Quantitative Finance

Quantitative Finance

  • Montserrat Guillen added an answer:
    Can anyone help with the scaling the time horizon for VAR (Value At Risk)?
    I would like to compute the value at risk for a portfolio of several financial instruments (their returns are not normally distributed). My underlying for all of them is the oil price, with normally distributed returns with mean of 0.

    My problem is that I want to compute the VAR for several days from now (10,15, maybe even 30). The common idea says that if the return is normally distributed with mean of 0 you can scale up the VAR by multiplying it with SQRT(Time). Obviously I cannot do that for the entire portfolio VAR.

    Am I allowed to compute VAR for oil price, scale it up by SQRT(Time) and then introduce that (my 5th quantile of oil) into the portfolio valuation and compute the portfolio once?
    Montserrat Guillen · University of Barcelona

    I sometimes go back to the original data and take the time gap I want to consider for VaR calculation. This is handy if you have enough data.

  • Krishna Reddy Chittedi added an answer:
    Best software for quants

    Hi all

    Which software do you think is better suited for statistics and quantitative finance; Matlab or SAS?

    Krishna Reddy Chittedi · Central University of Tamil Nadu

    If your working with high frequency data SAS would be Ideal choice.

  • Michael R Jonas added an answer:
    Is unit root testing good enough for testing random walk behavior or test for efficiency in market?
    There are a good number of empirical papers that conclude through unit root testing whether a given market is efficient or not and maximum times the series contains unit root which confirms that markets are efficient. I also tested for many time series related to stock market and exchange rates and found unit root at levels and stationary at first difference. But common sense says it can't be possible that every market is efficient as people makes money in market through trading rules also by following fundamentals of stocks. I find that confusing.
    Michael R Jonas · University of San Francisco

    Returns arising from an efficient market should follow a white noise process, an hypothesis which may be tested using the correlogram and Q (portmanteau) statistic.

  • Duc Pham-Hi added an answer:
    If you had to solve a Hamilton-Jacobi-Bellman equation and you only have to give a quick and dirty (sub optimal) solution, how would you proceed ?

    Say, to optimize buy/sell controls from a portfolio with transaction costs over 180 periods 

    Theoretically, you use spectral decomposition, search for viscosity solutions ,
    discretize, etc ... but run into curse of dimension and get too complex and unstable
    solutions anyhow. Some adaptive online sampling methods seem to work sufficiently well (Q-learning, TD learning, NDP, SMC etc.) . Has anyone used them ? Thanks

    Duc Pham-Hi · ECE Paris Graduate School of Engineering

    Thank you Anass, your clear answer.  

  • Fabrizio Rossi added an answer:
    What is Market Risk Premium that you are using in 2014 for your country?
    Market Risk Premium (MRP) that companies, analysts, and professors
    use to calculate the required return to equity in different countries.
    Fabrizio Rossi · Università degli studi di Cassino e del Lazio Meridionale

    This paper might be interesting "Market Risk Premium Used in 88 Countries in 2014: A Survey with 8,228 Answers"


  • Omar A Esqueda added an answer:
    Which is the best model for Event Study Methodology?
    There are different models that are being used to estimate the stock returns under event study methodology such as; arbitrage pricing theory (APT), capital asset pricing model (CAPM), modified market model (MMM) and market model (MM).

    My question is which one is better between the market model and CAPM to estimate the return while studying dividend announcements? How will alpha and Beta be estimated under the market model and CAPM in the equation for event study methodology’ i.e Rit = αi + β (market return) + εit?
    Omar A Esqueda · Tarleton State University

    Right, the market model is the preferred approach in event studies. Theory supports the CAPM, however, the market model is widely accepted in short return windows. See for instance Fama (1998).

  • Lucía Cuadro-Sáez added an answer:
    Theoretically, is there relationship between stock market movement and exhchange rate movement in developing countries?
    I am conducting an experiment by testing for co-integration (means long term equilibrium relation) between exchange rate movement and stock market index movement.
    The results indicate that there is no co-integration, which is against my intuition that in developing countries FIIs derive the stock market growth. As FII inflows increase, stock market goes up, and domestic currency is strengthened by Dollar inflows and the reverse happens in the case of FII outflows. But there has to be some link between these two variables.
    One reason for this behavior may be that exchange rate movement also depends upon trade flows. But what may be other reasons be? If somebody may have conducted a similar study then please throw some light on this problem.
    Lucía Cuadro-Sáez · Banco de España

    Dear Rajesh,

    As long as these countries do have a floating exchange rate and some degree of openness in the capital account, you could observe such relationship.

