2
votes
2answers
56 views

Why do we assume quadratic utility in portfolio theory?

In my text (Investments by BKM), the investor's mean-variance utility (given as $U = E[R] - \frac12A\sigma^2$) is stated to be the objective function we wish to maximize. Upon further digging, it ...
0
votes
1answer
16 views

What does each bar in the empirical average eigenvalues spectrum of the correlation matrix of log-returns of stocks represent?

An example diagram, taken from this paper, looks like follows: What is its physical interpretation? The highest eigenvalue, the paper says, represents market mode. So, what does the difference in ...
0
votes
1answer
19 views

Calculate historical duration based on current duration & historical prices

Suppose I have today current duration of a bond and it's historical daily prices. How from that I can calculate the historical duration? e.g. the value of duration I would saw if yesterday, week ago, ...
1
vote
1answer
24 views

How to compute the yield on the Ultra-Bond Treasury Futures

I am trying to compute the yield on the Ultra-Bond Treasury Futures which is roughly 172.2187. Heres the description of the contract: U.S. Treasury bonds with remaining term to maturity of not ...
9
votes
1answer
223 views

Which are useful applications of clustering in quantitative finance?

Several machine learning algorithms have been applied in finance/trading. Focusing on clustering (k-means, k-medoids) what are useful and successful applications in quantitative finance? What is used ...
0
votes
0answers
28 views

Selection of optimal backtesting parameters

Suppose I backtest some strategy on in-sample data while varying two parameters, say $X$ and $Y$. $X$ can take the values $\{3,6,9,12,15,18\}$ while $Y$ can take $\{10,15,20,25,30\}$. I want to select ...
3
votes
1answer
115 views

Consequence of negative mean reversion of hull white one factor model

I tried to calibrate the data for hull-white one-factor model. Sometimes, I get negative estimate of mean reversion factor after the calibration process. When I plug the negative mean reversion factor ...
0
votes
2answers
58 views

Compiling QuantLib example

I have followed the guidlines for installing QuantLib for mac from here http://quantlib.org/install/macosx.shtml and also fixed the flags using the commands: export CXXFLAGS = -stdlib=libstdc++ ...
0
votes
0answers
23 views

A Simple Stochastic Integral Asymptotics

Let $B(t)$ be the standard Brownian motion, $\mu(t,x)$ and $\sigma(t,x)$ are continuous functions, and (the short interest rate $r(t)$) $$dr(t) = \mu(t,r(t))dt+\sigma(t,r(t))dB(t).$$ $(\mu,\sigma)$ ...
1
vote
2answers
324 views

“Hedging” a put option, question on exercise

I have a question on the following exercise from S. Shreve: Stochastic Calculus for Finance, I: Exercise 4.2. In Example 4.2.1, we computed the time-zero value of the American put with strike ...
1
vote
0answers
28 views

Optimal portfolio construction questions [on hold]

I am working on a paper that tries to build an optimal portfolio to hedge various risks (mainly interest rate risk). I have never done this before. Which software program should I use to create an ...
1
vote
0answers
18 views

Dollar-Neutral in addition to Market-Neutral?

What is the point/benefit of using a dollar-neutral strategy in addition to a Beta-neutral strategy? What exactly does a dollar-neutral strategy buy the investor? What's useful about balancing long ...
6
votes
1answer
157 views

Extrapolating SVI

In his paper Gatheral presents the following parametrization of the implied total variance $w(k,T) = \sigma_{BS}(k,T)^2T$ $$ w(k) = a + b\{\rho (k-m) + \sqrt{(k-m)^2 + \sigma^2} \}.$$ Assuming that ...
3
votes
1answer
87 views

Mathematical Derivation of Residual Risk

I understand the difference between Excess, Residual and Active Returns. I also understand what Active Risk; defined as: $\sigma_{r_P-r_B}$ (i.e. standard deviation of the difference in returns ...
3
votes
3answers
84 views

What is the rationale behind using SV models with 2 distinct volatility processes?

