Questions tagged [modern-portfolio-theory]
A theoretical framework for analyzing investment portfolios based on their expected return and risk.
260
questions
2
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2answers
5k views
Calculating the efficient frontier from expected returns and SD
I'm trying to calculate the efficient frontier (and the optimal portfolio at the Sharpe ratio) given two vectors for a portfolio: (1) expected returns and (2) historical standard deviations. I would ...
1
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0answers
116 views
Transform MPT optimization problem
I am trying to teach myself about MPT and optimization.
I understand that MPT solutions can be found using three equivalent optimization problems:
Minimizing variance for given return limit
...
8
votes
4answers
2k views
Is there anyone still using Markowitz modern portfolio theory?
I was reading about the MPT (Use standard deviation as risk measure) on "Mathematics for Finance by Marek Capinski". I was just wondering is there anyone actually applying this theory to their ...
1
vote
1answer
744 views
CAPM (SML) Problem
I got 1.3636 for beta for the problem below(165/121).
But I became so unsure about the answer when I solved (c) because then the market risk becomes larger than the variance of Stock A.
Beta^2*σ(M)^2=...
2
votes
1answer
499 views
Efficient Frontier Derivation: why minimize half the portfolio variance instead of just the variance?
In Robert Merton's derivation of the efficient frontier of a portfolio, he minimizes
$\frac{1}{2}\sigma^2 $ over the investment weights in each asset, where $\sigma^2$ represents portfolio variance. ...
1
vote
1answer
60 views
MPT and the connection to asset prices / initial capital
I have some question about MPT. Suppose we want to build a portfolio given $N$ assets: $A_1,\dots,A_N$. At time $t$ we build the portfolio using MPT, which yields some weight vector $w_t=(\lambda_1,\...
4
votes
1answer
797 views
Recommended Literature for creating Factor Mimicking Portfolios
Is there a textbook that contains the basics for creating Factor Mimicking Portfolios? Although there is a lot of peer-reviewed literature on this, I cannot find textbooks on Asset Pricing that ...
2
votes
1answer
606 views
reference question about portfolio optimization
I know the "classical" modern portfolio theory. However I have quite a lot of different sources. It seems that there is not a book which cover this topic in a rigorous way:
theory
application
...
7
votes
4answers
3k views
Does Modern Portfolio Theory align with EMH?
I came to the conclusion that in literature Markowitz' Portfolio Theory is believed to be compliant with the Efficient Market Hypothesis. The weakest form states that the current price fully ...
2
votes
2answers
239 views
2 stocks, no shorting vs shorting. (concrete questions, mean-variance)
I'd appreciate help with the following questions.
Suppose there are two stocks $A$ and $B$ with expected returns $E_A, E_B >0$ and volatilities $v_A, v_B >0$, respectively . Also, suppose ...
5
votes
1answer
736 views
Electricity market : how to design an optimal hedging strategy using spot and futures markets for an industrial consumer?
Here is the problem : we should adopt the point of view of an industrial company which purchases electricity as an input in its production line and which wants to achieve the following two goals :
-...
0
votes
1answer
3k views
How do I do a mean variance optimization with constraints?
I am using python and the cvxopt library to calculate an efficient frontier, per the docs:
http://cvxopt.org/examples/book/portfolio.html
However, I cannot figure out how to add a constraint so that ...
3
votes
1answer
401 views
Create optimal portfolio by Treynor and Jensens Alpha
I would like to know which formula to use in order to optimize a portfolio based on highest Treynor and Jensens Alpha. I am aware that usually one optimize a portfolio by highest Sharpe ratio (the ...
1
vote
4answers
7k views
Calculate correlation between two sub portfolios and the combined portfolio
I have two sub portfolios (lets call them portfolio a & portfolio b - a portfolio is just a vector of weights that sum to 1) that combine to create a total portfolio. I also have a 2 x 2 ...
2
votes
1answer
682 views
What are the assumptions of portfolio optimisation with higher moments?
I was wondering whether there are a set of assumptions for portfolio optimisation with higher moments (including kurtosis and skewness) as there are for regular mean-variance optimisation?
