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Questions tagged [portfolio-optimization]

The tag has no usage guidance.

3
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3answers
123 views

Maximum Sharpe portfolio (no short selling restrictions)

Suppose we have $n$ assets whose expected return vector is $r$ and is positive, and whose covariance matrix is $\Sigma$. Is there a closed form or quasi closed form (like the eigenvector of a matrix ...
-2
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1answer
39 views

Filter the NASDAQ stocks for investment

I manage an investment portfolio since 3 years now. It might be interesting to filter all the NASDAQ stocks to tell us which ones have the greatest profit potential. Is there an arxiv or whatever ...
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0answers
36 views

Markowitz models with uncertain returns

I am analyzing the Markowitz models with uncertain returns as follows: after calculating the expected returns and the covariances of 30 monthly historical series of 30 stocks, I resolve the Markowitz ...
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0answers
50 views

Creating a hedge portfolio out of 10 assets

Suppose I have historical return data on 10 assets. How can I create a hedge portfolio that prices all these assets in a factor model? I have chosen 3 factors: excess market return, SMB and HML from ...
3
votes
1answer
87 views

Value-at-Risk for a portfolio model with Gearing

My models: Say I want to construct a portfolio so I maximize my expected return while keeping my risk (measured by Value-at-Risk) lower than my risk target. $$\max \sum x_i \mu_i \\ VaR_{0.05} \leq \...
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0answers
34 views

Another variation of the 'Sharpe ratio' in CVaR-based portfolio optimization?

Question What is the ratio S(p) shown below? Do we have a name for it like 'Sharpe ratio'? The ratio above is introduced in the academic paper Optimal portfolio selection in a Value-at-Risk framework ...
2
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1answer
44 views

Markowitz portfolio optimization and CAL [on hold]

Just had some questions regarding the efficient frontier and the CAL. As i understand it the point where the CAL is tangent to the efficient frontier is the optimal mix of risky assets. However I also ...
2
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0answers
44 views

Fixed Income portfolio type

Could someone kindly point me toward a primer that would cover the various type of fixed income portfolio strategies under modern portfolio theory ? In a nutshell, I would like to know what kind of ...
1
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0answers
46 views

Maximum Sharpe Ratio Portfolio

Conceptually, what are the drawbacks / unforeseen risks of running a portfolio whose weight are derived from what would have maximised the sharpe ratio over the previous time period (last 30 days) ?
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0answers
33 views

explanation of factor tilts that uses mathematical notation

Can anyone provide a definition of "factor tilt" that uses mathematical notation? Let's say that our returns vector $\mathbf{y}_t$ can be expressed in terms of a market return $x_t$: $$ \mathbf{y}_t ...
0
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1answer
48 views

Is the market portfolio i found desirable or practical as an investment?

Question i'm asked: Do you believe that the composition of the market portfolio that you have found is a desirable or practical one as an investment? Explain why or why not, based on the positions of ...
0
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1answer
43 views

How to calculate Market Capitalization weights for portfolio which has different currencies as assets?

I am implementing Black Litterman portfolio optimization on currency assets. But am not able to calculate market capitalization weights for currency. Please give some suggestion ...
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2answers
70 views

How to calculate risk of portfolio in last part [closed]

Investment decisions are not taken in insolation; investors have to consider market dynamics and firm level factors to choose among various available securities. Among different factors affecting the ...
3
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0answers
45 views

Is Ledoit-Wolf Shrinkage with a Constant Correlation Prior Reasonable for a Stock/Bond Mix?