In the Double Heston model, there are 2 distinct volatility processes. The SDEs read \begin{align} & ...
0
votes
2answers
43 views

NPV of two annuities

For exam preparation we are given some past papers, however there are no solutions and I would like to know if my logic is correct for the following question: Assume you are 25 years old. An ...
4
votes
2answers
178 views

Tradable information from BS Implied volatility

These are two follow up questions to: Implied volatility as price transform I understand that the BS model is used as a 'Blackbox' that takes a market price and maps it in a 1to1 fashion to a 'BS ...
3
votes
2answers
79 views

Using R with princomp to create hedge baskets

I am experimenting to try to find better ways to hedge some of our equity portfolios. It's easy enough to use R to get a PCA breakdown of exposure for a portfolio but I can't figure out how to then ...
0
votes
1answer
30 views

Volatility for time periods with little data

When I want the monthly volatility of stock and I only have data for about one month and I do calculation like this: ...
1
vote
1answer
38 views

Relation of survival and non-survival Marshall-Olkin copula

Let us have two random variables $A$ and $B$ representing lifetimes of two elements of a system, where $A$ has cdf $F_A(x)$, $A \sim Exp(\lambda_1 + \lambda_{12})$ and $B$ has cdf $F_B(y)$, $B \sim ...
1
vote
3answers
132 views

What does a negative stock amount mean in a single-period, binomial market model?

Consider a single-period, binomial market model with a $r > 0$ interest rate (in USD per period) and a portfolio $(x, y)$ consisting of two assets: a savings/lendings account and a stock, both ...
0
votes
0answers
12 views

Problem with determining weights in tangency portfolio (2 risky assets)

I use the following well known formula in order to determine the weight of asset i in the tangency portfolio (in the case of two risky assets): ...
0
votes
2answers
52 views

Simulate drifted geometric brownian motion under new measure

I have a very fundamental question regarding simulation of DRIFTED geometric brownian motion. We have the standard Blackos Scholes model: $dS(t)=r S(t)dt+\sigma S(t) dW^{\mathbb{P}}(t)$, where ...
0
votes
1answer
75 views

approximating fBm stochastic integral

Suppose I have the following stochastic integral: $$\int_a^b f(t)dB_H(t)$$ with the term $dB_H(t)$ a fractional brownian motion with associated $H$ parameter. Is it true that for $H \in (1/2,1)$, ...
0
votes
1answer
51 views

Portfolio with a certain pay-off curve

I would like to find a relevant optimization option's portfolio models which can describe a certain pay-off curve (objective function) under same assumptions. For example, assumptions on how to limit ...
2
votes
1answer
41 views

Copulas and default probability

Assume a basket of 3 credits, each with some unconditional default probability ${q_i}(t) = \Pr [{\tau _i} \le t]$. Consider the joint CDF $H$ of the default times is given by $H(t,t,t) = \Pr [{\tau ...
0
votes
0answers
11 views

How do I build a cross currency basis swap pricer using implied levels generated from fx forwards?

I'm building a strategy where I would take positions depending on whether the basis swap looks rich or cheap relative to the forwards, inside 1yr maturity. Depending on liquidity the market in ...
1
vote
0answers
18 views

How to apply Kelly criterion to a portfolio made by a stock plus a option?

First of all, assuming a Gaussian, Markowitz, well behaved world. Extensions for non-well behaved world will be welcomed. I know that by a portfolio made by only by one stock (and a risk free bond) I ...
14
votes
3answers
275 views

Regression model when samples are small and not correlated

I received this question during an onsite interview for a quant job and I'm still scratching my head on how to solve this problem. Any help would be appreciated. Mr Quant thinks that there is a ...
4
votes
1answer
30 views

What approaches are there for keeping local and remote order books in sync?

Scenario: developing a custom application which defines a structured workflow for manual order submission to Bloomberg EMSX; it should minimize own persisted state and rely on the remote order book as ...
0
votes
0answers
19 views

Yahoo Finance data scraper [duplicate]

I am building a small financial web application and I need a data source for price (Adj. Close) and volume data. I have written a scraper to scrape equity data for yahoo finance and can pass this to ...
2
votes
0answers
15 views

Polynomial interpolation of corrected lognormal distribution

Can anyone provide a formula for a polynomial interpolation of the corrected lognormal distribution used to model returns traditionally resulting from the wrong Brownian motion generated model? ...
1
vote
1answer
45 views

Calculating the global minimum variance portfolio in R?

