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Questions tagged [mean-variance]

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33 views

Notation for the variance in papers

Here is a screenshot from : LIM Quadratic hedging and mean variance portfolio selection with random parameters in an incomplete market When I deal with mean variance portfolios, I usually see the ...
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6answers
165 views

Is a more robust Covariance estimation possible?

I'm working on a mean-variance optimization problem, but instead of financial securities I'm choosing a 'portfolio' of N athletes. It is a 1-period optimization problem over one generic statistic ...
2
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1answer
44 views

ARMA moments proof

Consider a standard ARMA(1,1) process such as $$x_t - \beta x_{t-1} = \theta u_{t-1} + u_t$$ where $u_t$ is i.i.d. $u_t \sim N(0,\sigma^2)$. I know how to derive mean and variance with stationary ...
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1answer
71 views

Prove that the portfolio that maximizes utility lies on the efficient frontier

When maximizing mean-variance utility in a portfolio optimization framework $max \{R - \lambda \sigma ^2\}$ where R is portfolio return, $\lambda$ is a risk aversion parameter, and $\sigma^2$ is ...
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35 views

Stochastic discount factor for factor research

Often, after presenting a new factor technique, the paper calculates an SDF by doing $\Sigma ^{-1}\mu_F$ i.e. mean variance optimization on the factors. What is the significance of doing this ?
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73 views

Can variance change over time?

I'm working on a toy project that involves fantasy basketball, I know this is the quantitative finance stackexchange, but it seemed like the best place to ask this question. My goal is to make ...
4
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0answers
115 views

Quasi Random Monte Carlo in m.v. portfolio optimization

Not specifying a correlation matrix for the Monte Carlo Simulation's random returns is equivalent to assuming no correlation or a correlation coefficient of zero, which will seriously and adversely ...
2
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0answers
39 views

Mean Variance Optimization vs Risk Scaling

What would be the difference between the following. Both techniques will result is an ex-ante risk of $\sigma$. However, that would be achieved via two different values of h. I want to understand ...
3
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0answers
41 views

Sign retention in mean variance optimization

The mean variance optimization to the objective: $h^T\alpha - \lambda h^T V h$ results in the solution: $h = \frac{V^{-1} \alpha}{2 \lambda}$ Would a positive value for an asset in $\alpha$ result ...
4
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1answer
173 views

Monte Carlo (resampling) in m.v. portfolio optimization

The instability and high sensitivity of optimisation results can be augmented by adding another layer of quantitative methodology in the form of Monte Carlo Simulation. The name Monte Carlo alludes to ...
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0answers
35 views

Tangency portfolio with two additional constraints

I know that the formula for determining the weights of the Tangency portfolio is given as $w_{tan}$ = $\frac{\Sigma \mu}{\iota^{\prime}\Sigma\mu }$, but I was wondering how to derive the weights in ...
2
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0answers
106 views

In sample and out of sample in Mean Variance Optimization

Hello to everyone and thanks again for your help, i have find this forum really helpful while working on my final dissertation. However I'm here again because I have loads of doubts regarding the in-...
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0answers
39 views

Standard Deviation: Probablity analysis [closed]

Stock E has an average return of 13.6% and a standard deviation of 9%, what is the probability that Stock E will return less than -4.4%
3
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1answer
123 views

Mean-variance portfolio optimization: methods for superior estimates of returns

Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-...
1
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1answer
115 views

Leverage constraints

I am trying to complete my project on Mean-Variance Leverage Optimization, and I have found lots of helpful advice on this forum. I wanted to ask you if you have some idea on how to implement a ...
5
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1answer
98 views

Risk/Return Paradox in Markowitz Optimization?

