Strategy of Renaissance Technologies Medallion fund: Holy Grail or next Madoff?

Renaissance Technologies Medallion fund is one of the most successful hedge funds - ever! Yet it is very secretive. Do you have information on the strategy used that is not yet mentioned in the Wikipedia article above? Is there really something fundamental going on (the Holy Grail of investing) - or will this be the next Madoff?

The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the law of one price , also known as the principle of no riskless arbitrage and which you may already have heard of in the following terms: "there is no free lunch in financial markets". This law is at the heart of securities' relative valuation , see this very nice paper by Emmanuel Derman ("Metaphors, Models & Theories", 2011) and some part of this discussion. In what follows, assume for the sake of simplicity existence of a risk-free asset ; deterministic and constant rates, with risk-free rate $r$ ;...

There are a some information about Renaissance Technologies available in The Quants from Patterson. Basically, and it's also what I heard in general, they are using intensively algorithmic trading, and from what I understood there are using Information Theory (they worked with Shannon if I remember well). I'd say it'd be harsh to say it's the next Madoff given the background they have, I can easily see them being simply better than the rest... It's just my opinion of course...


What are the best sources for equity quantitative research?

What are the best sources of quantitative finance research in equities? I will list a couple and note an asterisk if the research is available by request (i.e. non-clients) or online: BAC-Merrill Lynch - Savita Subramanian Deutsche Bank - Yin Luo* Credit Suisse - Pankaj Patel Barclay's - Matthew Rothman HSBC - Ely Klepfish* Goldman Sachs - Quantitative Strategies Neuberger-Berman - Wai Lee Nomura - Joseph Mezrich Perhaps there are also more un-conventional sources of quant research besides sell-side wall street: Hussman Funds - John Hussman* Emanuel Derman's collection of papers

The minimum variance solution loads up on securities that have low variances and co-variances. Theoretically you are correct that this should have a low expected return profile. However, it turns out - in contradiction to modern portfolio theory - that securities that have low-volatility or low-beta experience higher returns than high-volatility or high-beta stocks. This is well-documented in the literature as the low-volatility anomaly . As a result, many funds and ETFs have been launched in recent years to exploit this phenomenon. There are a couple arguments as to why the anomaly exists. The paper I cite above argues that...

Sell Side Macquarie Quant - Venkat Eleswarapu Bernstein Research - Vadim Zlotnikov Nomura - Joe Mezrich JPMorgan Investment Strategies series Societe Generale - Alain Bokobza Independent CXO Advisory Empirical Finance Blog Russell Indexes: Research and Insights MSCI Research Papers Axioma Research Papers

Garabedian, Typically, the "swap curve" refers to an x-y chart of par swap rates plotted against their time to maturity. This is typically called the "par swap curve." Your second question, "how it relates to the zero curve," is very complex in the post-crisis world. I think it's helpful to start the discussion with a government bond yield curve to clarify some concepts and terminologies. Consider the US Treasury market, using the outstanding Treasury notes and bonds (nearly 300 of them...), we can either use bootstrapping or more sophisticated spline models to construct a "fitted curve." Since this yield curve...

This question goes to whether the historical returns to factors represent: Spurious results, overfitting, data mining... Mispricing Unexploitable effects Compensation for risk Case 1: Spurious results etc... If someone constructs a "stock tickers that begin with AAP or GOO" factor, the highly above average returns would almost certainly reflect a fishing expedition (or conditioning on future information) and would not be reproducible going forward. Under a null of no above average returns, you're going to get portfolios that have above average historical returns with t-stats over 2. Beware. For something like the Fama-French factor $\mathit{HML}$, this seems far less likely...


Proof that you cannot beat a random walk

There is much speculation to what degree financial series are random (and what kind of randomness prevails). I want to turn the question on its head and ask: Is there a mathematical proof that whatever trading strategy you use you cannot beat a random walk (that is the expected value will always be 0 assuming no drift)? (I found this blog post where the author used the so called "75% rule" to purportedly beat a random walk but I think he got the distinction between prices and returns wrong. This method would only work if you had a range of allowed prices (e.g. a mean reverting series). See e.g. here for a discussion.)

Because of: The (extreme) dominance of noise over signal The prevalence of non-repeating patterns (many of which we know are not going to repeat) A pathetic sample size for cross-validation Regime changes due to exogenous events. These are typically in the cross-val window which makes it even worse. (GFC, financial integration, trade law changes, interest rate adjustments by central banks, some idiot in a bank was hiding trades and loses 5 billions dollars, etc). It is well known that non-linear relationships are generally just artefacts of the in sample dataset There is also the following: Much price changes are driven...

I can help you beat random walk 'in the way you want', i.e. the expected value $E[\$]$ will always be positive even assuming no drift. However, I have to warn people that $E[\$] > 0$ is NOT really an adequate condition for 'beating' in reality (at least to myself). Let's define some mathematical notations for derivation, and rephrase (simplify) vonjd's question without losing generality. Assume a trader plays a fair game, and his surplus $X(0), X(1), X(2), ... X(t)$ is a martingale. Q: Can the trader find a stopping time $s$ such that $E[X($s$)] > X(0)$? A proof supporting Bootvis'...

Sell Side Macquarie Quant - Venkat Eleswarapu Bernstein Research - Vadim Zlotnikov Nomura - Joe Mezrich JPMorgan Investment Strategies series Societe Generale - Alain Bokobza Independent CXO Advisory Empirical Finance Blog Russell Indexes: Research and Insights MSCI Research Papers Axioma Research Papers

I have worked on this topic extensively (pricing and calculating IV in production) and believe can offer an informed opinion. First of all Mathworks - the company that creates Matlab is not a trading firm so you should probably not rely on their advice so much. There are few closed form options pricing models, and all have practical shortcomings. Barone-Adesi and Whaley (please correct my spelling of last names as I'm typing from memory) model is simple approximation for American options but is unfortunately not very accurate, and does not deal with dividends. Roll-Geske-Whaley deals with dividends, but not very...


Is the stock price process a martingale or a Markov process?

Some people claim that the data-generating process for stocks is a "martingale" and that is has the "Markov property". Are they unrelated? Is it that the Markov property implies some sort of martingale property, or is it the other way around? How do you statistically test for such properties? How far from reality is it to assume such properties?

I know that I have seen things like this in the past. Wasn't there something recently that used Twitter? Here are a few recent papers as examples, although I will be brutally honest that I don't know if they speak to your decent quality requirement: "Trading Strategies to Exploit Blog and News Sentiment" (Zhang, Skiena 2010) "The Predictive Power of Financial Blogs" (Frisbee 2010) "An analysis of verbs in financial news articles and their impact on stock price" (Schumaker 2010)

The volatiltiy surface is just a representation of European option prices as a function of strike and maturity in a different "unit" - namely implied volatility (while the term implied volatility has to be made precise by the model used to convert prices (quotes) into implied volatilities - for example: we may consider log-normal vols and normal vols). Volatility is often preferred over prices, e.g., when considering interpolations of European option prices (although this may introduce difficulties like arbitrage violations, see, e.g., http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1964634 ). A local volatility model can generate a perfect fit to the implied volatility surface via Dupire's...

From what I remember, there is no real relation between Markov and Martingale, and my intuition was confirmed by this post . Basically, it says that you can say neither of the following: If A is Markov, then A is a martingale. If A is a martingale, then A is Markov. further down the post, you can find two counter examples: $dX_t = a dt + \sigma dW_t$ is Markov but not a martingale and $dX_t = (\int_0^t X_s ds) dW_t$ is a Martingale but is not Markov. As for the assumption of these properties being true, I think it...

I recently read "Modeling financial data with stable distributions" (Nolan 2005) which gives a survey of this area and might be of interest (I believe it was contained in "Handbook of Heavy Tailed Distributions in Finance" ). Another more recent reference is "Alpha-Stable Paradigm in Financial Markets" (2008). I'm not aware of anything covering "risk of fluctuations" and this is still certainly not at the center of the field (i.e. most theory still includes some version of Gaussian or mixture of Gaussians). Would also be interested in other references.


Why is an inverted yield curve a problem?

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 was this viewed so negatively? What kind of effects does this have, in a more macro sense?

There are some cases where you can blend your portfolios using weights directly. One case involves corner portfolios . In this case a linear combination of weights is also efficient. Another case is where you can treat the two separate weights you have produced each as distinct portfolio under the assumption that the correlation between these portfolios is relatively stable. In this scenario, the problem reduces to a two-asset portfolio optimization problem (each asset is simply the linear combination of weights produced via your two methods). The other class of methods involves blending via the expected returns. If you arrived...

Nano answer : declining yield curve is a symptom that the market expects the economy to worsen. Short answer : yield curve is built on expected future interest rates. Yield curve will be downward sloping if you expect interest rates to fall in the future. Interest rates fall because the central bank react to worsening economy. So if the yield curve is downward sloping it means the market expects the economy to worsen to the point that the central bank will have to intervene.

One starts with the Black-Scholes equation $$\frac{\partial C}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2 C}{\partial S^2}+ rS\frac{\partial C}{\partial S}-rC=0,\qquad\qquad\qquad\qquad\qquad(1)$$ supplemented with the terminal and boundary conditions (in the case of a European call) $$C(S,T)=\max(S-K,0),\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad(2)$$ $$C(0,t)=0,\qquad C(S,t)\sim S\ \mbox{ as } S\to\infty.\qquad\qquad\qquad\qquad\qquad\qquad$$ The option value $C(S,t)$ is defined over the domain $0 Step 1. The equation can be rewritten in the equivalent form $$\frac{\partial C}{\partial t}+\frac{1}{2}\sigma^2\left(S\frac{\partial }{\partial S}\right)^2C+\left(r-\frac{1}{2}\sigma^2\right)S\frac{\partial C}{\partial S}-rC=0.$$ The change of independent variables $$S=e^y,\qquad t=T-\tau$$ results in $$S\frac{\partial }{\partial S}\to\frac{\partial}{\partial y},\qquad \frac{\partial}{\partial t}\to - \frac{\partial}{\partial \tau},$$ so one gets the constant coefficient equation $$\frac{\partial C}{\partial \tau}-\frac{1}{2}\sigma^2\frac{\partial^2 C}{\partial y^2}-\left(r-\frac{1}{2}\sigma^2\right)\frac{\partial C}{\partial y}+rC=0.\qquad\qquad\qquad(3)$$ Step 2. If we...


