risk Premia, Alternative Risk Premia and Factor Investing? |
I am investigating the potential for intra-exchange triangular arbitrage opportunities for the Cryptocurrency market. I believe that due its immaturity, relatively low volume and high volatility that such instances materialise and persist for periods of time long enough to be taken advantage of through an exchange API.... |
What are the driving factors behind prolonged instances of triangular arbitrage opportunities? |
What are the best metrics to evaluate an ML algo backtest, other than the nominal returns? |
I am having trouble modeling short selling mechanics in my backtesting system.
When I sell stock short, I make the following changed to account variables:
1. Credit Balance += 200% of the stock value sold short (assuming a 100% initial margin requirement)
2. Cash -= 100% of the stock value (the cash is transferr... |
OK, I'll share a lot of the scepticism voiced in the comments to the OP above. There is an important marekting>reality dimension here. The problem is that if an investor wants a core traditional risk premium like Treasuries or the S&P, there's an ETF costing single-digit basis points. Institutions can do liquid futures... |
OK, I'll share a lot of the scepticism voiced in the comments to the OP above. There is an important marekting>reality dimension here. The problem is that if an investor wants a core traditional risk premium like Treasuries or the S&P, there's an ETF costing single-digit basis points. Institutions can do liquid futures... |
I saw the quote as this: EUR/USD 1m ATM 0.3150/0.3190. I guess these are vol levels. What the units of these bid and offer quoted? |
From [this lecture][1] on YouTube the lecturer states that there are three ways to form the mean variance portfolio, however only goes into the first in detail. Are there any texts which cover the formulations of problems two and three? Lecture notes which accompany the series are [here][2] and problems are on slide 7.... |
From [this lecture][1] on YouTube the lecturer states that there are three ways to form the mean variance portfolio (minimize variance for a given return, maximize return for a given variance, maximize a "risk adjusted return" which is the return minus a penalty for variance) however he only goes into the first in deta... |
I am looking at the ARCH model where we have $\hat{\varepsilon}_t^2=\alpha_0 + \alpha_1\hat{\varepsilon}_{t-1}^2 + \alpha_2\hat{\varepsilon}_{t-2}^2 + \cdots + \alpha_q\hat{\varepsilon}_{t-q}^2 +v_t$
Any significant alpha 1 to q would mean that there is evidence of ARCH effects. So far so good.
What I am stru... |
I am looking at the ARCH model where we have $\hat{\varepsilon}_t^2=\alpha_0 + \alpha_1\hat{\varepsilon}_{t-1}^2 + \alpha_2\hat{\varepsilon}_{t-2}^2 + \cdots + \alpha_q\hat{\varepsilon}_{t-q}^2 +v_t$
Any significant alpha 1 to q would mean that there is evidence of ARCH effects. So far so good.
What I am stru... |
In my course on discrete-time finance we derived the following equality for a lower bound for the value of a not necessarily replicable contingent claim $D$. Here we are looking at a single period market with risk-free interest rate $r$ and $E$ is the expectation operator.
$$sup\{E[Y(1)/(1+r)]:Y \text{ replicable, }\t... |
@chrisaycock raises a valid point about the process not being particular rigorous.
There are reasons why it is not a rigorous or optimized sizing mechanism.
1) most market makers are quoting many strikes & expirations, usually multiple underlying assets these days. Depending on venue there may be ways to limit th... |
I have below here an excerpt from a book on (among other things) mean-variance analysis showing how to find the minimum variance portfolio. I am confused by the statement here saying that if short-selling isn't allowed, you can find the constrained minimum-variance portfolio simply by removing the offending equity and ... |
Is this methodology for finding the minimum variance portfolio with no short-selling sound? |
I am looking at the ARCH model where we have $\hat{\varepsilon}_t^2=\alpha_0 + \alpha_1\hat{\varepsilon}_{t-1}^2 + \alpha_2\hat{\varepsilon}_{t-2}^2 + \cdots + \alpha_q\hat{\varepsilon}_{t-q}^2 +v_t$
Any significant alpha 1 to q would mean that there is evidence of ARCH effects. So far so good.
What I am stru... |
I am looking at the ARCH model where we have $\hat{\varepsilon}_t^2=\alpha_0 + \alpha_1\hat{\varepsilon}_{t-1}^2 + \alpha_2\hat{\varepsilon}_{t-2}^2 + \cdots + \alpha_q\hat{\varepsilon}_{t-q}^2 +v_t$
Any significant alpha 1 to q would mean that there is evidence of ARCH effects. So far so good.