I am attempting to use the globalMin.portfolio command to calculate the global minimum variance portfolio in RStudio. My code is as follows (note that several libraries have been included which may ...
0
votes
1answer
48 views

wishart stochastic volatility models

Stochastic volatility models assume that volatility follow a random process.In the emerging market the volatility tend to be high. why is it that the wishart stochastic volatility model fit well the ...
0
votes
1answer
30 views

Beta = 1 and 0. Type of portfolios

I read in E. Quian's "Quantitative Equitity Portoflio Management" the following: A traditional long-only portfolio [with unit beta] would have most of its risk in the market risk. However, a zero ...
0
votes
1answer
24 views

Why is the Risk Free Rate 1 over Contingent Claim Prices?

Reading Asset Pricing by John Cochrane (2005), in his second chapter he defines the risk free rate as: Rf = 1 / sum [pc(s)] Where pc(s) are state contingent claims, where s is the state of nature ...
1
vote
0answers
27 views

Minimum Variance Portfolio problem [on hold]

Minimum Variance Portfolio Suppose there are N stocks in the investmentable universe and we have a fully invested portfolio investing 100% of the capital. The Covariance matrix is denoted as ∑. We ...
4
votes
1answer
94 views

How are Quandl monthly S&P500 earnings estimates derived?

Can someone explain how the monthly earnings estimates are derived for S&P500? Quandl sources multpl.com, who state: ...
0
votes
0answers
23 views

Estimating time-varying tail dependence for Archimedean copulas

Patton (2006) defines the upper tail dependence coefficient for a time-varying bivariate SJC copula as $$\tau^u_t=\Lambda \left(\omega_u + \beta_u \tau^u_{t-1}+\alpha_u ...
8
votes
4answers
895 views

Strategy Risk and Portfolio Allocation Model (copy from nuclear phynance)

Here is a very interesting question that I found at Nuclear Phynance (original author: Strange); I though it is so interesting that it is worthwhile to ask it here: I have $N$ strategies, across a ...
1
vote
2answers
57 views

Correlation between asset A and Portfolio X (which contains A)

After a few hours trying to solve this I give up! I need help. I need to calculate the BETA of an asset with respect to a portfolio that contains this asset. I have the volatility and correlations ...
4
votes
2answers
73 views

Realized “efficient” frontier. Is this reasonable?

I have performed some out-of-sample analysis of mean-variance optimization with monthly rebalancing. Studying the "realized efficient frontier", I am worried that something is wrong. Since the ...
1
vote
1answer
96 views

Second Moment of Stock Process

I have a stock process which I have decided to model as $$S_T=S_t\exp((r-q-\frac{1}{2}\sigma^2)(T-t)+\sigma(W_T-Wt))-D_T$$ where $D_T$ is a cash dividend at time $T$. This dividend is known. I then ...
2
votes
2answers
855 views

ex ante tracking error correlation between funds

I have two portfolio's called Comb & Global. They both have the same investable universe lets says 3000 stocks & are measured against the same benchmark. So it is possible that both funds hold ...
-4
votes
1answer
146 views

Is there an API to perform request about stocks and financial derivatives? [closed]

Is there an API to make a request such as: all the companies which thier P/E ratio is greater than 50 ? I know I can crawl google finance and have it locally on my ...
0
votes
1answer
41 views

long fra and a short ed future with same fixing dates, is convexivity negative or positive?

If you are long a FRA (forward rate agreement) and short a ED (Eurodollars) future with the same fixing dates, do you have positive convexity or negative convexity? Why? According to the following ...
1
vote
1answer
53 views

Can a momentum strategy be cast as a multilinear regression model?

Disclaimer: the question is similar to Can momentum strategies be quantitative in nature? and (to an extent) What is the expected return I should use for the momentum strategy in MV optimization ...
12
votes
1answer
600 views

Models crumbling down due to negative (nominal) interest rates

Given that the negative interest rates on a lot of sovereign bonds with maturity under 10 years are trading in the negative (nominal) interest rate territory (recently also the short term EURIBOR has ...
8
votes
2answers
176 views

Stochastic Calculus Rescale Exercise

I have the following system of SDE's $ dA_t = \kappa_A(\bar{A}-A_t)dt + \sigma_A \sqrt{B_t}dW^A_t \\ dB_t = \kappa_B(\bar{B} - B_t)dt + \sigma_B \sqrt{B_t}dW^B_t $ If $\sigma_B > \sigma_A$ I ...
0
votes
1answer
91 views

How to work out the forward outright price from the bid/ask quotes?

I'm facing this problem: Spot AUD/USD is quoted at 0.7634/39; six-months swaps are 112.1/111.1; at what forward outright rate can a price taker sell USD value spot/6 months? On the spot ...

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