Why is the VIX futures market usually in a state of contango?

I'm a VIX newbie and I'm trying to understand why the VIX futures market is usually in a state of contango. All I can figure is that the sellers of VIX futures contracts demand high "prices" (because the seller is the holder of the short position and makes money when the price falls), and since there are willing buyers, namely ETNs and ETFs that are trying to track the S&P 500 VIX SHORT-TERM FUTURES INDEX (SPVIXSTR) through the purchase and sale of VIX futures, the contracts get sold. Also, the farther out the futures contract expires, the less certain the seller is about what the value of the VIX and the SPVIXSTR will be at the future's expiration date. The greater uncertainty over a longer term results in the seller demanding higher premiums over a longer term than he would demand over a shorter term. It seems like a prudent buyer of VIX futures wouldn't buy contracts that are priced so high. It seems like the VIX futures market should be in a state of contango about as frequently as it is in a state of backwardation. What causes contango in the VIX futures market, and why is it the usual state of the market?

Your questions about contango in VIX futures have close analogies in options too. The Black & Scholes model suggests that all time frames and all strikes should have the same implied volatility, but they don't. I think one of the reasons is that the B&S model assumes that stock returns are distributed in a normal (gaussian) distribution, but the actual returns don't match a gaussian distribution all that well. For example the actual occurrence of big crashes / gains is much more likely than a normal distribution would predict. Since crashes do occur people are willing to pay what the...

I've worked at a hedge fund that allowed GA-derived strategies. For safety, it required that all models be submitted long before production to make sure that they still worked in the backtests. So there could be a delay of up to several months before a model would be allowed to run. It's also helpful to separate the sample universe; use a random half of the possible stocks for GA analysis and the other half for confirmation backtests.

The term has a different meaning to different people. to econometricians, microstructure noise is a disturbance that makes high frequency estimates of some parameters (e.g. realized volatility) very unstable. Generally this strand of the literature professes agnosticism as to the its origin; to market microstructure researchers, microstructure noise is a deviation from fundamental value that is induced by the characteristics of the market under consideration, e.g. bid-ask bounce, the discreteness of price change, latency, and asymmetric information of traders. The last example is frequently cited but I don't think it is accurate. Asymmetric information does not have to be a...

The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the law of one price , also known as the principle of no riskless arbitrage and which you may already have heard of in the following terms: "there is no free lunch in financial markets". This law is at the heart of securities' relative valuation , see this very nice paper by Emmanuel Derman ("Metaphors, Models & Theories", 2011) and some part of this discussion. In what follows, assume for the sake of simplicity existence of a risk-free asset ; deterministic and constant rates, with risk-free rate $r$ ;...


We all know it does mean revert. The question is why. What's making volatility mean-revert? Is it some sort of cyclical behaviour of option traders? The way it's calculated? Why?

One starts with the Black-Scholes equation $$\frac{\partial C}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2 C}{\partial S^2}+ rS\frac{\partial C}{\partial S}-rC=0,\qquad\qquad\qquad\qquad\qquad(1)$$ supplemented with the terminal and boundary conditions (in the case of a European call) $$C(S,T)=\max(S-K,0),\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad(2)$$ $$C(0,t)=0,\qquad C(S,t)\sim S\ \mbox{ as } S\to\infty.\qquad\qquad\qquad\qquad\qquad\qquad$$ The option value $C(S,t)$ is defined over the domain $0 Step 1. The equation can be rewritten in the equivalent form $$\frac{\partial C}{\partial t}+\frac{1}{2}\sigma^2\left(S\frac{\partial }{\partial S}\right)^2C+\left(r-\frac{1}{2}\sigma^2\right)S\frac{\partial C}{\partial S}-rC=0.$$ The change of independent variables $$S=e^y,\qquad t=T-\tau$$ results in $$S\frac{\partial }{\partial S}\to\frac{\partial}{\partial y},\qquad \frac{\partial}{\partial t}\to - \frac{\partial}{\partial \tau},$$ so one gets the constant coefficient equation $$\frac{\partial C}{\partial \tau}-\frac{1}{2}\sigma^2\frac{\partial^2 C}{\partial y^2}-\left(r-\frac{1}{2}\sigma^2\right)\frac{\partial C}{\partial y}+rC=0.\qquad\qquad\qquad(3)$$ Step 2. If we...

Volatility is mean reverting if the underlying security doesn't drop to zero. If the security has some underlying "value" then its price is co-integrated with that "value". The volatility is the uncertainty of that price as it tracks the security's "value". Edit 12/03/2011 ================================================= @pteetor, I may have missed something, but the question was " Why is volatility mean-reverting?". I realize that the standard answer is that the VIX (I'm assuming he's asking about the VIX) is related to the historical volatility of the S&P. A simple version of that relationship provides a reasonable R^2 (see Fig. 1). It relates...

This isn't really an answer, but it's too long to add as a comment. I've always had a real problem with the correlation/covariance of price . To me, it means nothing. I realize that it gets used (abused) in many contexts, but I just don't get anything out of it (over time, price has to generally go up, go down, or go sideways, so aren't all prices "correlated"?). On the flip side, correlation/covariance of returns makes sense. You're dealing with random series, not integrated random series. For example, below is the code required to generate two price series that have...

It's an interesting question. I particularly agree with the $\mathbb{Q}-\mathbb{P}$ dichotomy mentioned by many. I would add to the other answers that, come to think of it, the Black-Scholes postulated Geometric Brownian Motion could be interpreted as an AR(1) process on the logarithm of the stock price as you discretise the SDE from which it is a solution, which is exactly what you do when running Monte-Carlo simulations (same thing for the Ornstein-Uhlenbeck process as explained here and noted by @Richard). Actually, when taking the continuous-time limit, many more econometric models can be shown to correspond to stochastic processes frequently...


What does the VIX formula measure and how does it work?

I have read the CBOE's white paper on the VIX and a lot of other things, but I need to honestly say, I don't really get it, or I am missing something important. In semi-layman's terms, is the VIX simply the a measurement of the volume of protective options bought? That is, individual contract volatility increases when the option has been bid up by buyers due to desirability. One contract alone only marginally increases the overall market volatility, but if all contracts were bid up, then the entire VIX would be recalculated (on the fly) to reflect the higher value of protective options as a speculative/hedge solution. Do I understand this correctly, or do I really need to put more time into understanding that formula which comprises the VIX?

options volatility implied-volatility vix

VIX is a measure of implied volatility , specifically, model-free implied volatility , a concept originally developed by Demeterfi et. al. at Goldman Sachs in the 1990s . One of my recent questions, How to extrapolate implied volatility for out of the money options? , addressed some aspects of MFIV, and the papers mentioned in the question and answers will give you some more background on the concept. Also check out this JPMorgan research piece . The VIX is the square root of the market-implied variance swap rate, calculated based on the exchange-traded options portfolio typically used to hedge an...

Garabedian, Typically, the "swap curve" refers to an x-y chart of par swap rates plotted against their time to maturity. This is typically called the "par swap curve." Your second question, "how it relates to the zero curve," is very complex in the post-crisis world. I think it's helpful to start the discussion with a government bond yield curve to clarify some concepts and terminologies. Consider the US Treasury market, using the outstanding Treasury notes and bonds (nearly 300 of them...), we can either use bootstrapping or more sophisticated spline models to construct a "fitted curve." Since this yield curve...

Great question! I think the most useful starting point is Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options by Bakshi, Kapadia and Madan (2003) . Their paper proposes a definition of model-free implied skewness (they originally called it risk-neutral skewness, but MFIS is more accurate), which they prove will have a P&L directly proportional to the realized skewness of the underlier. Subsequent papers (there are literally dozens) have thoroughly explored the properties of MFIS. In particular, Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns? by Bali and Murray (2011) estimates the empirical...

Volatility is mean reverting if the underlying security doesn't drop to zero. If the security has some underlying "value" then its price is co-integrated with that "value". The volatility is the uncertainty of that price as it tracks the security's "value". Edit 12/03/2011 ================================================= @pteetor, I may have missed something, but the question was " Why is volatility mean-reverting?". I realize that the standard answer is that the VIX (I'm assuming he's asking about the VIX) is related to the historical volatility of the S&P. A simple version of that relationship provides a reasonable R^2 (see Fig. 1). It relates...


Papers about backtesting option trading strategies

I am looking for all kinds of research concerning option trading strategies. With that I mean papers that publish results on different option trading strategies properly backtested with real-world data.

options backtesting quant-trading-strategies research option-strategies

Wavelets are just one form of "basis decomposition". Wavelets in particular decompose in both frequency and time and thus are more useful than fourier or other purely-frequency based decompositions. There are other time-freq decompositions (for instance the HHT) which should be explored as well. Decomposition of a price series is useful in understanding the primary movement within a series. In general with a decomposition, the original signal is the sum its basis components (potentially with some scaling multiplier). The components range from the lowest frequency (a straight-line through the sample) to the highest frequency, a curve that oscillates with a...

The way you do it in the first place is a discretization of the Geometric Brownian Motion (GBM) process. This method is most useful when you want to compute the path between $S_0$ and $S_t$, i.e. you want to know all the intermediary points $S_i$ for $0 \leq i \leq t$. The second equation is a closed form solution for the GBM given $S_0$. A simple mathematical proof showed that, if you know the initial point $S_0$ (which is $a$ in your equation), then the value of the process at time $t$ is given by your equation (which contains $W_t$,...