I've been looking into Ledoit-Wolf shrinkage but I've found the papers concentrate on large numbers of assets that tend to all be highly correlated. Often a universe of large cap stocks. I'm ...
4
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1answer
102 views

Market Portfolio Optimization

Consider the minimization problem $$\min\left\{\frac{1}{2}x^T\Sigma x - \lambda(\mu-r_f)^Tx\right\}$$ and assume the CAPM model, i.e. $$r_i-r_f = \beta_i(r_m-r_f) + \varepsilon_i$$ Assuming $\...
0
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2answers
103 views

Calculate asset allocation given “long and short” optimized portfolio weights

If the amount of capital that has to be allocated for each asset given the "long only" optimized portfolio weights is: ...
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0answers
68 views

CAPM - market portfolio vs real portfolio

I'm trying to understand the relation (if there is any) between the market portfolio, as described by the CAPM theory, and a real portfolio (just like the one I plotted in the image below). More ...
0
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1answer
118 views

Portfolio Weight Sum and Negative Weights

I'm calculating the weights of 10 securities in a portfolio for a course project, with the objective of maximizing the sharpe ratio. I'm getting both positive and negative results for weights. The ...
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0answers
33 views

Mean-cVaR model: How can one include transaction cost

$$ \min \delta CVaR - (1-\delta) \sum_i^{n} \mu_i x_i \\ \sum x_i = \sum x^{old}_i \\ Losses(s) = \sum x_i - \sum_i^{n} (R(s,i))x_i \\ VaRDev(s) = Losses(s) - VaR \\ CVaR = VaR + \frac{\sum_s^{} ...
0
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1answer
73 views

Log returns of individual assets and calculating portfolio returns

I am researching optimal asset allocations and am wondering if I am making mistake(s) in calculating the portfolio return. I have three assets, of which I have monthly return data. I have calculated ...
1
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0answers
30 views

Can you take the mean of risk-free rates in (ex post) portfolio optimization?

I am researching the optimal asset allocations in a portfolio portfolio under different macroeconomic times during the past 50 years. The primary measure I am using is the Sharpe ratio. Because the ...
0
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2answers
40 views

ESG score for shorted stocks and for long-short portfolio

I was wondering how to compute an extra-financial score of a portfolio like, for instance, the ESG score. This score can is typical bounded between 0 and 10 (or 100) (see for example IVA methodology ...
3
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3answers
183 views

Compute tangency portfolio with asset allocation constraints

I am looking to compute the tangency portfolio of the efficient frontier, but taking into account min_allocations and ...
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0answers
36 views

Optimal allocation problem by finite differences

I am attempting to apply implicit finite difference to solve Merton's problem of optimal portfolio allocation for constant parameters. The equation to solve is the Hamilton-Jacobi-Bellman equation: $$...
1
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0answers
52 views

Is the Market Portfolio on the Markowitz Efficient Frontier?

I have seen "market portfolio" defined online (Wikipedia/Investopedia) as the bundle of all available investments where the assets are each weighted in proportion to their existence in the market. I ...
0
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1answer
61 views

What does risk tolerance represent for utility-maximizing optimization with linear constraints?

Referencing Wei Jiao (2003) p. 8, formula (1.12), for $Ax = b$ set of linear constraints in a portfolio, the solution for the optimum weights to maximize the utility is: $$w^* = \Sigma^{-1}A^T \left( ...
1
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1answer
80 views

Markowitz optimization - can two sets of returns produce the same set of weights?

The portfolio optimization problem I have in mind is a minimum variance optimization with positive weights, formulated as below: I am trying to show that the solution is unique, specifically in the ...
6
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1answer
149 views

Question about quadratic form of f* in the Continuous Kelly Criterion

I am trying to follow the Optimal Kelly derivation on Wikipedia for two continuous assets: one risky and one risk-free. The derivation begins by assuming that the risky assets follows a GBM (a ...
1
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0answers
32 views

VaR calculation using excel gives different value than VaR using R at all c values except at c=0.5

This is VaR calculation in excel using variance-covariance method. This is VaR calculation in R. ...
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0answers
67 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 ...
0
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1answer
81 views

Methods to improve systematic strategies

Soliciting advice on ways to improve systematic strategies. Some things that I can think of off the top of my head: Using a risk model (correlations) instead of 1/n or 1/vol weighting Including a ...
0
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1answer
63 views

Country allocation -optimization 3 countries

I have the following problem: an equity portfolio allocated to 3 countries. Each country has an independent indicator (signal) which takes values from -4 to 4. The allocation for each country at ...
1
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1answer
51 views