What I am stru... |
I have below here an excerpt from a book on (among other things) mean-variance analysis showing how to find the minimum variance portfolio (*Risk and Portfolio Analysis: Principles and Methods*, by Hult, Lindskog, Hammarlid, and Rehn). I am confused by the statement here saying that if short-selling isn't allowed, you ... |
I am using the Bittrex exchange API to ping markets to poll whether there are triangular arbitrage opportunities available for USD/BTC/LTC/USD. Note that I am not trading but rather synthesising them by using the API to collect bid and ask data for each of the 3 markets. My test polls also account for fees too. My curr... |
Would C++'s speed over Python make it a more applicable language for scalping arbitrage opportunities? |
I am looking at the ARCH model where we have $\hat{\varepsilon}_t^2=\alpha_0 + \alpha_1\hat{\varepsilon}_{t-1}^2 + \alpha_2\hat{\varepsilon}_{t-2}^2 + \cdots + \alpha_q\hat{\varepsilon}_{t-q}^2 +v_t$
Any significant alpha 1 to q would mean that there is evidence of ARCH effects. So far so good.
What I am stru... |
I had an example at work which I didn't have full intuition of. The example is as follows:
You have novated a forward starting cross-currency basis swap (let's say 10y10y EUR ccbs).
The PV is agreed with counter party 'A' stepping in. However, there is a CSA implication... the remaining counter-party 'B' is on US... |
Why are Hidden Markov Models (HMM) a good fit to describe the behaviour of the prices of fiancial assets, when these models require that the underlying stochastic process satisfies the first-order Markov property?
According to such property, the probability of future events it's only determined by the current state ... |
Why do we make the Markov assumption on financial markets? |
The markov property imposes a form of unpredictability on price dynamics within financial models. As you noted, if this was exactly true, technical traders would effectively be wasting their time.
Now, there is a bit of a problem in what you wrote about technical traders. **They believe** that some price patterns ca... |
I am working on a Fama MacBeth regression with excess returns on the LHS and Size, Value an Momentum factors on the RHS. In literature, the Momentum factor is often definded as the cumulative past 6 month returns of a certain equity.
The Fama Macbeth procedure accounts for cross-sectional correaltion of the residua... |
I am a newbie.
The risk neutral pricing has the following formulation:
$$P=\frac{\hat{E(d)}}{R}$$,
But the discounted expected value has the formulation of:
$$P=\frac{E(d)}{R}$$.
The text book says $\hat{E}(.)$ is the expectation over risk-neutral probability.
What exactly is that risk-neutral p... |
Examples like new research or findings but also older research or findings actually starting to get implemented. Is machine learning starting to get a foothold in finance? Are there any new practical differences in the market, such as new instruments being traded or new regulations having a large impact on the world of... |
What are the biggest new advancements in the field of quantitative finance in the last 10 years? |
Assume a model defined in a incomplete market. Assume that model contains some parameters $\theta_1 ... \theta_k$. In a risk neutral setting, one more parameter appears into the modeldynamics which is $\lambda$ (also known as the market price of risk). The market price of risk is unobservable. Does that mean it is subj... |
Is the market price of risk subjective? |
I am working on a Fama MacBeth regression with excess returns on the LHS and Size, Value an Momentum factors on the RHS. In literature, the Momentum factor is often definded as the cumulative past 6 month returns of a certain equity.
The Fama Macbeth procedure accounts for cross-sectional correlation of the residua... |
Why are Hidden Markov Models (HMM) a good fit to describe the behaviour of the prices of financial assets, when these models require that the underlying stochastic process satisfies the first-order Markov property?
According to such property, the probability of future events it's only determined by the current state... |
I am trying to understand the abbreviations in the Bloomberg European stock or STOXX data. Each ticker represents **company name abbreviation - Listed exchange**.
For example, CSP - LN is Countryside Properties PLC - **London stock exchange**. I am hoping to find a document where I can get the **"two-letter"** abbr... |
To price a call/put option with two possible future states of the world, I understand we can price the option by essentially calculating the price of a replicating portfolio that gives the same returns in either state of the world. However:
1) Why do we always consider a portfolio with the underlying asset and risk-... |
Can the Hodges-Tompkins adjustment be used to de-bias any estimator computed from overlapping observations? It appears that most implementations apply it under the assumption of constant volatility. Is this adjustment applicable to estimates obtained from close-close, Garman-Klass, Parkinson, etc. on overlapping observ... |
Is Hodges-Tompkins adjustment applicable for all volatility estimators? |
Vanilla options are traded interbank with delta hedge. The instrument employed to a delta
hedge is usually a forward with the same expiry (and opposite delta) as the option. This means
that in effect the traded instrument is a call and a put with the same strike.
Why is that so and how does the Put Call Parity fit... |
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