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Questions tagged [portfolio-optimization]

The tag has no usage guidance.

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1answer
34 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
23 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^{} ...
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1answer
50 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 ...
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0answers
27 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 ...
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0answers
38 views

How to model holding constraints in CVXPY

How could I model the number of asset to hold constrain in CVXPY portfolio optimization? This is an CVXPY documented example, the problem has 3000 assets, but I want to add a constraints says that ...
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2answers
36 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 ...
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3answers
114 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
33 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: $$...
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0answers
42 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 ...
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1answer
55 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
74 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 ...
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0answers
39 views

Monte Carlo Simulations vs Optimization techniques

It is a bit general question but I hope people experienced in this field have observed an answer. What works better for CVaR/VaR Optimization models? Using monte Carlo simulations or converting it ...
5
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1answer
123 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 ...
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0answers
29 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
64 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 ...
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1answer
72 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 ...
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0answers
35 views

Algorithm to allocating capital to multiple strategies with bias

If there are multiple strategies that trade in different time frequencies, how do you allocate capital across them algorithmic-ally? I would also like this algorithm to have gradual bias towards ...
0
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1answer
62 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
49 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 ...
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0answers
19 views

How to maximise utility in multi-periode model using martingale method

I am reading chapter 2.2 in Pascucci & Runggaldier (2012), Financial Mathematics - Theory and Problems for Multi-period Models about how to maximise utility in multi-periode model using martingale ...
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0answers
45 views

Portfolio Analysis for Non-Linear Products

How does one apply modern portfolio theory to optimize the allocation of a portfolio of interest rate derivatives?
5
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2answers
269 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
79 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
67 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
104 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
67 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{...
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2answers
134 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
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1answer
84 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
206 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 ...
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0answers
33 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
32 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
92 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
62 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
93 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 ...
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1answer
162 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
171 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
74 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 ...
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3answers
173 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 ...
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1answer
83 views

Portfolio turnover [closed]

Really easy question, but I am having doubts. If you want annual turnover, and you have monthly weights, wouldn't you just do in excel: {=ABS(CurrentMonthsWeights-LastMonthsWeights)*12} for each ...
1
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1answer
68 views

Adding a new strategy to an existing portfolio

I wanted some help in looking for suitable articles/literature. Suppose an investor has a bunch (bouquet?) of quantitative strategies already generating trading signals for him. If he comes up with a ...
3
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1answer
119 views

Optimal portfolio construction for tactical asset allocation

This is the first time I post question here so if there is anything that does not follow the rule, please bear with me and let me know. I am trying to solve this optimization question but I don't ...
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0answers
39 views

Why are there lower bounds on amounts sold of an asset?

I am reading a paper on a portfolio model. See the following snippet. The idea is simple. We've got $N + 1$ assets, and $T$ periods. At each period, and for each asset, we've got the decisions to buy ...
4
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1answer
152 views

Portfolio Allocation given Sharpe Ratio

If there are two portfolios with sharpe ratios of 1.2 and 0.5, what would be the allocation rationale. If the correlation between portfolios is: $a. 0 $ $b. 0.8 $ $c.-0.8 $ I see there is a ...
1
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1answer
102 views

R PortfolioAnalytics

I am not able to find PortfolioAnalytics package for windows from CRAN. New to R, will greatly appreciate any help how to find and install this package.
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0answers
18 views

Accounting for sensitivity of simulation model to small changes in assumptions

I am running a Monte Carlo simulation of correlated asset returns, based on this matlab function. The model's inputs are a vector of expected means and standard deviations for 9 assets, and their ...
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2answers
44 views

What is the return of risky asset in direct utility optimization probem?

I am trying to do this portfolio optimization for a one-month investment between S&P 500 as a risky asset and one risk-free asset: Assume that I have a power utility function, a risk-free rate ...
2
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1answer
421 views

maximize Sharpe ratio in portfolio optimization

I am trying to understand how to maximize Sharpe ratio in portfolio optimization. $\boxed{\begin{align}\max\>&\frac{r^Tx-r_f}{\sqrt{x^TQx}}\\ & \sum_i x_i = 1\\ & x_i\ge 0\end{align}}$ ...
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0answers
47 views

How to rebalance a partial replicated index portfolio?

i am currently doing a project on portfolio construction / optimization using a subset of the stocks in an index (buying a subset of stocks in an index to replicate the index performance). This will ...
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0answers
29 views

Portfolio Immunization from Yield Perspective

Let's say we have the following situation: an asset (mortgage) with fixed payments, a prepayment & oas models to run through, and calculations for duration, convexity, and price, based on them. ...
0
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1answer
103 views

Genetic Algorithm - Portfolio Optimization / Index Tracking crossover process

i am currently doing a research on index tracking using Genetic Algorithm (replicating the index using a subset of the index members). This is a new topic to me. I have been reading research paper on ...