Difference between constraining pre and post optimization

What's the implication of constraining the optimized portfolio weights obtained using no constraints vs obtaining the weights with the constraints in the objective? Let the asset returns be ...
5
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2answers
280 views

Portfolio Analysis Interview Question

Suppose you have a portfolio of 100 options. Then I give you a subset of trades in which you can make. The trades consist of possible buys/sells of different options from different clients. Discuss ...
2
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2answers
91 views

name of this portfolio optimization strategy

I have come across a portfolio selection strategy that buys in equal amounts the top decile of expected earners, and simultaneously short sells the lowest decile in a similar fashion. What is this ...
0
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1answer
115 views

Characteristic Portfolio for an Attribute [closed]

Given a vector of attributes(eg.E/P ratios, betas) for N assets $a^T = {a_1,a_2,...,a_N}$ The exposure of portfolio $h_P$ to attribute a is $a = \sum_{n}a_n h_{P,n}$ Proposition: There is a unique ...
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0answers
114 views

Minimizing Correlation to Index

In his PhD thesis in the chapter Market Neutral Portfolios, page 69, [1] Valle sets up an optimization problem which minimizes the absolute correlation of the portfolio log returns to the log returns ...
0
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1answer
71 views

Sequential Optimization

I am looking for the name of a sequential optimization, if that technique makes indeed any sense and exists. Given the solution $x^*$ to a non-linear non-convex problem \begin{equation*} \begin{...
1
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2answers
143 views

Zero Beta Portfolio in R

I am trying to solve the zero portfolio problem in R. Given n assets, the objective function is to minimize the variance of the portfolio $$Min_x\;\; \frac{1}{2}x^T\Sigma x$$ subject to $$COV\left(x^...
2
votes
1answer
94 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-...
4
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1answer
254 views

Struggling with tau in Black-Litterman

According to the omega formula in B-L tau is used in the Omega estimation to determine the degree of uncertainty given to views of the investor: So, if tau is given a low value then the inverse of ...
0
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0answers
35 views

References for Risk Adjusted Portfolio Optimization

I'm trying to formulate BL portfolios which use Mean VaR, Mean CVaR optimization to calculate risk-adjusted equilibrium returns. Can someone point me to any references on this topic? I'm looking for ...
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0answers
33 views

Benchmarking of Portfolio weights

I have 5 stocks and a commodity in my portfolio which I have allocated based on maximum Sharpe Ratio optimization. I need to benchmark them against an Index and compare the portfolio weights. How do I ...
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0answers
110 views

Calculate monthly returns for a QUARTERLY and YEARLY rebalanced portfolio in R

I built a minimum variance, equal weight, inverse volatility, and equal risk contribution portfolios based on the same data set of monthly returns for 30 different companies. The covariance matrix is ...
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0answers
69 views

Imposing qualitative views in Black -Litterman model

I'm trying to construct a ETF portfolio with various asset classes using Black Litterman model. To impose views, I'm considering only qualitative views like {strong bearish, bearish, bullish, strong ...
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0answers
116 views

What to use for Tracking error minimization

What programs/packages can one use to minimize a portfolio's tracking error? What I am trying to do is see what ex post TE, portfolio returns and variance can be achieved when adding CSR constraints ...
1
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1answer
216 views

Implementing the Sharpe's return-based style analysis on Python

I am trying to implement the Sharpe's return-based style analysis on Python. The problem is formulated as follows: ...
4
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2answers
227 views

Risk Parity / Equal Risk Contribution with Tail Risk Measures

Risk Parity or (synonymous) Equal Risk Contribution is an approach to portfolio construction which could work in theory with a broad class of risk measures. Yet, all references I have found so far ...
1
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1answer
76 views

Questions related to Sharpe's return-based style analysis

I have been reading about Sharpe's return-based style analysis, which tries to determine the manager's exposure/effective asset mix to changes in the values of the asset classes. It does so by using ...
2
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3answers
212 views

Negative variance?

Using the formula w*Cov*t(w) I can generate a negative portfolio variance. What are the implications of a negative variance? Should I just assume it's zero? A negative variance is troublesome ...