I did some digging and found the following papers - most of them offering quite a distinct perspective compared to classical option pricing theory! Stock Options as Lotteries by Brian H. Boyer et al. (2011) The Efficiency of the Buy-Write Strategy: Evidence from Australia by Tafadzwa Mugwagwa et al. (2010) The following is my favorite: You could do some backtests on your own with freely available data (using the VXO as volatility information) and with any spreadsheet - easy and elegant: How Students Can Backtest Madoff’s Claims by Michael J. Stutzer (2009) Loosening Your Collar: Alternative Implementations of QQQ Collars...

Strictly speaking, data snooping is not the same as in-sample vs out-of-sample model selection and testing, but has to deal with sequential or multiple tests of hypothesis based on the same data set. To quote Halbert White: Data snooping occurs when a given set of data is used more than once for purposes of inference or model selection. When such data reuse occurs, there is always the possibility that any satisfactory results obtained may simply be due to chance rather than to any merit inherent in the methody yielding the results. Let me provide an example. Suppose that you have...


How do I adjust a correlation matrix whose elements are generated from different market regimes?

Say I want to calculate a correlation matrix for 50 stocks using 3-year historical daily data. And there are some stocks that were recently listed for one year. This is not technically challenging because the correlation function in R can optionally ignore missing data when calculating pair-wise correlation. But honestly it worried me after deep thought: all the correlations for the short listed stock will bias to the regime it live in. For example, a stock that exists only in last few months will inevitably have higher correlation than the stocks that have full 3-year history. And I think it will cause bias and annoying problems in the following applications using this correlation matrix. So, my question is: how do I adjust my correlation matrix whose elements are generated from different market regimes? I feel a dilemma. In order to assure that the whole matrix live in the same regime, it seems that either I need to use least possible samples, or I have to throw that stock away. But either way looks a waste to me. I know the correlations for that stock got to be lower, but how much lower? Is there an approach or formula derived from solid arguments? I did some research and surprisingly found that all public research on correlation matrix assuming adequateness of data. How can it be possible in practice?! A mystery for me to see this seemingly common problem has not been publicly addressed.

1. Determine Factors Economically, the use of factor models can be either motivated using the ICAPM or the APT . Although there are some theoretical differences between the model, for empirical and practical work these differences are irrelevant. In the end, both models stipulate that returns and expected returns are linear functions of the factors: $$ r_{i,t} = \alpha_i + \sum_j \beta_{i,j} F_{j,t} + \epsilon_{i,t} \quad (1)$$ $$ \mathbb{E}[ r_{i,t}] = \lambda_o + \sum_j \beta_{i,j} \lambda_j \quad\quad\quad(2)$$ where $F_{j,t}$ is the factor surprise of factor $j$ at time $t$ and $\lambda_j $ is the factor risk premium of factor $j$....

Quant Guy's list is really impressive! However, I am not sure they will readily solve your specific problem? I think there is one missing piece . Please note that imputing missing data is a very broad topic. There are many recipes to impute missings but that's for their specific 'assumptions' and purposes. They do not necessarily intend to well address your specific problem: the regime change. To best address your specific problem, you have to quantitatively define the market regime as a part of your adjusting formula. Otherwise, it wouldn't logically make sense that your model is aware of and...

Because of: The (extreme) dominance of noise over signal The prevalence of non-repeating patterns (many of which we know are not going to repeat) A pathetic sample size for cross-validation Regime changes due to exogenous events. These are typically in the cross-val window which makes it even worse. (GFC, financial integration, trade law changes, interest rate adjustments by central banks, some idiot in a bank was hiding trades and loses 5 billions dollars, etc). It is well known that non-linear relationships are generally just artefacts of the in sample dataset There is also the following: Much price changes are driven...

There are some cases where you can blend your portfolios using weights directly. One case involves corner portfolios . In this case a linear combination of weights is also efficient. Another case is where you can treat the two separate weights you have produced each as distinct portfolio under the assumption that the correlation between these portfolios is relatively stable. In this scenario, the problem reduces to a two-asset portfolio optimization problem (each asset is simply the linear combination of weights produced via your two methods). The other class of methods involves blending via the expected returns. If you arrived...


Discrete returns versus log returns of assets

There have been similar posts here already but nevertheless I find the question worth posting: why do some people claim that log returns of assets are more suitable for statistics than discrete returns. E.g. in the ESMA CESR guidliens about SSRI log returns are used. I personally think that discrete returns are as good for means of risk management as continuous returns. Furthermore in portfolio context I can calculate the portfolio return by weighting the discrete returns of the assets which does not work with log returns. The time-aggregation of log returns is easier that's true. But people rather think in discrete returns. If my NAV drops from $100$ to $92$ then I have lost $8\%$ and that's it. Is there any study on this - any good reference? Anything that I can tell my regulator why I stick to discrete returns.

Arithmetic returns allow for easier cross-sectional aggregation and log returns allow for easier time-aggregation. The reason people use log returns (for equities) is that they are approximately invariant and hence easier to work with in estimating distributions. Meucci does better justice in describing invariance here . The basic idea (again, for equities) is that the distribution of security prices is log-normal, so the arithmetic returns will also be. However, making a log transformation results in approximately normal returns, which are easier to work with. Also, if you do assume them to be normally distributed, then there are convenient results for...

Consider the standard error , and in particular the distance between the upper and lower limits: \begin{equation} \Delta = (\bar{x} + SE \cdot \alpha) - (\bar{x} - SE \cdot \alpha) = 2 \cdot SE \cdot \alpha \end{equation} Using the formula for standard error, we can solve for sample size: \begin{equation} n = \left(\frac{2 \cdot s \cdot \alpha}{\Delta}\right)^{2} \end{equation} where $s$ is the measured standard deviation, which you already have from your IR calculation. High-frequency Example I was testing a market-making model recently that was expected to return a couple basis points for each trade and I wanted to be confident...


What are modern algorithms for trade classification?

When dealing with trade data, for example from TAQ, a common problem is that of determining whether a trade was a buy or a sell . The most commonly used classifier is the Lee-Ready algorithm ( Inferring trade direction from intraday data , 1991). Unfortunately, this method is known to be inaccurate: Lee and Radhakrishna ( Inferring investor behaviour: evidence from TORQ data , 2000) report that Lee-Ready incorrectly classifies 24% of the trades inside the spread. How to improve on Lee-Ready's recipie? What are the best algorithms for trade classification?

I've not yet read it, but Lehalle's recent book is bound to be a goldmine of good micro-structure bits and pieces. Market Microstructure in Practice EDIT: I'm reading the book now, so far it's quite good.

There are a few approaches to use trade prices and quotes to classify the aggressor as "buy" or "sell." Also, many of these methods have historically had to deal with unsynchronized data streams. Classification of Approaches We can largely break trade classification methods into four types: Tick tests , advocated by Finucane (2000) , compare a trade price to the previous differing trade price with upticks (downticks) being evidence of a buy (sell); Midpoint tests , advocated by Lee and Ready (1991) , compare a trade price to a contemporaneous midpoint (average of bid and ask prices) with trades above...

Here couple pointers that may make it clearer: Drift can be replaced by the risk-free rate through a mathematical construct called risk-neutral probability pricing. Why can we get away with that without introducing errors? The reason lies in the ability to setup a hedge portfolio, thus the market will not compensate us for the drift above and beyond the risk free rate under risk-neutral probability pricing. As long as such hedge exists and couple other conditions are met (please look up Girsanov's Theorem) we can introduce a risk-neutral measure so that when applying it to the differential equation and through...


I'm trying to understand why it's useful to shrink the covariance matrix for portfolio construction or in fact general. Think I missing something. I know if you have 5,000 stocks it's a lot of calculations but if we assume that computing power is not a problem.

statistics portfolio-management covariance portfolio-optimization

Have a look at this classic paper: Honey, I Shrunk the Sample Covariance Matrix by O. Ledoit and M. Wolf The abstract answers your question already: The central message of this article is that no one should use the sample covariance matrix for portfolio optimization. It is subject to estimation error of the kind most likely to perturb a mean-variance optimizer. Instead, a matrix can be obtained from the sample covariance matrix through a transformation called shrinkage. This tends to pull the most extreme coefficients toward more central values, systematically reducing estimation error when it matters most. Statistically, the challenge...

The term has a different meaning to different people. to econometricians, microstructure noise is a disturbance that makes high frequency estimates of some parameters (e.g. realized volatility) very unstable. Generally this strand of the literature professes agnosticism as to the its origin; to market microstructure researchers, microstructure noise is a deviation from fundamental value that is induced by the characteristics of the market under consideration, e.g. bid-ask bounce, the discreteness of price change, latency, and asymmetric information of traders. The last example is frequently cited but I don't think it is accurate. Asymmetric information does not have to be a...

In my experience, a VaR or CVaR portfolio optimization problem is usually best specified as minimizing the VaR or CVaR and then using a constraint for the expected return. As noted by Alexey, it is much better to use CVaR than VaR. The main benefit of a CVaR optimization is that it can be implemented as a linear programming problem. Another option I have tried is the technique in this paper: http://www.math.uwaterloo.ca/~tfcolema/articles/bank_article.pdf Another option is the two-step heuristic where one first finds the mean-variance efficient frontier and then you could calculate whatever are the relevant portfolio statistics on only the...

Just to be painfully clear, it only seems to make sense to consider the logarithm of returns, i.e. $X=\log (1+\frac r{100})$ for a simple return of $r\%$ in an arbitrary period because this is what sums when returns are temporally aggregated. A basic property of cumulants is that cumulants of all orders are additive under convolution, for which a proof can be found here here . So if $X_1$, $X_2$, ... $X_n$ are i.i.d. , then all the cumulants of $$Y_n = \sum_{i=1}^nX_i$$ scale linearly with $n$, i.e. $$\kappa_k(Y_n)=n\kappa_k(Y_1).$$ However, I suspect that you are normalizing this sum so that...