    Imagine a country that exports, for instance, IT services, like India does. The more IT services the country exports, other things equal, the better the results for the exporting companies, and these will be reflected in stock prices. Then, this better economic performance will probably attract capital flows and this will tend to appreciate the exchange rate.

    The other way around should be also at play. Imagine now that the underlying fragilities in the country, as large external or fiscal deficits, make foreign investors reluctant to maintain their money in the country, so that you have net capital outflows which end up depreciating the currency. The deterioration in capital flows and the focus on the underlying fragilities will probably make stock market investors to reconsider the prospects for companies, and this will possibly induce a correction in stock prices.

    As William pointed out, these mechanisms can get very complicated through multiple factors, but intuitively, I hope the above explanation helps.

  • David Binder added an answer:
    What are the assumptions of CAPM? Are the assumptions relevant or irrelevant in today's context?
    The development of portfolio theory by Markowitz.
    David Binder · University of Liverpool
    I do not see that as a "technical problem" as the CAPM is intended to estimate the required rate of return for "well diversified" investors. In the CAPM Beta is intended to measure the risk an investment contributes to the market portfolio. Actual investors range from wholly undiversified (hold one security) to quite diversified (hold the market portfolio proxy). One can calculate stand-alone risk by the standard deviation of a security's returns, and that is one factor one can use to calculate Beta, along with the standard deviation of the market returns and the correlation between security and market returns.

    An undiversified investor does face both systematic and unsystematic risk and, therefore, has a greater required rate of return. Market prices assume diversified investors and an undiversified investor cannot be compensated for the additional (unsystematic) risk. Such an investor would need to pay less (to get a higher return) than a diversified investor and there is no reason a willing and uncompelled seller would sell for less than the market price.

    I think that terminology over the years has become a bit sloppy. What the CAPM estimates is the rate of return required to justify assuming a level of risk as measured by Beta. It does not predict the return for any specific investment. A well managed company should have a positive EVA ... that is, it should have a return in excess of its cost of capital. There is no economic gain if all it earns is its cost of capital. If all an investor earns is the cost of capital, that is return of investment and not return on investment.

    I distinguish to my students three returns: required rate of return being the return needed to justify assuming the risk; expected rate of return being what one expects to happen based on the specifics of the situation; realized rate of return being what actually happened. The first two are ex ante returns and are reflected in the NPV calculation ... a positive NPV means that the expected rate of return exceeds the required rate of return used as the discount rate. Realized rate of return is an ex post return and cannot be known at the time an investment decision must be made.
  • Ahmad Y. Khasawneh added an answer:
    What is your opinion on: "The benefits of Naive and Markowitz diversifications have the same origins. They vary only in degree"?
    Not true.
    Naive diversification is combining assets into portfolios randomly and ignore correlation. In contrast, Markowitz diversification is combining assets with correlation coefficients.
    Ahmad Y. Khasawneh · Hashemite University
    Investor can be naive if he/she operates in an efficient market but can't be naive in no efficient market. In efficient market alpha will be close to zero and at that time it does not matter to invest 1/N in each security of choice but in no efficient market abnormal return is possible and the 1/N won't form the best return portfolio.
  • Refk Selmi added an answer:
    Who are the top researchers in Behavioral finance?
    Who are they, what are they researching and what are the universities leading the topics?
    Refk Selmi · ESC, University of Manouba, Tunisia.
    John W. Payne, Campbell Y. John and Robert J. Shiller
  • Richard Crane added an answer:
    Which method is the best for an analysis of the mutual funds industry performance as a whole?
    I am currently working on my thesis which is the analysis of mutual funds industry performance in U.S. but i am having a difficult time finding the best method to do that. Can anyone help me with some ideas?
    Richard Crane · Eva Corporation
    Yes, Muthusway, and many institutions are allocating assets according to MPT. That's why index funds like spy, iwm, and lqd are very large. The interesting question to me is, at what boundary does efficient market theory break down? The efficient market requires that the market behave as though information is almost instantaneously transmitted. So, it's very hard to profit by selecting similar stocks. You can't profit by buying PG and shorting KMB, because the information that would justify a higher PE for one is already in the market. On the other hand, low beta and low P/B stocks have historically outperformed. I think it's unlikely the latter will do so in the future, because Fama's work has become so widely accepted. You could look at the recent past's significant outperformance of IWN as a reflection of the acceptance of Fama's ideas.