4
votes
3answers
903 views
Capital Allocation for Portfolio of Multi-Strategy and Multi-Instrument
I would like to know if there is a way (or theory) to manage a multi-strategy, multi-instruments portfolio that would calculate the optimal weight to allocate capital for each combination of strategy ...
8
votes
1answer
406 views
Overview of robust/regularized portfolio selection
I am looking for either a review paper or individual papers on portfolio selection using robust statistics or regularization (e.g. LASSO, Ridge, etc.)
I.e. a review on methods along the lines of:
M ...
4
votes
1answer
2k views
Mean-variance portfolio & quadratic programming
I am somewhat confused when it comes to modern portfolio theory, mean-variance portfolio optimization and its quadratic programming formulation.
Issue 1: Formulation of mean-variance portfolio ...
2
votes
1answer
131 views
Is the volatility of a trader's wealth equal to the volatility of the underlying assets traded?
Assume that a trader trades in several stocks with different volatilities. The return of the trader's portfolio would be the weighted average of returns and the risk would be a function of the the ...
1
vote
0answers
50 views
evaluating portfolio performance without knowing the amount held on cash accounts
I would like to evaluate the performance of a portfolio mananger.
I know his trades, and the initial portfolio holdings. I do not know, however the amount held on his cash account.
That is, I ...
8
votes
2answers
7k views
Definition of Return of A Long/short Portfolio
This can either be a silly question or a question with no sure rigorous answer but defined with some convention. Any way, here it is.
What is the (industrial recognized) definition of the return of a ...
1
vote
0answers
56 views
How do I determine what is a separate objective in a multi-objective portfolio optimization?
Is there a general rule to determining when to separate objectives when developing a multi-objective portfolio optimization? For example, one might start with a standard portfolio optimization of ...
3
votes
2answers
492 views
Why does it “say” portfolio diversification not suitable during market turmoil?
Currently I am trying to get a hold of MPT, asset allocation and related applications.
While reading a particular resource, it says diversification works best for "normal" financial markets and ...
2
votes
1answer
357 views
How to score a portfolio's diversity based on security returns?
What is the best way to score a portfolio's diversity based on it's returns covariance matrix?
I know that if my portfolio has two securities and their returns' correlation coefficient is -1 that is ...
4
votes
1answer
632 views
How are the Hamilton–Jacobi–Bellman equations used to solve optimal control problems?
I would like to learn more on how optimal control problems are solved for financial applications.
The approach seems to have a lot of interesting applications such as
optimal consumption
choosing ...
0
votes
1answer
1k views
Step-by-Step PCA algorithm (checking correctness without math packages)
I would appreciate if someone could correct me if i am wrong in my suggestion.
I am using PCA to :
find measure of cointegration between selected assets
find the eigenvector and its portfolio with ...
13
votes
1answer
823 views
Portfolios from Sorts
Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see
portfolios ...
10
votes
0answers
1k views
Formula for the efficient portfolios (mean-variance optimisation)?
Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$.
For a certain fixed $...
2
votes
1answer
188 views
What's wrong with this asset growth simulation?
Sorry if this is too basic, but I have this spreadsheet that simulates asset growth of a portfolio under a given return and risk using MPT.
Here is a plot of probability distribution of asset ...
4
votes
1answer
536 views
In Mean-Variance Analysis, why not the efficient frontier being pushed to the left near the axis?
I took some classes in portfolio theory, and learnt the Markowitz Mean-Variance Analysis.
If only two risky assets, the efficient frontier would be a hyperbola passing through the two points; now if ...
2
votes
0answers
272 views
Portfolio optimization with absolute position constraints
I'm looking to optimize a portfolio maximizing expected return for a particular risk budget, but with absolute constraints on the individual instrument positions.
I've been experimenting with QP, ...
1
vote
1answer
901 views
VaR Calculation - Covariance matrix is not positive semidefinite
This is a basic question.
I have three assets, equally weighted, and all the mutual covariances are -1. Then, the covariance matrix looks like -
...
15
votes
3answers
22k views
Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio Theory?
I have seen the following formula for the tangency portfolio in Markowitz portfolio theory but couldn't find a reference for derivation, and failed to derive myself. If expected excess returns of $N$ ...