I often hear people talking about the skew of the volatility surface, model, etc... but it appears to me that there isn't a clear standard definition unanimously used by practitioners. So here is my question: Does anyone have a clear and unifying definition that can be stated in mathematical terms of what skew is in the context of risk neutral pricing? If not, do you have a set of definitions of the skew with respect to a specific context?

options option-pricing implied-volatility volatility-skew

Intro: Great answer given by Kevin. I would like to contribute an additional perspective. My experience with and my understanding of the Risk Neutral measure is entirely based on "no arbitrage" and "replication / hedging" arguments. The way I would like to explain this view is via the following three-step construction : (i) First, I want to build the intuition with a one-period discrete model: only a single stock and a risk-free account, no derivatives . The aim is to show that even without trying to price derivatives, one can create a mathematical object called a "risk-neutral probability measure", just...

I have worked on this topic extensively (pricing and calculating IV in production) and believe can offer an informed opinion. First of all Mathworks - the company that creates Matlab is not a trading firm so you should probably not rely on their advice so much. There are few closed form options pricing models, and all have practical shortcomings. Barone-Adesi and Whaley (please correct my spelling of last names as I'm typing from memory) model is simple approximation for American options but is unfortunately not very accurate, and does not deal with dividends. Roll-Geske-Whaley deals with dividends, but not very...

In general there are two basic ways to make money out of your option pricing models: Sell side (market maker, risk neutral): You use these models to calculate your greeks to hedge your portfolio, so that you live on the spread. Buy side (market/risk taker): You use your model to find mispriced options in the market and buy/sell accordingly. (A third possibility would be to write fancy books and papers about these models and get rich and/or tenure this way ;-)

Scott Mixon argues in What Does Implied Volatility Skew Measure that among all measures of implied volatility skew, the (25 delta put volatility - 25 delta call volatility)/50 delta volatility is the most descriptive and least redundant (volatility is Black-Scholes implied volatility). His paper, recently published in the Journal of Derivatives , gives a number of both theoretical and empirical arguments in favor of this measure. He distinguishes between "skew", which is a measure of the slope of the implied volatility curve for a given expiration date, and "skewness", which is the skewness of an option implied, risk neutral probability...


How to quickly estimate a lower bound on correlation for a large number of stocks?

I would like to find stock pairs that exhibit low correlation. If the correlation between A and B is 0.9 and the correlation between A and C is 0.9 is there a minimum possible correlation for B and C? I'd like to save on search time so if I know that it is mathematically impossible for B and C to have a correlation below some arbitrary level based on A to B and A to C's correlations I obviously wouldn't have to waste time calculating the correlation of B and C. Is there such a "law"? If not, what are other methods of decreasing the search time?

Yes, there is such a rule and it is not too hard to grasp. Consider the 3-element correlation matrix $$\left(\begin{matrix} 1 & r & \rho \\ r & 1 & c \\ \rho & c & 1 \end{matrix}\right)$$ which must be positive semidefinite . In simpler terms, that means all its eigenvalues must be nonnegative. Assuming that $\rho$ and $r$ are known positive values, we find that the eigenvalues of this matrix go negative when \begin{equation} c Therefore the right hand side of this expression is the lower bound for the AC correlation $c$ that you seek, with $\rho$ being...

It is hard to find a stable non-trivial dependence structure in financial data. Usually when such is found it is hard to rationalize. One of my favorite (although I am sure there are others) is the so called "Presidential Puzzle". This is an old finding by Santa-Clara and Valkanov (2003) They find that " Excess return in the stock market is higher under Democratic than Republican presidencies: 9 percent for the value‐weighted and 16 percent for the equal‐weighted portfolio. At the time the finding was very robust and did not seem to be explained by anything else. What is more...

Wavelets are just one form of "basis decomposition". Wavelets in particular decompose in both frequency and time and thus are more useful than fourier or other purely-frequency based decompositions. There are other time-freq decompositions (for instance the HHT) which should be explored as well. Decomposition of a price series is useful in understanding the primary movement within a series. In general with a decomposition, the original signal is the sum its basis components (potentially with some scaling multiplier). The components range from the lowest frequency (a straight-line through the sample) to the highest frequency, a curve that oscillates with a...


What is the necessary level of Econometrics-Know-How for a quant

It seems quants increasingly use econometric models at work. As someone who has sold his soul to probability theory and stochastical analysis I would like to catch up. What are the econometric tools a quant should be able to wield ? As I see it, the answer will be highly dependant on where one works. Thus perhaps it would make sense to distinguish: Buy side Sell side Fixed Income Equity Risk Management and Model Validation Book suggestions that cover the necessary knowledge will be appreciated. Also, if someone feels like it, a list of topics (e.g. ARCH, GARCH etc.) would also be very helpful.

I can only talk about quantitative trading. As a rule of thumb, the lower frequency you work in, the more econometrics is important, whereas for a higher frequency, the more econometrics becomes useless . (I would still recommend a top econometrician for HFT since they have what it takes to succeed, it's just the models aren't out-of-the-box applicable.) But if I was interviewing someone who was educated in econometrics for a quantitative research position, I would hope for (given the relevance to financial time-series): I have tried to put in a legend, ^ is something you should learn later and...

There are some cases where you can blend your portfolios using weights directly. One case involves corner portfolios . In this case a linear combination of weights is also efficient. Another case is where you can treat the two separate weights you have produced each as distinct portfolio under the assumption that the correlation between these portfolios is relatively stable. In this scenario, the problem reduces to a two-asset portfolio optimization problem (each asset is simply the linear combination of weights produced via your two methods). The other class of methods involves blending via the expected returns. If you arrived...


Why dynamics of local volatility is wrong?

In Dupire's local volatility model, the volatility is is a deterministic function of the underlying price and time, chosen to match observed European option prices. To be more specific, given a smooth surface $(K,T)\mapsto C(K,T)$ where K is the strike and T is time to maturity. Dupire equation implies that there exits an unique continuous function $\sigma_{loc}$ defined by $$\sigma_{loc}^{2}(K,T)=\frac{\partial_{T}C(K,T)+rK\partial_{K}C(K,T)}{\frac{1}{2}K^{2}\partial_{KK}C(K,T)}$$ for all $(K,T)\in(0,\infty)\times(0,\infty)$ such that the solution to the stochastic differential equation $dS_{t}/S_{t}=rdt+\sigma(t,S_{t})dW_{t}$ exactly generates the European call option prices. What do the dynamics of the local volatility mean? Are dynamics equivalent to the volatility surface? Why the dynamics of local volatility model is highly unrealistic?

I've worked at a hedge fund that allowed GA-derived strategies. For safety, it required that all models be submitted long before production to make sure that they still worked in the backtests. So there could be a delay of up to several months before a model would be allowed to run. It's also helpful to separate the sample universe; use a random half of the possible stocks for GA analysis and the other half for confirmation backtests.

A general model (with continuous paths) can be written $$ \frac{dS_t}{S_t} = r_t dt + \sigma_t dW_t^S $$ where the short rate $r_t$ and spot volatility $\sigma_t$ are stochastic processes. In the Black-Scholes model both $r$ and $\sigma$ are deterministic functions of time (even constant in the original model). This produces a flat smile for any expiry $T$. And we have the closed form formula for option prices $$ C(t,S;T,K) = BS(S,T-t,K;\Sigma(T,K)) $$ where $BS$ is the BS formula and $\Sigma(T,K) = \sqrt{\frac{1}{T-t}\int_t^T \sigma(s)^2 ds}$. This is not consistent with the smile observed on the market. In order to match...

The minimum variance solution loads up on securities that have low variances and co-variances. Theoretically you are correct that this should have a low expected return profile. However, it turns out - in contradiction to modern portfolio theory - that securities that have low-volatility or low-beta experience higher returns than high-volatility or high-beta stocks. This is well-documented in the literature as the low-volatility anomaly . As a result, many funds and ETFs have been launched in recent years to exploit this phenomenon. There are a couple arguments as to why the anomaly exists. The paper I cite above argues that...

This isn't really an answer, but it's too long to add as a comment. I've always had a real problem with the correlation/covariance of price . To me, it means nothing. I realize that it gets used (abused) in many contexts, but I just don't get anything out of it (over time, price has to generally go up, go down, or go sideways, so aren't all prices "correlated"?). On the flip side, correlation/covariance of returns makes sense. You're dealing with random series, not integrated random series. For example, below is the code required to generate two price series that have...


I am reading paper High-frequency trading in a limit order book by Marco Avellaneda and Sasha Stoikov. At the end of the paper they obtain a closed-form solution to the optimal market-maker quotes under diffusion without drift. They found that the optimal behaviour of the market-maker would be to set a bid/ask spread of size: $$ spread = \gamma\sigma^2(T-t) + \frac{2}{\gamma}ln(1+\frac{\gamma}{k}), $$ where $\gamma$ is a discount factor, $\sigma^2$ is the variance of the process, $k$ is the parameter corresponing to the intensity of arrival of market orders, $T$ is terminal time and $t$ is curent time, around a reservation price given by: $$ price = s - q\gamma\sigma^2(T-t), $$ where $q$ is the state of the inventory and $s$ is the current price. However, I do not see any specification of bounds for this reservation price and therefore I think there is no guarantee that ask prices computed by the market-maker will be higher or bid prices will be lower than the current price of the process. | How is this necessity of market makers' ask prices being higher and bid prices being lower than the actual price enforced in their model (e.g. in their simulations)? Edit : To be more concrete, I just specify, that in my opinion, it needs to hold that: $$ price + spread/2 - s > 0 $$ Lets denote $price$ by $p_{mm}$ and $spread/2$ by $s_{mm}$ . Then $$ p_{mm} + s_{mm} - s > 0, \\ s - q\gamma\sigma^2(T-t) + \frac{\gamma\sigma^2(T-t)}{2} + \frac{1}{\gamma}ln(1+\frac{\gamma}{k}) - s >0 \\ (...) \\ \frac{1}{2} + \frac{ln(1+\frac{\gamma}{k})}{\gamma^2\sigma^2(T-t)} > q $$ However, this situation does not need to happen, so there is no guarantee he will set prices compatible with current market prices.