    Move the boundary one more step. What about asset allocation? Are the prospects of each asset class the same on a risk adjusted basis compared to others at all times? What the stock market was half it's current value in 2009, which treasuries had zero or negative yields, were the two equally attractive?I didn't think so, and acted accordingly.

    At some point, obvious market moving information becomes less important than judgement about the future course of events.
  • Pallavi Kiran Ingale added an answer:
    What are the hot topics in behavioral finance in the spot now?
    Bias, experiments and methods. What is the trend?
  • Jason Liu added an answer:
    How can I get factor return if I have factor loading and stock return (including market return) in a factor model like Fama-French 3 factor model?
    Especially if this is a multi-factor model.
    Jason Liu · Tsinghua University
    Yes, I agree. Fama and MacBeth regression seems to tell us that we can get more accurate risk premium than original factor return. And thus we should use the cross section results as 'real' factor return instead of the original ones.
    It is a pity that we cannot get the original factor returns from betas, which I have planned to do.
  • Ovidiu Racorean asked a question:
    Is there anybody that uses the time-independent pricing of options equation for pricing bitcoin/ binary/ weekly/ American options?
    One ex-VP at a big investment bank said once that it uses Racorean’s equation (see. http://arxiv.org/abs/1307.6727 ) for pricing bitcoin options.

    -σ^4/r(σ^2+r) (d^2 ψ_((S) ))/(dS^2 )+1/S^2 ψ_((S) )=r/σ ψ_((S) )

    Is there anybody else that uses the time-independent pricing for pricing bitcoin options or for trading binary /weekly/American options?
  • Technical analysts use some methods in determining/evaluating their buy/hold/sell strategies. Any ideas where to find such strategies?
    Melquiades Pereira Lima Junior · Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte
    If the question is how to calculate the return of the recommendation: I'm using the calculation of return on realized based on the recommendation farooq (2013). The annual cumulative return of the recommendation CRR is calculated by the return from the recommendation for 12 months from the difference between the last price LP_ {12} it-traded 12 months before and the price LP_ {it} negotiated later. \ begin {equation} \ label {eq: CRR} CRR = \ left \ {\ begin {matrix} LP_ it-{12} / LP_ {it} -1 & 1
  • Nilakantan N Sundararaman asked a question:
    How to figure out Qn reg Jarrow-Rudd formula with skewness and kurtosis adjustments in actual conditions?
    I am trying to implement the Jarrow-Rudd formula for valuing options with adjustment terms for skewness and kurtosis. The Jarrow-Rudd formula in its simplest variation, gives the value of the option C (F) as:

    C (F) = C (A) +λ1Q3 +λ2Q4
    where C(A) is the Black-Scholes Option price, Q3 and Q4 involve some term of derivative of St at strike price K.

    I don't understand how to work out this derivative in actual conditions. Their paper on approximate valuation of option pricing does not give any indication of this and I do not have access to their other paper on the testing of the formula with market prices (this paper is part of the book on option pricing edited by M Brenner.) Does anyone have an idea as to how to decode this type of derivative?

