Questions tagged [mean-variance]
The mean-variance tag has no usage guidance.
95
questions
3
votes
1answer
334 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
votes
1answer
69 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 ...
0
votes
0answers
52 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
votes
0answers
25 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
votes
1answer
60 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
votes
1answer
90 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 ...
1
vote
0answers
49 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
vote
1answer
44 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 ...
0
votes
1answer
61 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?
0
votes
0answers
37 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 ...
3
votes
6answers
225 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
48 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
votes
1answer
86 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
vote
0answers
47 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
votes
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
183 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
46 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
74 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
231 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
votes
0answers
130 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-...
1
vote
0answers
40 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
votes
1answer
134 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
166 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
105 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
92 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
106 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
114 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
598 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
votes
1answer
62 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
votes
0answers
92 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:
$$
\text{max}_{x}
(1-\lambda)\sum_i^n\mu_ix_i-\lambda\sum_i^n\sum_j^n x_i Q_{ij}x_j
$$
$$\text{ s.t. }\sum_i^nx_i=1 \text{ , } x_i \geq ...
3
votes
1answer
162 views
Portfolio optimization with non-linear cost
I am trying to solve a mean-variance problem with a non-linear market impact cost term in there. This is the problem I am trying to solve
$$ \max_x \left ( \alpha x - \gamma x' \Sigma x - a\sqrt{|x-...
1
vote
1answer
58 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
vote
0answers
244 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 ...
-1
votes
1answer
53 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.
1
vote
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
107 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
397 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
votes
2answers
2k 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
votes
0answers
268 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 ...
1
vote
1answer
157 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 ...
0
votes
0answers
100 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 ...
8
votes
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
votes
2answers
168 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: ...
1
vote
0answers
47 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
votes
1answer
248 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
vote
1answer
561 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 ...
1
vote
2answers
299 views
Mean-variance portfolio returns illogical weights
I have a dataset with 5 assets.
I apply mean-variance portfolio:
...
0
votes
1answer
737 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
votes
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 +...