The market-maker makes a bid-ask spread $\delta$ around the reservation price $r$. So at any time, the market-maker quotes the bid price $$ p_b = r - \delta/2, $$ and the ask price $$ p_a = r + \delta/2. $$ Bid price is hence always below the reservation price and ask price is always above the reservation price. The reservation price $$ r = s - q\gamma\sigma^2(T-t) $$ is the market price minus a term that depends on the inventory $q$ that the market-maker is holding. If $q$ is positive the reservation price moves lower (below the market price) and...

The lead paper in the January 2011 Journal of Finance ( Hendershott, Jones, and Menkveld ) addresses algorithmic trading (AT). In short, they find that AT improves liquidity as measured by bid-offer spreads. Taking the econometrics as correct (it is in the Journal of Finance) the next question is if bid-offer spreads are a sufficient statistic for measuring liquidity (or any other benefits). It is a difficult question to answer because, given current market structure, AT may improve liquidity (as measured by bid-offer spreads), but without data on other market structures, it is hard to say that we wouldn't better...

The volatiltiy surface is just a representation of European option prices as a function of strike and maturity in a different "unit" - namely implied volatility (while the term implied volatility has to be made precise by the model used to convert prices (quotes) into implied volatilities - for example: we may consider log-normal vols and normal vols). Volatility is often preferred over prices, e.g., when considering interpolations of European option prices (although this may introduce difficulties like arbitrage violations, see, e.g., http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1964634 ). A local volatility model can generate a perfect fit to the implied volatility surface via Dupire's...

There seems to be a basic fallacy that someone can come along and learn some machine learning or AI algorithms, set them up as a black box, hit go, and sit back while they retire. My advice to you: Learn statistics and machine learning first, then worry about how to apply them to a given problem. There is no free lunch here. Data analysis is hard work . Read "The Elements of Statistical Learning" (the pdf is available for free on the website), and don't start trying to build a model until you understand at least the first 8 chapters....


What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in portfolio choice?

I'm just providing a global answer to the question, as I think it can be interesting for some beginners in quant finance. The properties given by TheBridge: Normalize $\rho (\emptyset)=0$ This means you have no risk in taking no position. Sub-addiitivity $\rho(A_1+A_2) \leq \rho(A_1)+\rho(A_2)$ Having a position in two different can only decrease the risk of the portfolio (diversification) Positive homogeneity $\rho(\lambda A) = \lambda \rho(A)$ Doubling a position in an asset A doubles your risk. And finally, Translation invariance $\rho(A + x) = \rho(A)-x$ That is, adding cash to a portfolio only diminishes the risk. So a risk-measure is...

There seems to be a basic fallacy that someone can come along and learn some machine learning or AI algorithms, set them up as a black box, hit go, and sit back while they retire. My advice to you: Learn statistics and machine learning first, then worry about how to apply them to a given problem. There is no free lunch here. Data analysis is hard work . Read "The Elements of Statistical Learning" (the pdf is available for free on the website), and don't start trying to build a model until you understand at least the first 8 chapters....

Here couple pointers that may make it clearer: Drift can be replaced by the risk-free rate through a mathematical construct called risk-neutral probability pricing. Why can we get away with that without introducing errors? The reason lies in the ability to setup a hedge portfolio, thus the market will not compensate us for the drift above and beyond the risk free rate under risk-neutral probability pricing. As long as such hedge exists and couple other conditions are met (please look up Girsanov's Theorem) we can introduce a risk-neutral measure so that when applying it to the differential equation and through...

I would offer the distinctions are i) pure statistical approach, ii) equilibrium based approach, and iii) empirical approach. The statistical approach includes data mining. Its techniques originate in statistics and machine learning. In its extreme there is no a priori theoretical structure imposed on asset returns. Factor structure might be identified thru Principal Components, for example. The goal here is to maximize predictive accuracy at the expense of intuition and explanatory power. This approach increasingly dominates at very short frequencies in modeling market microstructure, market making algorithms, volatility modeling, etc. However, even in high-frequency trading one can impose a factor...


Does mean-variance portfolio optimization provide a real edge to those who use it?

Mean-variance optimization (MVO) is a 50+ year concept, and perhaps the first seminal idea of quantitative finance. Still, as far as I know, less than 25% of AUM in the US is quantitatively managed. While a small minority of fundamental managers use MVO, that is counterbalanced by statistical arbitrage and HF strategies that often use optimization but not MVO, so the percentage of AUM not allocated using Markowitz' invention is surely not less than 70%. My questions: if MVO is such a great idea, why after all this time, so few people use it? if MVO was such a bad idea, how come companies like Axioma, Northfield and Barra still make money off it? is there there a rationale for the current mixed equilibrium of users and non-users? A few caveats on what I just said: i) perhaps the first and most important idea in finance is that of state-contingent assets, which is Arrow's; ii) I am focused on the buy side. I believe that optimization is widely used for hedging on the sell side.

I would offer the distinctions are i) pure statistical approach, ii) equilibrium based approach, and iii) empirical approach. The statistical approach includes data mining. Its techniques originate in statistics and machine learning. In its extreme there is no a priori theoretical structure imposed on asset returns. Factor structure might be identified thru Principal Components, for example. The goal here is to maximize predictive accuracy at the expense of intuition and explanatory power. This approach increasingly dominates at very short frequencies in modeling market microstructure, market making algorithms, volatility modeling, etc. However, even in high-frequency trading one can impose a factor...

Hey, it's early days yet. After all it is still called MODERN portfolio theory. I think there are two main issues and they are both really cultural: 1) specifying alphas 2) wild results Alphas I agree with Gappy that alphas are the key thing you need to have effectiveness (unless you are doing minimum variance). Having a vector of expected returns is quite a natural thing for quant managers. But it is something foreign to fundamental managers. They have to map their views into a number for each asseet in the universe. That is not necessarily an easy task, and...

1. Determine Factors Economically, the use of factor models can be either motivated using the ICAPM or the APT . Although there are some theoretical differences between the model, for empirical and practical work these differences are irrelevant. In the end, both models stipulate that returns and expected returns are linear functions of the factors: $$ r_{i,t} = \alpha_i + \sum_j \beta_{i,j} F_{j,t} + \epsilon_{i,t} \quad (1)$$ $$ \mathbb{E}[ r_{i,t}] = \lambda_o + \sum_j \beta_{i,j} \lambda_j \quad\quad\quad(2)$$ where $F_{j,t}$ is the factor surprise of factor $j$ at time $t$ and $\lambda_j $ is the factor risk premium of factor $j$....

In general there are two basic ways to make money out of your option pricing models: Sell side (market maker, risk neutral): You use these models to calculate your greeks to hedge your portfolio, so that you live on the spread. Buy side (market/risk taker): You use your model to find mispriced options in the market and buy/sell accordingly. (A third possibility would be to write fancy books and papers about these models and get rich and/or tenure this way ;-)


Why are options trades supposed to be delta-neutral?

I'm reading Natenberg's book, and he says that all options trades should be delta neutral. I understand that this prevents small changes in the underlying price from changing the price of the option, but couldn't there be a case where you would want that? I (think I) also understand that if you're betting against just volatilty, it would make sense, since you don't care what direction the underlying price moves, but I don't entirely understand why he says all options trades should be delta neutral.

Garabedian, Typically, the "swap curve" refers to an x-y chart of par swap rates plotted against their time to maturity. This is typically called the "par swap curve." Your second question, "how it relates to the zero curve," is very complex in the post-crisis world. I think it's helpful to start the discussion with a government bond yield curve to clarify some concepts and terminologies. Consider the US Treasury market, using the outstanding Treasury notes and bonds (nearly 300 of them...), we can either use bootstrapping or more sophisticated spline models to construct a "fitted curve." Since this yield curve...

Scott Mixon argues in What Does Implied Volatility Skew Measure that among all measures of implied volatility skew, the (25 delta put volatility - 25 delta call volatility)/50 delta volatility is the most descriptive and least redundant (volatility is Black-Scholes implied volatility). His paper, recently published in the Journal of Derivatives , gives a number of both theoretical and empirical arguments in favor of this measure. He distinguishes between "skew", which is a measure of the slope of the implied volatility curve for a given expiration date, and "skewness", which is the skewness of an option implied, risk neutral probability...

I haven't read Natenberg but it of course depends on your side in the trade: Are you a market maker or a risk taker? So do you live on the spread (first) or are trying to make money based on e.g. forecasts on direction (second). This is the great divide in QuantFinance! Only in the first case will all your option trades be delta neutral. There is a nice short paper which elaborates on both concepts (it calls the first one Q and the second P ): Meucci: 'P' Versus 'Q': Differences and Commonalities between the Two Areas of Quantitative...


Not sure if this is a relevant question for site, but I am looking to move to www.eoddata.com as my data source. If anyone has used it, can you tell me how the data quality is ? I am currently parsing yahoo for my prices but its not a very efficient process. What are the other sources of equity data out there ( affordable for retail investors like me) ? I am willing to pay \$250-\$300 per year for it.

