Questions tagged [mean-variance]
Mean-variance is the starting point of most portfolio optimisation techniques.
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The use of L2 Regularization in portfolio optimization
In portfolio optimization, the goal is to calibrate the weights of assets in a portfolio according to a stated objective (mean-variance, minimum-variance, risk parity etc.). Often, mean-variance or ...
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Explaination and Reference of Formula for Portfolio Optimization
I stumbled upon Pricing Currency Risks by Chernov and Dahlquist (Jrl Fin, 2023). They state on page 698-699: "Suppose that we have $N$ basis assets with an $N × 1$ vector of excess returns $R^e_{...
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Calculating the minimum variance portfolio given a desired expected return as a constraint
I'm replicating the equations in Cochrane 2005 using all the stocks in the S&P 500. I am questioning my results - I get that the daily volatility of a portfolio with a return of 10% (annualised) ...
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Question about the mean-variance frontier asset with payoff m/E(m^2)
In the book Asset Pricing by Cochrane (2005), page 18, point 3, the author says that an asset with pay off m/E(m^2) is on the mean-variance frontier. However he didn't provide any explanation for why ...
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What is the proper way to derive risk definitions from utility functions?
In typical mean-variance analysis, the risk-adjusted relative value of an individual asset takes the general form
$\frac{\mu}{\sigma^2}$,
with further weighting and normalization depending on the ...
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Portfolio optimization with Scipy in Python
I performed Scipy portfolio optimization in two scenarios: 1) when I cannot lend or borrow at the risk-free rate; 2) when I can lend and borrow at rf=1.5%. Now, optimal risky portfolio weights anyway ...
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Calculating marginal risk contribution of FX for foreign asset portfolio
I am a European investor investing in US equities. My US equities portfolio returns in EUR can be broken down into (1) equities returns in USD terms, and (2) USDEUR spot currency returns.
Using the ...
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Calculate minimum variance hedge ratio for foreign-denominated asset hedged to domestic currency
The formula for minimum variance hedge ratio (MVHR) is conceptually the correlation multiplied by the ratios of volatilities.
correl (Y,X) * (STDEV Y / STDEV X)
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Find variance of Asset with lesser return to make a pure portfolio of it the min-variance portfolio [duplicate]
I need to solve the question mentioned above. For an asset with a worse payoff than another, I need to determine a variance for which the minimum-variance portfolio only consists of this asset.
There ...
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Robust estimates of variance covariance matrix
I am looking for help from other people with experience creating variance covariance matrix that have enough predictive power to actually lower portfolio volatility out of sample.
Using real world ...
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How to change the covariance matrix for a parallel-shift of the efficient frontier?
I'm trying to obtain a parallel shift in my efficient frontier based on the Merton 1972-parameters. As i think a picture tells you more than 1000 words here is what i tried:
The setting of my problem ...
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Markowitz Optimization with 2 assets
Suppose there are only two risky assets and we want to optimize our portfolio. Constraints are that we have a minimum return $\overline{r}$ and we can only invest $w_1 + w_2 = 1$.
Is it possible that ...
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Naive Diversification under mean variance
I'm looking for a way to introduce naive diversification bias in a mean variance framework and had the idea to model it as some sort of "aversion to extreme portfolio weights" of the ...
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Maximizing Mean+Variance in a Portfolio
Mean-Variance optimization trades off expected returns with portfolio variance. The idea is that excess variance is not desirable.
But what if you weren't averse to high variance and you wanted to ...
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Is this equation correct for portfolio optimization for CARA normal with N risky and one riskless asset?
Suppose the consumer Solves $\max -e^{-\gamma W}$ where $W=X^T D -X^Tp R_f$ where $X$ is the vector invested in a risky asset and $D\sim N(E[D],\Sigma^2_D)$ and $R=\sim N(E[R],\Sigma^2_R)$. Then ${ X=(...
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Why is the dynamic mean-variance problem time-inconsistent?
A lot of the literature in dynamic mean-variance problem states that the dynamic mean-variance problem is time-inconsistent. Now I was not able to find an example of why the problem is time ...
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Why does the mean term have a higher effect than the covariance term in MV optimization? [closed]
I am trying to use the mean-variance (MV) optimization framework. When I change the mean term using future-ground-truth return (I am not supposed to do so), it has a higher effect on the MV ...
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Tangency portfolio negative maximum Sharpe ratio
Suppose I have three assets: the market, factor A and factor B. The market is in excess returns of the risk free rate. The other two factors are long-short portfolios. I have net returns for these ...
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Utility Theory and Mean Variance Analysis
I was wondering if it's pertinent to use this interpretation of the expected utility function given by the Taylor series expansion,
$${E(U(W)}\approx{U[E(W)}]+\frac{U''[E(W)]\sigma^2_W}{2}\tag{1}$$
to ...
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Questions about Merton's derivation of the security market line
In Merton's "An Analytic Derivation of the Efficient Frontier" (PDF), he derives the security market line for the CAPM using the definition of the tangency portfolio. He writes:
Here, $m$ ...
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mean-variance optimization === max sharpe ratio portfolio?
Noobie here. I just wanna ask a simple question:
in the context of portfolio optimization, is Mean-Variance optimization the same as the max sharpe ratio portfolio?
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Monte Carlo vs. Block Bootstrapping vs. Bootstrapping
Because I can fit e.g. ~25 distributions via empirical cumulative distribution fitting to correlated data (including stable dist.), and then simulate the original data based on correlation (covariance)...
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Proof that mean-variance opportunity set is closed
In the book Financial Economics (2010) by Hens and Rieger, on page 101 we find the following Lemma 3.1: If we have finitely many assets, the minimum-variance opportunity set is closed and connected.
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Black-Litterman for quant portfolio
I have seen a lot of research around the Black-Litterman approach and I think theoretically, it is a nice framework. However, it appears that its main strength is from a practitioner's point of view, ...
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Mixed-integer programming approach for index tracking
Suppose you currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. The weights of these two portfolios are shown in the following table:...
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