Questions tagged [modern-portfolio-theory]
A theoretical framework for analyzing investment portfolios based on their expected return and risk.
243
questions
4
votes
1answer
1k 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
130 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 ...
7
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
488 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
345 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
617 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
806 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
186 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
525 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
266 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
856 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
21k 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
9k 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 $U(w) = w'\mu - \...
2
votes
2answers
356 views
Portfolio risk-return when assets have limited and inconsistent historical data / time series?
Lets say we have "today's" snapshot of asset allocation and need to determine the 6mo, 1 yr and 5 yr risk and returns of this portfolio. If the time series for every asset is very long, longer than ...
2
votes
1answer
160 views
Find a paper about portfolio management
Where to find the following paper of the noble prize Paul Samuelson (2003) “When and Why Mean-Variance Analysis Generically Fails,”. I was looking for it desperately on Google and Google Scholar but ...
3
votes
2answers
237 views
Comparing Cash Equivalent of risky portfolios
To compare two risky portfolios, Mean-Variance (M-V) portfolios for example, many compare their Cash Equivalent ($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
589 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
994 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
892 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
275 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 ...
4
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 ...
7
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
514 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 ...
1
vote
2answers
522 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
226 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
339 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 ...
40
votes
12answers
27k 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 ...
14
votes
5answers
2k views
How can higher co-moments be applied to portfolio optimization in an asset allocation context?
Traditional portfolio optimization involves mean variance optimization, where only the mean and covariance matrix of returns are estimated. What asset allocation and portfolio optimization techniques ...
13
votes
1answer
5k views
Why is the first principal component a proxy for the market portfolio, and what other proxies exist?
Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you ...
2
votes
1answer
501 views
What are some “Must Know” investment/portfolio management theories out there?
What are the most important portfolio management theories you must know in order to competently manage an investment portfolio?
In order to keep the topic focused, I would like to narrow down the set ...
8
votes
1answer
555 views
How can I simulate portfolio risk (diversification) with a 'Wheel of Fortune' like investment options/returns?
Say I have 6 possible investment options with the following probability of success and the corresponding returns:
...
15
votes
3answers
2k views
What is the relationship between risk aversion and preference for skewness and kurtosis in portfolio optimization?
Is there any relationship between the risk aversion coefficient in an individual's utility function (commonly used in portfolio optimization) and the preference for higher moments such as skewness and ...
20
votes
1answer
2k views
Portfolio optimization with monte carlo sampling from predictive distribution
Let's say we have a predictive distribution of expected returns for N assets. The distribution is not normal. We can interpret the dispersion in the distribution as reflection of our uncertainty (or ...
16
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3answers
3k views
6
votes
4answers
555 views
Given two portfolios with identical correlation matrices, which one will have a better risk/reward ratio?
I have one portfolio with high beta stocks, and one with low beta stocks. Is it better to have higher expected return with high volatility, or medium expected return with medium volatility? (All from ...
22
votes
3answers
9k views
What is a “coherent” risk measure?
What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in ...
26
votes
5answers
6k views
What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework?
One of the main problems when trying to apply mean-variance portfolio optimization in practice is its high input sensitivity. As can be seen in (Chopra, 1993) using historical values to estimate ...