Yahoo rounds the adjusted price to 2 decimals even though dividend amounts often have 3 decimal places. Since they apply the adjustment formula to adjusted prices, if you go far enough back in time, the value they give for Adjusted Price will be different than it would be if there were no rounding. edit: For example, for C (Citigroup), on January 2, 1990, Yahoo gives a close value of 29.37 and an Adjusted value of 1.50. Using the dividend data that Yahoo supplies, if they didn't round to cents on every adjustment, the adjusted value would be 1.677.

From my experience, EODData is pretty much that you get what you pay for. Its not a very sophisticated product. They email you the files you subscribe to, and thats that. I have had an issue before of where the emails didn't go through anymore and I never heard anything from them. On Quality, I can't make a claim on its accuracy. It seems good. I find issue with three things about the data: There is no way to signal an exchange change It doesn't give you an easy way to grab the symbol info [Names, etc] If there is...


Did Citigroup really fail three times in the last 40 years?

I watched a speech by Simon Johnson at UCSB and, at one point, he claimed that Citigroup has failed three times since the 1980s. For example, he claims that Citigroup failed and was saved by the government in 1982 because of "bad loans made in emerging markets". The second such failure is at the end of the 1980s because of "bad loans to commercial real estate". The third is of course the 2008/2009 financial crisis. What strikes me as odd is that the first two alleged failures are not mentioned in Wikipedia on Citigroup ! He doesn't appear to me as a crackpot as he is the former chief economist of IMF and effective whitewashing of the US's biggest bank holding company on Wikipedia is as unlikely. Does anyone know what affairs is he referencing?

(I worked there for 23 years.) Simon Johnson is correct. Citi (or its predecessors) was insolvent on those 3 occasions, and would have gone into liquidation without the bailouts by U.S. taxpayers.


What is the "delta" option quoting convention about?

At my work I often see option prices or vols quoted against deltas rather than against strikes. For example for March 2013 Zinc options I might see 5 quotes available for deltas as follows: ZINC MARCH 2013 OPTION DELTA -10 POINTS ZINC MARCH 2013 OPTION DELTA -25 POINTS ZINC MARCH 2013 OPTION DELTA +10 POINTS ZINC MARCH 2013 OPTION DELTA +25 POINTS ZINC MARCH 2013 OPTION DELTA +50 POINTS The same 5 values -10, -25, +10, +25, + 50 are always used. What are these deltas? What are the units? Why are those 5 values chosen?

Delta is the partial derivative of the value of the option with respect to the value of the underlying asset. An option with a delta of 0.5 (here listed as +50 points) goes up \$0.50 if the underlying asset goes up \$1.00. Or goes down \$0.50 if the underlying asset goes down \$1.00. Keep in mind that delta is an instantaneous derivative, so the value will change both in time (charm is the change in delta with time) and with changes in value of the underlying asset (gamma is the change in delta with the underlying asset, which is also...

VIX is a measure of implied volatility , specifically, model-free implied volatility , a concept originally developed by Demeterfi et. al. at Goldman Sachs in the 1990s . One of my recent questions, How to extrapolate implied volatility for out of the money options? , addressed some aspects of MFIV, and the papers mentioned in the question and answers will give you some more background on the concept. Also check out this JPMorgan research piece . The VIX is the square root of the market-implied variance swap rate, calculated based on the exchange-traded options portfolio typically used to hedge an...


How do you evaluate a covariance forecast?

Suppose you have two sources of covariance forecasts on a fixed set of $n$ assets, method A and method B (you can think of them as black box forecasts, from two vendors, say), which are known to be based on data available at a given point in time. Suppose you also observe the returns on those $n$ assets for a following period (a year's worth, say). What metrics would you use to evaluate the quality of these two covariance forecasts? What statistical tests? For background, the use of the covariances would be in a vanilla mean-variance optimization framework, but one can assume little is known about the source of alpha. edit : forecasting a covariance matrix is a bit different, I think, than other forecasting tasks. There are some applications where getting a good forecast of the eigenvectors of the covariance would be helpful, but the eigenvalues are not as important. (I am thinking of the case where one's portfolio is $\Sigma^{-1}\mu$, rescaled, where $\Sigma$ is the forecast covariance, and $\mu$ is the forecast returns.) In that case, the metric for forecasting quality should be invariant with respect to scale of the forecast. For some cases, it seems like forecasting the first eigenvector is more important (using it like beta), etc . This is why I was looking for methods specifically for covariance forecasting for use in quant finance.

This isn't really an answer, but it's too long to add as a comment. I've always had a real problem with the correlation/covariance of price . To me, it means nothing. I realize that it gets used (abused) in many contexts, but I just don't get anything out of it (over time, price has to generally go up, go down, or go sideways, so aren't all prices "correlated"?). On the flip side, correlation/covariance of returns makes sense. You're dealing with random series, not integrated random series. For example, below is the code required to generate two price series that have...

A general model (with continuous paths) can be written $$ \frac{dS_t}{S_t} = r_t dt + \sigma_t dW_t^S $$ where the short rate $r_t$ and spot volatility $\sigma_t$ are stochastic processes. In the Black-Scholes model both $r$ and $\sigma$ are deterministic functions of time (even constant in the original model). This produces a flat smile for any expiry $T$. And we have the closed form formula for option prices $$ C(t,S;T,K) = BS(S,T-t,K;\Sigma(T,K)) $$ where $BS$ is the BS formula and $\Sigma(T,K) = \sqrt{\frac{1}{T-t}\int_t^T \sigma(s)^2 ds}$. This is not consistent with the smile observed on the market. In order to match...

You are correct: evaluating volatility forecasts is quite different from evaluating forecasts in general, and it is a very active area of research. Methods can be classified in several ways. One criterion is to consider evaluation methods for single forecasts (e.g., for the time series of returns of a specific portfolio) vs multiple simultaneous forecasts (e.g., for an investable universe). Another criterion is to separate direct evaluation methodsfrom indirect evaluation methods (more on this later). Focusing on single-asset methods: historically the most commonly used approach by practitioners, and the one advocated by Barra is the "bias" statistics. If you have...


When should you build your own equity risk model?

Commercial risk models (e.g., Barra , Axioma , Barclays , Northfield ) have evolved to a very high level of sophistication. However, all of these models attempt to solve a very broad set of problems. The optimal risk model for, say, risk attribution in a fundamental portfolio may differ substantially from the optimal risk model for downside risk estimation of an optimized quantitative strategy or for hedging unwanted exposures in a pure relative value play. Suppose that one already subscribes to a decent risk model provider, so that cost is not an issue. For what applications is it most appropriate to build your own equity risk model? What are the main benefits of a customized risk model? When is it worth the time and effort to replicate the increasingly sophisticated data cleaning/analysis and statistical methods to reap these benefits?

Here couple pointers that may make it clearer: Drift can be replaced by the risk-free rate through a mathematical construct called risk-neutral probability pricing. Why can we get away with that without introducing errors? The reason lies in the ability to setup a hedge portfolio, thus the market will not compensate us for the drift above and beyond the risk free rate under risk-neutral probability pricing. As long as such hedge exists and couple other conditions are met (please look up Girsanov's Theorem) we can introduce a risk-neutral measure so that when applying it to the differential equation and through...

I think you're overlooking a third explanation: Nobody that found a successful technique to generate alpha has published it. I can think of the following causes: If you're an academic, why share your brilliant idea? These techniques require a lot of data and financial data can be expensive, researches that work at firms that have access to this data don't share their findings with the public. Academics did find a lot of signals already the old fashioned way. Despite this, fancy techniques such as AAD and Reinforcement Learning are discussed publicly. These methods don't generate any alpha however.

Great question. We would expect 3rd party risk providers to have specialized expertise (robust regression techniques, factor research, data cleansing etc.). We might grant them these advantages but still find weakness in the product design. Let's start off with the different uses of risk models and the procedure or metric which is maximized to solve for that use case. What we will see is that solving for a particular objective diminishes our ability to achieve other objectives. Portfolio construction = If you want to construct a minimum variance portfolio, for example, then the key here is developing a covariance matrix...


How to combine multiple trading algorithms?

Is it possible to combine different algorithms so as to improve trading performance? In particular, I have read that social media sentiment tracking, digital signal processing and neural networks all can be used for trading algorithms. Would it be possible to create a trading algorithm that combines elements from these three areas or are these methods mutually exclusive in that they are incompatible with each other? If you commit to one, can you use the other?

trading algorithmic-trading quant-trading-strategies performance

In order to answer your question (for you) you would need something to compare to . You would need numbers to know if it is slower/faster, how much, and if it will impact your system overall. Also knowing your performance goals could narrow down the options. My advice is to take a look at your overall architecture of the sytem you have or intend to build. To just look at QuickFIX is rather meaningless without the whole chain involved in processing information and reacting to it . As an example, say QuickFIX is 100 times faster than some part (in...

Yes. First, it is much easier to proceed if you standardize the output of your forecast so they are in the same units (returns, for example, or probabilities of an event/condition occurring). After you have done this, there are 3 general approaches: Signal weighting: Then you need to define a weighting scheme for your factors. Richard Grinold has an one answer to this question in his paper " Signal Weighting ". Note there are quite a few methods to weight signals (optimization, meta-models, forecast pooling, Bayesian model averaging, weighing based on out-of-sample performance, etc.). The general problem of "Signal Weighting"...


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 accessible proof for the above statement preferably for all higher moments. This question is inspired by this question by Richard which deals with, among other things, the behaviour of the higher moments of returns under temporal aggregation. I know about two papers that answer this question. Hawawini (1980) is wrong and Hon-Shiang and Wingender (1989) is behind a paywall and a bit inscrutable.

statistics returns volatility-skew kurtosis

Just to be painfully clear, it only seems to make sense to consider the logarithm of returns, i.e. $X=\log (1+\frac r{100})$ for a simple return of $r\%$ in an arbitrary period because this is what sums when returns are temporally aggregated. A basic property of cumulants is that cumulants of all orders are additive under convolution, for which a proof can be found here here . So if $X_1$, $X_2$, ... $X_n$ are i.i.d. , then all the cumulants of $$Y_n = \sum_{i=1}^nX_i$$ scale linearly with $n$, i.e. $$\kappa_k(Y_n)=n\kappa_k(Y_1).$$ However, I suspect that you are normalizing this sum so that...

