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Questions tagged [portfolio-optimization]

The tag has no usage guidance.

2
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1answer
38 views

Expected value of stochastic optimization

I have a optimization problem where the SDE is: $$ dX(t) = [X(t)(u(t)-\beta(t))+\theta(t)]dt+X(t)u(t)\sigma dW(t), t \in [0,T], X(0) = X_0 $$ where $u(t)$ is the portfolio, $\beta(t)$ and $\theta(t)$ ...
0
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0answers
30 views

Learning short-rate dynamics and how it affects optimal portfolio strategy

I'm looking for some advise. Here is the problem: For absolute simplicity, assume that we have one risky asset with price process \begin{align} dS_{t} = \mu S_{t}dt + \sigma S_{t}dW_{t}, \end{align} ...
1
vote
2answers
91 views

R: Book with extensive examples for either portfolio optimization or volatility forecasting?

I'm at a new job and there's the option to use R (you don't have to, but I'd like to). I used R years ago, so I while I'm somewhat familiar with it, I have forgotten most of it. For me, the best ...
1
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0answers
16 views

Show that the variance of the portfolio market portfolio is function of the betas of its consituents [closed]

Let us assume that the market portfolio consists of n assets. Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
-2
votes
0answers
55 views

Show that the variance of the market portfolio is the weighted average of the covariance of its constituents with the market portfolio itself [closed]

Let us assume that the market portfolio consists of n assets. Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
1
vote
1answer
54 views

Formula in Markowitz Optimization Problem (without riskless asset)

(hope this is not too basic, I'm new to this forum) Im struggling to understand the optimization problem (global minimum variance portfolio) formula in Markowitz Theory: $$\arg\ \min\ Var(Return\ x) =...
1
vote
1answer
53 views

Achieving desired fx exposure with using minimum pairs possible

Let say my algorithm tells me to get the following positions through opening fx positions: CUR NET POSITIONS GBP 236.96379 USD -310.58000 CHF 0.02000 There are 2 ways to achieve this: Long ...
2
votes
1answer
65 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, ...
2
votes
0answers
46 views

Possible application of Polya's Urn on Portfolio's Investments?

I wanted to find some more information of this topic, but I found very little. I might be interested in optimizing a stock investment portfolio. Maybe I could use beta or some other common risk ...
-3
votes
0answers
27 views

Adding argument to ERC function in Python makes it break down

I am using xlwings to implement Python code in Excel. I put the following code in Spyder and imported it into Excel to arrive at equal risk contribution weights for a 7-asset portfolio. ...
1
vote
1answer
82 views

Objective function: as close to equal weight as possible

I am having trouble coming up with a function to optimize the weights to be as equal as possible. It is a long-short portfolio with 6 positions weights is a cvx variable: [long, long, short, short, ...
0
votes
1answer
36 views

Portfolio Risk-Return

I have a question on risk-return portfolios. How do I go about calculating up to 200 opportunity sets by varying the weights of three assets for each portfolio $w_1$,$w_2$ and $w_3$ given: Mean ...
0
votes
2answers
116 views

calculate portfolio return with one long position and one short position

I was trying to learn how to work out the performance of a portfolio where you are long one stock and short another. I found an example below. The NAV is calculated by adding the value of the long ...
2
votes
0answers
87 views

Calculating weights of tangency portfolio

Im having trouble calculating the market portfolio weights (tangency portfolio) for a portfolio consisting of 5 risky assets and 1 risk free asset with 2% return. The data is from 5 assets from the ...
2
votes
1answer
68 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*} \...
1
vote
2answers
235 views

Regularizers to compute Minimum Variance Portfolio weights

I need to compute the mimimum variance portfolio using different regularizers, to compare the results and use validation methods to find the optimal parameters. Currently my work has been performed ...
4
votes
1answer
238 views

Optimal Portfolio from Efficient Frontier

I found this code on plotly site, using CVXOPT to find the efficient frontier, and then, the optimal Portfolio. The optimal function is ...
2
votes
2answers
151 views

Optimizing Investment Portfolio

I might be interested in optimizing an stock investment portfolio. With or without using programming, is there an article I should refer to optimize my portfolio and help me taking good investment ...
1
vote
0answers
40 views

How to find the tangency portfolio using quadprog in R with different risk free rates

I am trying to find the optimal tangency portfolio for the efficient frontier (calculated using qp.solver in quadprog) but subject to different risk-free rates. Demos for quadprog in R show that to ...
3
votes
0answers
35 views

Bounded solution for a SDE

I have this SDE $$ dX(t) = [X(t)(u(t)(\delta-r)+r-\beta(t))+\theta(t)(1-\alpha(t))]dt+X(t)u(t)\sigma dW(t), t \in [0,T] \\ X(0) = X_0(1-\alpha(0)) $$ I've checked some books and I find the solution ...
6
votes
3answers
316 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 ...
-3
votes
1answer
51 views

Filter the NASDAQ stocks for investment [closed]

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 ...
1
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0answers
43 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 ...
1
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0answers
52 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
95 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 \...
0
votes
0answers
39 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
votes
1answer
51 views

Markowitz portfolio optimization and CAL [closed]

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
votes
0answers
51 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
vote
0answers
66 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) ?
1
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0answers
35 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 ...
1
vote
1answer
69 views

How to measure the practicality of a market portfolio for long-term investment?

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 your stocks. I ...
1
vote
1answer
86 views

How to calculate market capitalization weights for a currency portfolio?

I am implementing Black-Litterman optimization on a currency portfolio and I could not calculate market capitalization weights for currencies. Please give me some suggestion.
-1
votes
2answers
77 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
votes
0answers
50 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 ...
6
votes
1answer
130 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
votes
2answers
151 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: ...
1
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0answers
79 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
votes
1answer
353 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 ...
1
vote
0answers
44 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
votes
1answer
171 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
vote
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
votes
2answers
43 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
votes
3answers
328 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 ...
1
vote
0answers
39 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
vote
0answers
90 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
votes
1answer
66 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
vote
1answer
93 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 ...
7
votes
1answer
154 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
vote
0answers
34 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. ...
1
vote
0answers
74 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 ...