7
votes
2answers
10k views
Typical risk aversion parameter value for mean-variance optimization?
What are typical values for risk aversion parameters $\lambda$ used in mean-variance optimization? Please provide references.
Just to be clear, I'm talking about the $\lambda$ in $U(w) = w'\mu - \...
2
votes
2answers
364 views
Portfolio risk-return when assets have limited and inconsistent historical data / time series?
Lets say we have "today's" snapshot of asset allocation and need to determine the 6mo, 1 yr and 5 yr risk and returns of this portfolio. If the time series for every asset is very long, longer than ...
2
votes
1answer
162 views
Find a paper about portfolio management
Where to find the following paper of the noble prize Paul Samuelson (2003) “When and Why Mean-Variance Analysis Generically Fails,”. I was looking for it desperately on Google and Google Scholar but ...
3
votes
2answers
240 views
Comparing Cash Equivalent of risky portfolios
To compare two risky portfolios, Mean-Variance (M-V) portfolios for example, many compare their Cash Equivalent ($CE$). $CE$ is defined as the amount of cash that provides the same utility as the ...
7
votes
3answers
19k views
What do the terms in-sample and out-of-sample estimates mean in MVO?
How do the in-sample estimates and out-of-sample estimates I so often hear authors refer to in emperical analysis of MVO differ?
3
votes
3answers
205 views
How to see if a set of asset returns corresponds to a known correlation matrix?
Let's say I have an arbitrary set of $n$ period returns for $k$ assets, and a given $k \times k$ correlation matrix (of asset returns), which is known a priori.
Does it makes sense, or is it even ...
3
votes
3answers
609 views
Why is the CAPM securities market line straight?
Let $\gamma$ be the expected return, in terms of its exponential growth rate, of the market asset. If we set $\gamma=\mu-\sigma^2/2$ as explained by the Doléans-Dade exponential, then the expected ...
2
votes
1answer
1k views
Is it possible to derive the “risk tolerance” from the portfolio efficient frontier?
I am trying to solve the Portfolio Optimization Problem using a "Multi-objective Evolutionary Algorithm". After obtaining the efficient frontier, I would like to know if we can infer for each point of ...
9
votes
2answers
899 views
Why do low standard deviation stocks tend to have superior future returns?
I've recently stumbled on something that really surprised me. These papers (1, 2) find that past standard deviation of returns is inversely related to future returns. That is, portfolio of low ...
1
vote
1answer
279 views
Resampled efficient frontier length of simulation
I was provided with a VBA program from my lecturer that applies the resampled efficient frontier. We have an investment horizon $T$ (6 years) and he uses a multivariate normal distribution with ...
5
votes
1answer
3k views
Michaud's Resampled Efficient Frontier - Out of Sample Simulation Testing
I will be putting ALL my account points on bounty to whoever answers this question [if your answer is crap but it's the only answer, you're getting the 165 points]. You will have to wait 2 days or so ...
8
votes
2answers
3k views
Comparing MVO with Resampled Efficient Frontier
My question: How can I compare the Resampled Frontier (REF) to the standard MVO frontier when I have been provided with $\mu$, $\Omega$, and don't have access to true future data to test real out of ...
2
votes
1answer
520 views
Use of AI in portfolio optimization [closed]
A new Danish hedge fund has received quite a large amount of attention in the last month or so. They are launching a new investment fund that uses proprietary AI to select stocks to invest in. They ...
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2answers
531 views
Proxy for risk in portfolio theory when return can take only two values
I'm trying to adapt tools from portfolio theory for another use, and I have a question about how I might do so.
Suppose that instead of having normally distributed returns, the return $R_i$ is ...
8
votes
2answers
228 views
Is there an optimal covariance one would want forecasts to have?
Often in a quant process, one will generate a time series of return forecasts and use them in some sort of optimization to generate a portfolio. Generally, there will be a covariance matrix of market ...
8
votes
1answer
354 views
Do weights from portfolio theory contain bias?
I want to experiment with some portfolio modelling and I was wondering if you guys could help me with something. If I try to estimate and implement the traditional two-fund portfolio consisting of one ...
41
votes
12answers
28k views
Why does the minimum variance portfolio provide good returns?
I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get ...