There are some cases where you can blend your portfolios using weights directly. One case involves corner portfolios . In this case a linear combination of weights is also efficient. Another case is where you can treat the two separate weights you have produced each as distinct portfolio under the assumption that the correlation between these portfolios is relatively stable. In this scenario, the problem reduces to a two-asset portfolio optimization problem (each asset is simply the linear combination of weights produced via your two methods). The other class of methods involves blending via the expected returns. If you arrived...


Portfolio optimisation with VaR or CVaR constraints using linear programming

I would like to optimize a portfolio allocation (maximizing the exposure or the expected return), but with VaR or CVaR contraints. (some parts of my portfolio cannot exceed a certain VaR) How can I achieve that? Is there a way to turn the problem into a linear programming problem? or to approximate the results? Any links or ideas are welcome.

portfolio-management portfolio-optimization optimization value-at-risk

In my experience, a VaR or CVaR portfolio optimization problem is usually best specified as minimizing the VaR or CVaR and then using a constraint for the expected return. As noted by Alexey, it is much better to use CVaR than VaR. The main benefit of a CVaR optimization is that it can be implemented as a linear programming problem. Another option I have tried is the technique in this paper: http://www.math.uwaterloo.ca/~tfcolema/articles/bank_article.pdf Another option is the two-step heuristic where one first finds the mean-variance efficient frontier and then you could calculate whatever are the relevant portfolio statistics on only the...

I've worked at a hedge fund that allowed GA-derived strategies. For safety, it required that all models be submitted long before production to make sure that they still worked in the backtests. So there could be a delay of up to several months before a model would be allowed to run. It's also helpful to separate the sample universe; use a random half of the possible stocks for GA analysis and the other half for confirmation backtests.

This question goes to whether the historical returns to factors represent: Spurious results, overfitting, data mining... Mispricing Unexploitable effects Compensation for risk Case 1: Spurious results etc... If someone constructs a "stock tickers that begin with AAP or GOO" factor, the highly above average returns would almost certainly reflect a fishing expedition (or conditioning on future information) and would not be reproducible going forward. Under a null of no above average returns, you're going to get portfolios that have above average historical returns with t-stats over 2. Beware. For something like the Fama-French factor $\mathit{HML}$, this seems far less likely...


What is the most stable, non-trivial dependence structure in finance?

The highest rated answer to the question on What concepts are the most dangerous ones in quantitative finance work? is this one: Correlation Correlations are notoriously unstable in financial time series [...] My question My question is a little bit broader than just about linear dependence, it is: What is the most stable, non-trivial dependence structure in financial data? With non-trivial I mean that I don't want answers that are about direct connections, e.g. between derivative and underlying. The dependence structure can be either cross-sectional or through time with univariate time series, it can also be non-linear . The context of my question is that I am preparing the documentation for a new machine learning R package I wrote and I am looking for a good showcase in the financial sphere. Now this is not a trivial feat given that correlations are notoriously... see above ;-)

It is hard to find a stable non-trivial dependence structure in financial data. Usually when such is found it is hard to rationalize. One of my favorite (although I am sure there are others) is the so called "Presidential Puzzle". This is an old finding by Santa-Clara and Valkanov (2003) They find that " Excess return in the stock market is higher under Democratic than Republican presidencies: 9 percent for the value‐weighted and 16 percent for the equal‐weighted portfolio. At the time the finding was very robust and did not seem to be explained by anything else. What is more...

I would consider a motion chart that plots the eigenvalues of the covariance matrix over time. For a static view you can create a table: rows represent dates, and columns represent eigenvectors. The entries of the table represent changes in the angle of the eigenvector from the previous row. This will show how stable your covariance structure is. You can also create a second table this time with eigenvalues as the columns sorted from high to low (and the corresponding values below for each date). This shows the variance described by each eigenvector so you can see whether correlation as...

I have worked on this topic extensively (pricing and calculating IV in production) and believe can offer an informed opinion. First of all Mathworks - the company that creates Matlab is not a trading firm so you should probably not rely on their advice so much. There are few closed form options pricing models, and all have practical shortcomings. Barone-Adesi and Whaley (please correct my spelling of last names as I'm typing from memory) model is simple approximation for American options but is unfortunately not very accurate, and does not deal with dividends. Roll-Geske-Whaley deals with dividends, but not very...


What are reasons not to do factor investing in equity markets?

Factor investing in equity markets is one of the hot topics of these days. Many manufacturers of investment products offer exposure to small cap, momentum, minvol, value and other pure factors or factor blends. Many of them beating the cap-weighted index at relatively low cost. I think of various reasons but I woud like to discuss: What are the reasons not everybody just invests in factor portfolios? What could be limitations, regulations, fears or other reasons not to invest in factor portfolios?

This question goes to whether the historical returns to factors represent: Spurious results, overfitting, data mining... Mispricing Unexploitable effects Compensation for risk Case 1: Spurious results etc... If someone constructs a "stock tickers that begin with AAP or GOO" factor, the highly above average returns would almost certainly reflect a fishing expedition (or conditioning on future information) and would not be reproducible going forward. Under a null of no above average returns, you're going to get portfolios that have above average historical returns with t-stats over 2. Beware. For something like the Fama-French factor $\mathit{HML}$, this seems far less likely...

Have a look at this classic paper: Honey, I Shrunk the Sample Covariance Matrix by O. Ledoit and M. Wolf The abstract answers your question already: The central message of this article is that no one should use the sample covariance matrix for portfolio optimization. It is subject to estimation error of the kind most likely to perturb a mean-variance optimizer. Instead, a matrix can be obtained from the sample covariance matrix through a transformation called shrinkage. This tends to pull the most extreme coefficients toward more central values, systematically reducing estimation error when it matters most. Statistically, the challenge...

From what I remember, there is no real relation between Markov and Martingale, and my intuition was confirmed by this post . Basically, it says that you can say neither of the following: If A is Markov, then A is a martingale. If A is a martingale, then A is Markov. further down the post, you can find two counter examples: $dX_t = a dt + \sigma dW_t$ is Markov but not a martingale and $dX_t = (\int_0^t X_s ds) dW_t$ is a Martingale but is not Markov. As for the assumption of these properties being true, I think it...

I know that I have seen things like this in the past. Wasn't there something recently that used Twitter? Here are a few recent papers as examples, although I will be brutally honest that I don't know if they speak to your decent quality requirement: "Trading Strategies to Exploit Blog and News Sentiment" (Zhang, Skiena 2010) "The Predictive Power of Financial Blogs" (Frisbee 2010) "An analysis of verbs in financial news articles and their impact on stock price" (Schumaker 2010)


Why does Gamma Pnl have exposure to realised volatility, but Vega Pnl only has exposure to implied volatility? I am confused as to why gamma pnl is affected (more) by IV and why vega pnl isnt affected (more) by RV? Essentially how do you show what gamma pnl will be mathematically and how do you show what vega pnl will be? I believe that gamma pnl is spot x (vega x IV - RV) Also does gamma pnl usually dominate (in $ terms) the vega pnl of an options, as most literature is on gamma pnl?

options implied-volatility option-strategies gamma vega

The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the law of one price , also known as the principle of no riskless arbitrage and which you may already have heard of in the following terms: "there is no free lunch in financial markets". This law is at the heart of securities' relative valuation , see this very nice paper by Emmanuel Derman ("Metaphors, Models & Theories", 2011) and some part of this discussion. In what follows, assume for the sake of simplicity existence of a risk-free asset ; deterministic and constant rates, with risk-free rate $r$ ;...

The volatiltiy surface is just a representation of European option prices as a function of strike and maturity in a different "unit" - namely implied volatility (while the term implied volatility has to be made precise by the model used to convert prices (quotes) into implied volatilities - for example: we may consider log-normal vols and normal vols). Volatility is often preferred over prices, e.g., when considering interpolations of European option prices (although this may introduce difficulties like arbitrage violations, see, e.g., http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1964634 ). A local volatility model can generate a perfect fit to the implied volatility surface via Dupire's...

For an option with price $C$ , the P $\&$ L, with respect to changes of the underlying asset price $S$ and volatility $\sigma$ , is given by \begin{align*} P\&L = \delta \Delta S + \frac{1}{2}\gamma (\Delta S)^2 + \nu \Delta \sigma, \end{align*} where $\delta$ , $\gamma$ , and $\nu$ are respectively the delta, gamma, and vega hedge ratios. Then it is clear the vega P $\&$ L has exposure to the change of the implied volatility $\sigma$ . Note that, for the gamma P $\&$ L, \begin{align*} \frac{1}{2}\gamma (\Delta S)^2 = \frac{1}{2}\gamma S^2 \frac{1}{\Delta t}\left(\frac{\Delta S}{S}\right)^2\Delta t, \end{align*} where...


How are distributions for tail risk measures estimated in practice?

Let's say you want to calculate a VaR for a portfolio of 1000 stocks. You're really only interested in the left tail, so do you use the whole set of returns to estimate mean, variance, skew, and shape (let's also assume a skewed generalized error distribution - SGED)? Or would you just use the left tail (let's say the bottom 10% of returns)? For some reason, using the whole set of returns seems more correct to me (by using only the left 10% or returns you'd really be approaching a non-parametric VaR). But using the whole set of returns would likely cause some distortion in the left tail in order to get a better fit elsewhere. How are the pros doing this? Thanks!

risk probability estimation value-at-risk expected-return

Perhaps you may want to consider article by D. Levine - Modeling Tail Behavior with Extreme Value Theory who gives practicale example on how EVT can be used to calculate probabilities on returns in tails with use of the Pickands-Balkema-de Haan Theorem and generalized Pareto distribution. It also contains some criterias and points on other methods that can be used to determine threshold value for PBH theorem: Contrary to this notion is the fact that the PBH theorem states a result based on the assumption of threshold values approaching the right endpoint of the distribution F. This implies that better...

