Questions tagged [mean-variance]
The mean-variance tag has no usage guidance.
107
questions
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33 views
Selecting the best characteristic portfolio per rebalance date
An investor typically decides a portfolio objective and sticks with that objective for every rebalance date in the portfolio's life. Common characteristic portfolios that the investor chooses are:
...
3
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1answer
66 views
Ledoit/Wolf covariance shrinkage in risk-parity optimisation
This is more of a theoretical question.
I have been working on some mean-variance / Black-Litterman models and played around with Ledoit/Wolf's covariance shrinkage method (sklearn function in Python)....
3
votes
2answers
96 views
Do normal returns make the mean-variance portfolio model perform properly?
The Markowitz mean-variance model is known to suffer from estimation error due to financial returns not meeting the assumptions of a normal distribution, providing portfolio weights that underperform ...
1
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3answers
463 views
Any portfolio theories not based on asset returns?
For data, the mean-variance model for portfolio optimization uses asset returns to minimize portfolio risk (covariance matrix), which is asset returns volatility, and sometimes simultaneously ...
1
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1answer
55 views
How do i find the covariance between two portfolios?
I know that the formula for covariance is
But this is for two securities. How do I find the covariance between two portfolios? more specifically between the global minimum variance (GMV) and the mean-...
0
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0answers
19 views
Risk aversion coefficients for multi objective quadratic programming
I am solving different quadratic programming optimizations in a setting that involves the usual mean variance problem plus other objectives. My concern is how to choose the many so-called risk ...
3
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3answers
250 views
Any portfolio models not based on asset return moments?
The mean-variance model for portfolio optimization minimizes portfolio risk (covariance matrix), which is the second statistical moment of multivariate asset returns, and sometimes simultaneously ...
1
vote
1answer
55 views
Is this methodology for finding the minimum variance portfolio with no short-selling sound?
I have below here an excerpt from a book on (among other things) mean-variance analysis showing how to find the minimum variance portfolio (Risk and Portfolio Analysis: Principles and Methods, by Hult,...
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44 views
Mean variance portfolio - alternative formulations
From this lecture on YouTube the lecturer states that there are three ways to form the mean variance portfolio (minimize variance for a given return, maximize return for a given variance, maximize a "...
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26 views
Calculating R* in a two-asset world
In chapter 5 of John Cochrane's Asset pricing, we derive a state-space interpretation of the mean variance frontier by defining $R^*$ and $R^{e*}$. A little forward, we have this formulation:
$$R^* = \...
2
votes
1answer
78 views
Mean-Variance optimization with no short selling
I am wondering how I can find the vector of Lagrange multipliers $\mu$ for the non-negativity constraint of the following problem:
$$ L(w,\lambda, \mu) = w^{T}\Sigma w - \lambda(w -1) + \mu w $$
So ...
3
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0answers
161 views
How good is the inverse-volatility portfolio?
Heuristic portfolio construction techniques include the equally-weighted portfolio (1/N) and the inverse volatility portfolio (IVP), which is based on the low-volatility effect. They can be assembled ...
3
votes
1answer
455 views
Can a capital market line have a negative slope?
I am struggling to interpret my mean-variance / efficient frontier / capital market line results.
I have no issues calculating the efficient frontier. However, I do increase the risk-free rate from ...
0
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1answer
81 views
How to stress test a correlation matrix
As part of a mean variance portfolio task, I am calculating portfolio risk and optimal allocations between assets given required level of return. Input: expected returns, volatility and correlation ...
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0answers
78 views
Finding the Efficient Frontier in Tensorflow
I have two assets A and B. Asset A has an expected return of 0.92% with a standard deviation of 2.10. Asset B has an expected return of 1.39% and a standard deviation of 2.20. I want to find the set ...
0
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0answers
35 views
How to obtain tangency portfolio of the resampled efficient frontier in MATLAB?
I have generated the resampled frontier according to Michaud's approach. In order to compare it with the classical mean variance approach I want to invest in the respective tangency portfolios. While ...
0
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1answer
66 views
What if all the weights are negative in mean-variance optimization during a crisis?
Usually the constraint is that all weights sum up to 1. But in a crisis when all assets are falling in prices, intuitively, all the weights should be negative in the optimization.
But it contradicts ...
0
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1answer
114 views
Fixes of quadratic utility when probability of decreasing utility is large
In finance and specifically portfolio theory, a popular utility function is quadratic utility
$$
u(x)=x-\frac{\lambda}{2}(x-\mu_X)^2
$$
where $x$ is wealth and $\lambda$ is the parameter of risk ...
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0answers
63 views
Mean Semivariance Optimization VS PMPT
Mean Semivariance optimization defines semivariance, variance only below the benchmark/required rate of return, as:
$(1/T).\sum_{t=1}^{T} [Min(R_{it}-B,0)]^2$
where $B$ is the benchmark rate, $R_{i}$...
1
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1answer
45 views
Surface plots of the mean-variance efficient frontier
3d surface plots contain an X, Y and Z axis. For the mean-variance efficient frontier:
X axis is portfolio volatility ($\sigma_p$)
Y axis is portfolio expected return ($\mu_p$)
any ideas for what ...
3
votes
2answers
139 views
What does the concept “standard Markowitz approach” include?
Does "standard Markowitz approach" include only mean-variance approach or does it also include other approach such as minimum-variance approach?
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0answers
42 views
Notation for the variance in papers
Here is a screenshot from :
LIM Quadratic hedging and mean variance portfolio selection with random parameters in an incomplete market
When I deal with mean variance portfolios, I usually see the ...
4
votes
6answers
247 views
Is a more robust Covariance estimation possible?
I'm working on a mean-variance optimization problem, but instead of financial securities I'm choosing a 'portfolio' of N athletes. It is a 1-period optimization problem over one generic statistic ...
2
votes
1answer
50 views
ARMA moments proof
Consider a standard ARMA(1,1) process such as
$$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 ...
0
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1answer
91 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 ...
1
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0answers
51 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 ?
2
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0answers
75 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 ...
5
votes
1answer
209 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
votes
0answers
50 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
votes
1answer
93 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
votes
1answer
292 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 ...
2
votes
0answers
39 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
156 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
42 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
142 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
vote
1answer
205 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
votes
1answer
108 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 ...
1
vote
2answers
104 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
votes
1answer
128 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
votes
2answers
118 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
votes
3answers
726 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
65 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
95 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
votes
1answer
172 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-...
1
vote
1answer
59 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 ...
1
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0answers
280 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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votes
1answer
56 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
105 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
vote
1answer
108 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 ...
6
votes
3answers
415 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 ...