It is possible that from the efficient frontier obtained varying the "lambda" parameter of the risk-appetite coefficient, in the Mean Variance Parametric Quadratic programming problem, it results that ...
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2answers
83 views

Extend mean-variance optimisation to fama five factor

I'm new to quant finance, and as I'm not a mathematician, I am using python to try an understand it. There are a number of blogs on the internet which explain mean variance optimisation, but no-one ...
2
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1answer
91 views

Mean-variance maximization

I denote by $W_0$ and $W_1$ the wealth of an investor at $t=0$ and $t=1$, respectively. Let $r_f$ be the risk free rate, $r$ the vector of returns of the risky assets in excess of the risk free rate, ...
3
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2answers
107 views

Multi-period portfolio allocation: Time-inconsistent approach

Consider a multi-period mean-variance portfolio optimization so that at time $t$ I find the strategy that maximizes my expected terminal wealth $X_T$, subject to a constraint on risk, \begin{align*} \...
2
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3answers
457 views

Efficient frontier doesn't look good

Hi I'm trying to draw an efficient frontier. Below is what I used. returns parameter consists of 9 column returns of portfolio. I selected 10,000 portfolios and this is how my efficient frontier ...
0
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1answer
56 views

Mean Variance optimization on hourly data with gaps

I'm building a mean variance optimizer for a portfolio of FX, commodity and bond futures. The input data is hourly returns for each underlying. Given each underlying has different market opening hours,...
2
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0answers
88 views

Mean-Variance portfolio: How do I compute the variance when the portfolio is normalized

Let's consider the very basic of a Mean-Variance Portfolio: $$ \text{max}_{x} (1-\lambda)\sum_i^n\mu_ix_i-\lambda\sum_i^n\sum_j^n x_i Q_{ij}x_j $$ $$\text{ s.t. }\sum_i^nx_i=1 \text{ , } x_i \geq ...
3
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1answer
145 views

Portfolio optimization with non-linear cost

I am trying to solve a mean-variance problem with a non-linear market impact cost term in there. This is the problem I am trying to solve $$ \max_x \left ( \alpha x - \gamma x' \Sigma x - a\sqrt{|x-...
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1answer
52 views

Smart transaction cost model (for spread contracts)

In futures there exist exchange traded calendar spread contracts, which trade as a single unit (think May/June Crude Oil). The bid ask spread for the spread contracts is the same as that of the ...
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0answers
223 views

Mean Variance Optimization of 2000 pairs of securities (Python)

I would like to take the opportunity to ask for your help on an assignment I'm trying to complete. For this 'Modern Robo Advisory' course we are asked to solve a (target) goal-based investment ...
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1answer
50 views

How to find beta from the information given? [closed]

This is an exam question. I know that to find beta I need the covariance between the portfolio and asset A but don't know how to find it.
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0answers
98 views

“Porting” an alpha strategy to a different benchmark

I'm reading about the mean-variance optimization of active portfolios. A bit of prior background from the book I'm reading: the author discusses the mean-variance optimal portfolios without cash, ...
1
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1answer
101 views

Economic intuition behind pricing cash flow

I read the book of Skiadas Asset Pricing Theory 2009. I don't quite understand what does mean pricing cash flow. In the book it's written: $\textbf{Definition 2.9}$ A cash flow $x^*$ is a pricing ...
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3answers
391 views

Generalized Mean Variance Portfolio

Utility based portfolio optimization deals with the problem of finding the optimal portfolio $x_T$ by maximizing the utility/objective function $O(x_T,x_0)$ where $x_0$ is the current portfolio. In ...
2
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2answers
1k views

mean variance optimization vs max sharpe ratio

I keep reading/hearing that the results from mean-var optimization is max Sharpe ratio. It seems making sense if you fix either target return or target risk, but in general, it doesn't seems right, ...
2
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0answers
210 views

Trouble computing the VaR for Student's t-distribution for a minimum-variance portfolio composed of four cryptocurrencies (BTC, ETH, LTC, and XMR)

I have modelled the time-series of daily log-returns from August 2015 to October 2017 of a minimum-variance portfolio composed of four cryptocurrencies (BTC, ETH, LTC, XMR) by fitting the data to four ...
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1answer
155 views

Solving a system of two equations with non-convex matrix multiplication for MV optimization

Scenario: I am trying to do a variation of the MV optimization for a portfolio. In this instance, I already have a vector of mean returns ($\mu$), a vector of ones, a covariance matrix ($\Sigma$), and ...
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99 views

Units of Risk: Variance vs Standard Deviation

Suppose you are trading two mean-reverting assets, A and B, and that $Covar(A, B) > 0$. You are currently long one unit of A, and are considering buying one unit of B. Compared to the situation ...
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2answers
3k views

Why does the Markowitz mean-variance model require the assumption of normality?

