Questions tagged [correlation]

A measure of the degree of linear association between a pair of random variables.

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121 views

Effect of correlation on a best-of rainbow option

EDIT 2: I found the problem(s) and the prices seem to behave as expected now. For anyone interested there was a bug when normalizing the dependant ranom normal variates used in the simulation, so ...
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35 views

Cumulative returns are more correlated than non-cumulative

I was just comparing two daily returns series and noted that the correlation between them is a lot higher if they are cumulated (about .95 for cumulative returns, vs .15 for non-cumulative). I feel ...
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Conditional and unconditional variance, autocovariance and autocorrelation of an ARMA process

Given an ARMA(1,1) process $x_t = a + bx_{t-1} + \varepsilon_t + \theta\varepsilon_{t-1}$, how can we find the conditional variance, i.e. $Var_{t-1}(x_t)$, find the unconditional variance, i.e. $Var(...
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Is non-linear correlation problematic in financial time series prediction?

Many traditional finance models assume linear relationships between variables and features. Aren't linear correlations/covariances unable to capture financial processes empirically since they actually ...
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35 views

how to construct a diversified portfolio based on correlation

I have a porfolio of indexes and I built up a python model based on spearman correlation (I used a spearman and not a pearson because, after running some test on outliers and normality ...
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1answer
43 views

Covariation of Ito semimartingales

If we have two Ito semimartingales over $[0,T]$: $$d X_t^i=a^i_tdt+\sigma_t^idW_t^i,\quad i=1,2$$ What is the relationship between $$\langle X^1,X^2 \rangle_t \quad \text{and} \quad \langle W^1,W^2 \...
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mixing fractional Brownian motions

Given two Brownian motions $W_t^1, W_t^2$, we can have them correlated by $$dW_t^1 = \rho d W_t^2+\sqrt{1-\rho^2}dZ_t$$ where $W_t^{2}$ and $Z_t$ are independent of each other. My question then: is ...
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1answer
152 views

Cega - Correlation Delta from multi-asset derivative

I want to calculate the Cega, i.e. correlation delta, for a multi-asset derivative numerically (the difference of the price from a tiny move in correlation). However, I found it is difficult to follow ...
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32 views

calibration of correlation in vasicek model

how can I calibrate the correlation by numerical integration of the normal bivariate distribution assuming that the standardized asset returns of two firms are described by the single-factor Vasicek ...
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Cleansing covariance matrices via Random matrix theory

I am exploring de-noising and cleansing of covariance matrices via Random Matrix Theory. RMT is a competitor to shrinkage methods of covariance estimation. There are various methods expressed usually ...
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1answer
55 views

Hedge Ratio Calculation

My question is if I have a spot position of a commodity e.g Naturals Gas I want to hedge, how would I determine, which futures e.g. quarterly, yearly I should pick. Should I just take the one it is ...
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163 views

Questions about beta, correlation, and covariance

Currently, I calculate beta, correlation, and covariance measures using daily log normal returns of Security A and Benchmark A. What would it mean if I were to use daily log normal excess returns in ...
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realized correlation estimation

I'm trying to implement the Hayashi - Yoshida estimator for correlation (T. Hayashi, N. Yoshida: On covariance estimation of non-synchronously observed diffusion processes, 2005) and there's something ...
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1answer
227 views

Correlation between stock prices given correlation between returns

assume I have two stocks with known volatilities and a known correlation coefficient of returns - does anyone know how to determine the correlation between the prices and NOT THE RETURNS
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How can I find the exit equity value from my dataset (please read description and see screenshot below)

I am investigating the returns of private equity using a public market equivalent (PME) and have been given a dataset from the that has provided us with the deal level IRR, the entry equity data and ...
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1answer
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Proving an Identity between a pair of correlated Wiener processes

Suppose we have the following subordinated stochastic differential equations: $dR(t)=\mu dt+\sigma (Y(t))dW_{1}(t)$ $dY(t)=f(Y)dt+g(Y)dW_{2}(t)$, where $W_i$'s are standard Wiener process such that ...
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Trading Ranges for Tactical Asset Allocation