    Thanks for your assistance in advance.
  • Lorenzo Peccati added an answer:
    What's the solution for the summation: 1/(1+a.x) with x = 1,...,n?
    Searching for the present value for a linear interest rate series.
    Lorenzo Peccati · Università commerciale Luigi Bocconi
    Dear Michele,
    we should decide what a "closed form solution" turns out to be.
    My be that if you think that "Digamma function", together with its derivative, implies closed form, almost all is "closed form". And such a notion looses interest.
    My earlier suggestion, which turned out to raise no attention, is summarized as follows:
    In the framework of the so-called M-test for series convergence.
    The expression (Sum(M,p) f(m) - Int(M,p+1) of f(x)d)x) has a limit when p-> + infinity. Such result is not always cited,
    The limit of the difference between Sum (1,p) [(1/m)-ln(p+1)] is nothing but Euler-Mascheroni constant.
    What I think is that tools must be (somehow) proportional to the relevance of problems I understand that this is can create some problem for a mathematician, but the original question was far both from maths...
  • Arta Hashimi added an answer:
    Is there any article/paper about the performance of US Mutual Funds during the financial crisis of 2008?
    For a while now I have been searching for an article that describes the performance of the US Mutual Funds during the sub-prime crisis, but I haven't found a particular one. Could anyone help me out?
    Arta Hashimi · Masaryk University
    I actually have the raw data and the results, but I wanted to check if they are consistent with any other previous findings.
    Thank you for the answer!
  • John Ryding added an answer:
    Why is the correlation among stock prices larger when the return is negative?
    The correlation is asymmetric. Is there a model or theory able to explain it?
    John Ryding · RDQ Economics
    Another factor is forced liquidation of leveraged positions because of margin calls. No one ever gets a margin call when stocks are going up (unless you are short!)
  • Nemiraja Jadiyappa added an answer:
    Does capital structure affect firm growth or growth affect it?
    Is there a model of growth as a dependent variable and leverage as independent?
    No...Purely from finance perspective growth is not dependent on your financial policies....growth opportunities are exogenous. But, having said that, utilization of growth opportunities depends on your financial policy. In some states of the nature, if you use debt, some growth opportunities would yield negative NPV and thus firm will not pursue those opportunities which reduces their actual growth.....so firms actual growth does depend on your financial policy. Note here that we have made a distinction between Opportunities and the actual use of those opportunities
  • Murat Kizildag added an answer:
    Is there any other method of measuring the performance of a mutual fund scheme than Sharpe Ratio, Beta and R Squared ?
    Generally, this is measured through Sharpe Ratio.
    Murat Kizildag · University of Central Florida
    Good Answer Robert
  • Bradut Vasile Bolos added an answer:
    What are the priority changes for development countries in financial market infrastructure after the crisis?
    Harmonization with EMIR regulation
    Bradut Vasile Bolos · University of Buraimi
    Dear Sergiy

    By "development countries" you mean "developed countries" or "developing countries"?
    By "EMIR regulation" you mean European Market Infrastructure Regulation i guess.
    So if you mean "EMIR" use in developing countries, it has little if any significance, as OTC traded there have marginal value. So i would say EMI and EMIR should not be a priority there as the underlying markets are to under-capitalized and volatile to accommodate a healthy OTC market.
  • Michal Kravec added an answer:
    Can someone suggest any references where there is formula 2^m=<n in cluster analysis?
    Where m - number of parameters
    n - number of observed objects
    Michal Kravec · University of Economics in Bratislava
    Thank you. I knew that number of observed objects must be higher than the number of variable by which the objects are classified. I found the above equation but without any explaination and source
  • Viktor Zharkov added an answer:
    Is Schrodinger's equation truly adequate to model the stock market? What do you think?
    Finance is becoming more and more a field of research for physics.
    Viktor Zharkov · Perm State University
    I do not use Grassmannians. I use grassman valued (odd) functions.
    These are different things. The basic idea is to use the functional integral, which allows us to describe the duality. For example such duality: (stochastic)accident - determinism, evolution (continuous function) - crashes (p-adic functions). Just for the sake of this is to use a functional integral. With its formulation such a problem occurs. We have classical system of traders. When lifting the system of equations describing the ensemble of traders to functional integral we get a supersymmetric scheme. It summarizes the Minority game, because it takes into account both orders ( buy and sell), and cash flows. And so. Cash flows are described by the spin variables. Orders are described by Grassmann functions. This Jacobi field appears in mechanics. As I know no such theory formulate for stock market.
  • Roberta Ann Barra added an answer:
    Can anybody tell me more about "DB" formula in Microsoft Excel, as a financial function? In fact, what is it's mathematical base of calculations?
    notice that it is similar to DDB, but not exactly. so what's the difference?
    best regards..

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