Given $N$ assets, the Markowitz mean-variance model requires expected returns, expected variances and a $N \times N$ covariance matrix. The joint distribution is fully defined by these measures. ...
2
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2answers
161 views

Help on minimum variance optimization on U.S. Equity/Bond ETFs - Intuition

I run a MVP on 10 ETFs: SPY, SDY, IWB, XLP, VGT, BND, XLF, IJR, XLY, XLI from 2008 to 2016 on monthly return data. The weighs array (I am using a MATLAB function "Portfolio" - constraints are simple: ...
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0answers
46 views

How to hedge a MV portfolio against crises

I have constructed an adjusted Mean-Variance portfolio optimization method that optimizes the exposure in a set of X assets. The portfolio works perfectly fine during normal periods (even when there ...
2
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1answer
240 views

Optimize portfolio of non-normal binary return assets

I am facing t = 1,..T investment periods where each period I have x$ to invest. Suppose each period I can build a portfolio from thousands of assets (some are uncorrelated whilst some are highly ...
1
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1answer
540 views

For any efficient portfolio, does there exist another efficient portfolio which has zero correlation with it?

For any portfolio on mean-variance efficient frontier, does there exist a portfolio on the frontier which has zero correlation with it? I tried to play around with the covariance, by setting ...
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2answers
259 views

Mean-variance portfolio returns illogical weights

I have a dataset with 5 assets. I apply mean-variance portfolio: ...
0
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1answer
679 views

CVXPY 's constrains doesn't work

I am trying to implement a max return optimization with a large number of assets. I am not sure why this problem won't work. ...
2
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2answers
3k views

Risk contribution of part of a portfolio

Is it quantitatively sound to say that if I have assets $x, y,$ and $z$ in a portfolio, and that the total variance of the portfolio is defined as $\sigma_p ^2 = w_x^2\sigma_x^2 + w_y^2\sigma_y^2 +...
2
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3answers
441 views

Mean and standard deviation of price series with Kalman

I like to calculate the mean and standard deviation of a price series, using the Kalman filter. I am somehow stuck with the deviation, or have some problem in understanding, which my research could ...
3
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1answer
2k views

Mean Variance portfolio optimisation (Long Only) CVXPY including cardinality constraint

I am working on a portfolio optimisation that requires me to constrain on the number of assets used, e.g from S&P500 build a 20 asset portfolio that is feasible. After doing some research I came ...
2
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0answers
110 views

Relation between mean and variance of a portfolio in modern portfolio theory:

I hope that this is the right place to ask my question! Let a market with $N\ge1$ risky assets and denote by $(R_i,i=1,\cdots, N)$ their returns and $R$ the vector of these $N$ returns. In addition, ...
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0answers
121 views

Should the number of Markowitz Optimization steps be counted as backtest trials?

I'm backtesting a strategy that involves monthly investments in a few stocks out of a given set, that is, each month some of the stocks are shortlisted from an index and a long position is taken in ...
3
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1answer
491 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 ...
2
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0answers
244 views

Minimum Variance Portfolio problem [closed]

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 ...
2
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1answer
67 views

Are financial returns considered more volatile in recessionary times as opposed to expansionary times?

I need help in understanding some results that I have obtained. I am doing some out-of-sample performance analysis for different targets of volatility in mean-variance optimization where I solely ...
3
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0answers
595 views

Modelling log-returns and calculating the portfolio return

I know this might be a trivial question, however, I would be grateful for some clarification. I am working on weekly log-return data, doing volatility-foracasting using GARCH models and then using ...
4
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3answers
397 views

Is this realized “efficient” frontier 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 ...