Great question. We would expect 3rd party risk providers to have specialized expertise (robust regression techniques, factor research, data cleansing etc.). We might grant them these advantages but still find weakness in the product design. Let's start off with the different uses of risk models and the procedure or metric which is maximized to solve for that use case. What we will see is that solving for a particular objective diminishes our ability to achieve other objectives. Portfolio construction = If you want to construct a minimum variance portfolio, for example, then the key here is developing a covariance matrix...

One starts with the Black-Scholes equation $$\frac{\partial C}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2 C}{\partial S^2}+ rS\frac{\partial C}{\partial S}-rC=0,\qquad\qquad\qquad\qquad\qquad(1)$$ supplemented with the terminal and boundary conditions (in the case of a European call) $$C(S,T)=\max(S-K,0),\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad(2)$$ $$C(0,t)=0,\qquad C(S,t)\sim S\ \mbox{ as } S\to\infty.\qquad\qquad\qquad\qquad\qquad\qquad$$ The option value $C(S,t)$ is defined over the domain $0 Step 1. The equation can be rewritten in the equivalent form $$\frac{\partial C}{\partial t}+\frac{1}{2}\sigma^2\left(S\frac{\partial }{\partial S}\right)^2C+\left(r-\frac{1}{2}\sigma^2\right)S\frac{\partial C}{\partial S}-rC=0.$$ The change of independent variables $$S=e^y,\qquad t=T-\tau$$ results in $$S\frac{\partial }{\partial S}\to\frac{\partial}{\partial y},\qquad \frac{\partial}{\partial t}\to - \frac{\partial}{\partial \tau},$$ so one gets the constant coefficient equation $$\frac{\partial C}{\partial \tau}-\frac{1}{2}\sigma^2\frac{\partial^2 C}{\partial y^2}-\left(r-\frac{1}{2}\sigma^2\right)\frac{\partial C}{\partial y}+rC=0.\qquad\qquad\qquad(3)$$ Step 2. If we...

Nick Higham's specialty is algorithms to find the nearest correlation matrix. His older work involved increased performance (in order-of-convergence terms) of techniques that successively projected a nearly-positive-semi-definite matrix onto the positive semidefinite space. Perhaps even more interesting, from the practitioner point of view, is his extension to the case of correlation matrices with factor model structures. The best place to look for this work is probably the PhD thesis paper by his doctoral student Ruediger Borsdorf. Higham's blog entry covers his work up to 2013 pretty well.


If a company agrees to pay travel cost for a job interview, is the promise binding and enforceable?

There is a question on workplace.SE about a company which offered to pay travel costs for a job interview, but canceled the return ticket after ending the interview - Potential Employer Cancels Return Flight . Generally, when arranging a job interview which requires the candidate to travel, it is common for the potential employer to pay travel cost and lodging for the candidate. In practice, the employer will ususally offer this, often in writing, but not write up a formal contract or similar document. In that situation, can the employer later renege on the promise to pay costs? In particular, can they renege after the candidate has begun their journey, thus saddling the candidate with the travel cost? My thoughts: On the one hand, a simple one-sided promise is usually not binding, as a binding agreement requires both sides to give something (called consideration in Common law). On the other hand, there is the notion of detrimental reliance , which appears to fit here. Also, one could argue that the candidate does provide something in exchange, namely their presence and willingness to attend the interview (basically, the company trades travel costs for having the candidate present for the interview). So, is the promise to pay the candidate's cost enforceable or not? Im interested in any jurisdiction, particularly European and US.

This aspect (and many others) of contract law is applicable in the US and various countries of the EU. can they renege after the candidate has begun their journey, thus saddling the candidate with the travel cost? No. The company would incur breach of contract. There is no need for a formal contract. The candidate only needs to prove that the company agreed (in writing, orally or clearly through its conduct) to cover or reimburse those expenses and that this elicited a meeting of the minds . The agreement would be void if the candidate incurred the expenses despite knowing...

The Plan For A Clearly Guilty Client Without Bargaining Power This question underestimates how much of a criminal defense lawyer's work involves sentencing rather than a determination of guilt or innocence. Suppose as the OP does that the prosecution can easily prove beyond a reasonable doubt that your client is guilty, you client has no plausible defenses, and the prosecutor won't budge on a plea. As a criminal defense lawyer, you may well advise your client that there is no percentage in fighting guilt on the charges, and have your client plea guilty. This prevents the prosecutor from spelling out...

No Parliament is sovereign : Parliamentary sovereignty is a principle of the UK constitution. It makes Parliament the supreme legal authority in the UK, which can create or end any law. Generally, the courts cannot overrule its legislation and no Parliament can pass laws that future Parliaments cannot change . Parliamentary sovereignty is the most important part of the UK constitution.

There Is Little Pressure To Improve Contract Drafting One piece of the puzzle is tradition and habitual writing style. A customary writing style for legal documents evolved over time, some of those conventions have evolved overtime (e.g. "Party of the first part, party of the second part"), others have not. Archaic vocabulary is slowly being weeded out, but again, it is almost never the goal of someone drafting a contract to reduce the reading level of the document. As long as the judge, or other lawyers, know what it means, it is an aesthetic stylistic issue more than it is...


Who is supposed to teach the law to the citizens?

As I understand, in general, not knowing the law does not excuse violating it . That should apply to most if not all jurisdictions in most cases with very few exceptions . From personal experience, never in my life has school, family or anyone ever actually taught me any laws or showed me where I could consult them myself, and I have already reached legal age a couple of years ago. So my question is, who, by law or morality, is supposed to teach citizens the law so that they can be aware and abide by it? Answers can be generalized to include most jurisdictions or be specific.

The answer from @user6726 is a good one. But, I'd like to add to it by pointing out that the body of law applicable to an individual is usually much, much smaller than the entire body of law. I'm a lawyer who has been in private practice for almost 25 years with an extremely diverse practice compared to the average lawyer, and I've never even looked at perhaps 80% of the laws on the books in the states where I practice, and even less elsewhere. By statutory and regulatory volume, the vast majority of statutory and regulatory law is applicable...

Most leases have a provision allowing a landlord to make entry without notice in an emergency, but the better course of action, as noted in a comment by @BlueDogRanch, is to call the police and ask them to make a "welfare check." You would ordinarily be permitted to cooperate with police by unlocking doors in furtherance of their welfare check. The police are trained to do this properly in a way that properly balances the need to aid someone who is sick or ill, the need to preserve evidence if there was a death or crime that needs to be...

There isn't any indication in that news story that the disabled son was anywhere nearby. I agree the situation you describe sounds like a legitimate use of the placard, but it seems in this situation, the placard was being used in a manner totally unrelated to the transport of a disabled person. My guess is that the cops cited her because the son wasn't in the car, and was not inside the establishment at which she parked. California code has this to say: A person to whom a disabled person placard has been issued may permit another person to use...

The Plan For A Clearly Guilty Client Without Bargaining Power This question underestimates how much of a criminal defense lawyer's work involves sentencing rather than a determination of guilt or innocence. Suppose as the OP does that the prosecution can easily prove beyond a reasonable doubt that your client is guilty, you client has no plausible defenses, and the prosecutor won't budge on a plea. As a criminal defense lawyer, you may well advise your client that there is no percentage in fighting guilt on the charges, and have your client plea guilty. This prevents the prosecutor from spelling out...


I want to leave Islam, but they would execute and kill me. What do I do?

I live in an Islamic country, but I don't want to be a Muslim. I have no choice but to claim to be a Muslim: If I leave Islam, they will execute me according to Muslim law. Where can I go to have a peaceful, non-religious life? Can I get asylum in any English-speaking countries? For example, would the Republic of Ireland accept me as a refugee? This is a hypothetical/abstract question of law. I am not making any personal statements about my beliefs or intentions.

Yes you can, and you can even include "editorials or subjective content". However, if you include factual statements, or words that imply factual statements, the company could claim that they are false, and therefore defamatory. Indeed they might claim that in any case. If you make no false statements of fact, they should not be able to win a defamation suit, but you might need to spend time and money defending yourself if they choose to sue. The detailed rules on defamation vary by jurisdiction, in the US by state. But in no US state can defamation be found against...

There isn't any indication in that news story that the disabled son was anywhere nearby. I agree the situation you describe sounds like a legitimate use of the placard, but it seems in this situation, the placard was being used in a manner totally unrelated to the transport of a disabled person. My guess is that the cops cited her because the son wasn't in the car, and was not inside the establishment at which she parked. California code has this to say: A person to whom a disabled person placard has been issued may permit another person to use...

Public nudity is illegal in New York as it is in almost every U.S. jurisdiction. And, if the police had arrested the nude protesters, the arrests probably would have been upheld in court, because a ban on nudity in public would probably be viewed as a time, place and manner restriction on the freedom of speech which is constitutionally valid. For example, the Ninth U.S. Circuit Court of Appeals recently upheld San Francisco’s public nudity ordinance in Taub v. City and County of San Francisco (2017). As the court in that case explains in a factually very similar case: Public...

Legally speaking, very many nations grant asylum, and religious persecution is one of the most basic grounds for granting asylum, following the 1951 Refugee Convention . This newspaper article compares asylum statistics in Ireland versus other parts of Europe. The Irish immigration authorities spell out the details for an asylum application. Note that you must already be in Ireland, to apply for asylum in Ireland (you should apply when you enter the country). One could also apply to Norway (almost an English-speaking country), but again you have to be in Norway to do so. There is a generic solution to...