Do methods exist to determine trading ranges around benchmark weights/strategic asset allocation weights for a tactical asset allocation from the correlation structure between the individual asset ...
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1answer
118 views

question about spot/vol correlation

In this paper The Interplay between Stochastic Volatility and Correlations in Equity Autocallables by Alvise De Col, Patrick Kuppinger (2017) https://papers.ssrn.com/sol3/papers.cfm?abstract_id=...
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47 views

Exact solution stock price with Vasicek interest rate model

Define two correlated stock price- and interest rate (Vasicek) processes, governed by the Wiener processes $W^{S}(t)$ and $W^{r}(t)$ $$dS(t)=r(t)S(t)dt+\sigma S(t)dW^{S}(t)$$ $$dr(t)=\kappa(\theta-r(...
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Simulate correlated Brownian motions conditioned on future state(s)

Consider a model defined by 2 geometric Brownian motions $$dY_{1}(t) = \sigma_{2} Y_{1}(t)dW_{1}(t)$$ $$dY_{2}(t) = \sigma_{2} Y_{2}(t)dW_{2}(t)$$ with $Y_{1}(0) = y_{1}$, $Y_{2}=y_{2}$ and $dW_{1}(...
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Transform Hierarchical Correlation structure to Standard Form

In the standard portfolio risk setup, we have $\sigma_{\Pi} = \sqrt{(w' B (VFV) B' w) + w'Dw}$ where $w$ is our weight vector for N assets $B$ is the Nxm factor beta matrix $V$ is the factor ...
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129 views

Spot variance drift consequently to style drift

I am looking for some information on how to spot variance drift for a portfolio in accordance to its benchmarks, Let's say that we have returns of the portfolio $\textbf{P}=(P_1,...,P_t,...,P_n)$ and ...
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1answer
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What are non-variance (non Markowitz) based theories of capital allocation between non-correlated assets?

A large amount of literature in finance accepts the standard deviation in return as if it were an accurate measure of "risk." What are some other financial theories for how to allocate capital ...
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Correlation in GARCH model

I don't think I have ever come across the concept of stochastic correlation so I imagine it's not very widespread, but I had the idea to implement a Monte Carlo VaR model for a portfolio of stocks by ...
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Literature and Intro to Dispersion Trading

I am familiar with the basic idea of the dispersion trade i.e. index vol vs constituent vol and implied correlation. I am wondering if there are any standard resources (pdfs, books, presentations) ...
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91 views

Average portfolio correlation vs. external metric

I am coming across a problem I can't seem to wrap my head around, and I am not sure I am using the right words so cannot find much info in it! I have a portfolio of assets, with data on historical ...
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146 views

Estimate covariance matrix using prices

We generally estimate the covariance matrix of assets using their returns instead of prices. Why is that the case? I can think of two possible reasons and would appreciate comments/feedback regarding ...
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37 views

Portfolio of Assets with non-constant correlation - Maximum Drawdown

How could I calculate the maximum drawdown (given a specified confidence interval, ie. 99%) of a portfolio whose assets have non-constant (deterministic or stochastic) correlation? Is there a ...
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2answers
291 views

Creating a Covariance Matrix

Lets say that you have the correlation of x,y and you have the standard deviations of x and y , how would you then find the covariance of x,y using the correlation of x,y and and the standard ...
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1answer
256 views

target market correlation for long / short equity portfolio

Given a long / short equity portfolio, I want to have some net long market exposure. My portfolio volatility is fixed to a target, so I don't think it makes sense to target market beta. I think I ...
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Simulating Returns

I'll start this off with a rather broad question: I am trying to simulate returns of a large number of assets within a portfolio of different classes - equity and fixed income in a first step, say 100 ...
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1answer
72 views

Two commodities which are normal distributed and perfectly correlated

The daily price change in commodity 1 is distributed $N(0,0.15^2)$ and the daily price change in commodity 2 is distributed $N(0,0.3^2)$. The two commodities are 100% correlated. 1) Does the relative ...
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Sharpe ratio of strategy exploiting correlations that vary by time interval

The Epps effect "is the phenomenon that the empirical correlation between the returns of two different stocks decreases with the length of the interval for which the price changes are measured" (...
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1answer
57 views

Creating a matrix of average correlations for sub-industry from individual stock correlation matrix

I am having trouble trying to figure out how to do this in Python. I have created it in Excel, but I would like to automate this for any sector or grouping of sub-industries. I first start with ...
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Robust bounds or approximations on implied volatility skew when $\lvert \rho \rvert \rightarrow 1$

Are there any robust / non-parametric results for pure stochastic volatility models, in terms of bounds or preferably accurate approximation, for the implied volatility skew $\partial IV(k) / \partial ...
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Correlation Gold and SPX in BBG

I was always under the impression that gold as a safe haven was more or less inversely correlated to the general market. After using the HRA function in Bloomberg I saw that the correlation is just -...
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1answer
82 views

Correlation between the perfect market-timing strategy and the market itself?

What would be the correlation between a perfect market-timing strategy [that it always goes long (short) one unit of the market the day before the market goes up (down)] and the market itself, given ...
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1answer
274 views

How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?

Introduction My goal is to retrieve a single Value-at-Risk (VaR) of a N(0, H) random variable $X$ at the $\alpha \in (0,1)$ confidence level where H is a known d-dimensional positive definite matrix ...
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1answer
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Correlation of a portfolio of trading strategies to a benchmark [closed]

I have two trading strategies, both having a correlation of 0.5 to an indicator 'i'. If I take a portfolio of these two strategies, what will be the correlation of this portfolio with the indicator 'i'...
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1answer
67 views

How to test ESG score as a factor against traditional factors

I have created my own ESG scoring system. I would like to test it as a factor against the traditional factors (growth, Value, quality, size etc) In essence a correlation test. Could anyone please ...
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1answer
57 views

Negatively Correlated Assets with similar medium-term trends

Theoretically, one could have stock prices with returns $\rho_1(k)$ and $\rho_2(k)$ having mean values $\mu_1$ and $\mu_2$, but still be negatively correlated with $$ \mathbb{E}[(\rho_1(k)-\mu_1)(\...
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135 views

FX Correlation Risk from cross ccy pairs

Suppose you are long a TRYJPY call option. And lets say you can delta hedge using USDTRY, AUDJPY, and AUDUSD. In this case I would delta hedge by buying USDTRY, selling AUDJPY, and buying AUDUSD. If ...
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807 views

Why isn't it appropriate to use correlation between prices in a pairs trade strategy?

I've already seen this question and read through all the answers, but I'm still confused about why you shouldn't use price correlation in a pairs trade strategy. For example, if I'm looking at the ...
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Change of measure for BGM (LMM) Model

I've been checking the demos for BGM (LFM) forward rate model. Here's a short reminder to help you follow: Now, take the following $$\frac{dL_j(t)}{L_j(t)} = \sigma_j. dW^j(t) = \mu_{ij} dt + \...
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Relationship between correlations of long only and short only portfolio with long-short portfolio?

I am working on one quality and value factor, the correlation between a long-only or short only portfolio of these two factors is respectively 0.7 and 0.8, and the correlation between combined long-...
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1answer
3k views

Estimating correlation using EWMA

I am using an EWMA model to evaluate the correlation between yearly time series. I know Riskmetrics uses $\lambda=0.94$ for daily data and $\lambda=0.97$ for monthly data. Is there a value ...
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4k views

Why does the VIX index have *any* correlation to the market?

It appears that the log 'returns' of the VIX index have a (negative) correlation to the log 'returns' of e.g. the S&P 500 index. The r-squared is on the order of 0.7. I thought VIX was supposed to ...
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2answers
842 views

Futures and Forward Prices vs interest rates

Textbooks usually state that if an asset's prices are positively correlated with interest rate movements, then its Futures price is going to be greater than its Forward Price assuming the same ...
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34 views

How does the implied correlation change when the spot price of the Basket Call/ Put option goes up?

Given a basket Call/Put: $BasketCall_{payoff} = max[0, \Sigma^n_{i=1} w_iS_i(T) - K]$ If the spot price of the basket goes up/down, how would the implied correlation change? I guess what I am not ...
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Variance swap correlation trade

I found two highly correlated assets that have spread in 3M realized and implied vol at historical minimum. To go long on this spread I thought of using two variance swaps. Would it be cheaper to ...

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