Questions tagged [modern-portfolio-theory]
A theoretical framework for analyzing investment portfolios based on their expected return and risk.
275
questions
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 ...
28
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 ...
23
votes
3answers
11k 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 ...
21
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 ...
17
votes
3answers
23k 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 $N$ ...
16
votes
3answers
3k views
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 ...
14
votes
1answer
6k 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 ...
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 ...
14
votes
3answers
9k views
Which algorithms do robo-advisors use?
Some pundits claim that there is a revolution in portfolio management under way: The rise of the robots, a.k.a. robo-advisors. The most well known are Betterment.com, FutureAdvisor, Schwab Intelligent ...
13
votes
2answers
1k views
Models crumbling down due to negative (nominal) interest rates
Given that the negative interest rates on a lot of sovereign bonds with maturity under 10 years are trading in the negative (nominal) interest rate territory (recently also the short term EURIBOR has ...
13
votes
1answer
854 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 ...
12
votes
1answer
181 views
portfolio optimization averaging weights, what are benefits?
I'm playing around with different portfolio optimization techniques. Amongst others I was also looking at the resampling method, especially the one described in Meucci. I have two general questions ...
11
votes
3answers
650 views
Portfolio construction in reality?
There are various models for portfolio selection in literature, like,
Harry Markowitz (HM) model ( Mean-Variance Model) [well known model]
Konno and Yamazaki (1991) model: minimizes the sum of ...
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 $...
9
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 ...
9
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 ...
9
votes
2answers
923 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 ...
8
votes
1answer
361 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 ...
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 ...
8
votes
1answer
563 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:
...
8
votes
1answer
421 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 ...
8
votes
2answers
234 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 ...
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 ...
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?
7
votes
2answers
722 views
Why is the variance of a portfolio a quadratic form?
I was reading about MPT http://en.wikipedia.org/wiki/Modern_portfolio_theory and notices that the total variance of a portfolio is $x' \Sigma x$, where x is the weighting of the assets and $\Sigma$ ...
7
votes
3answers
316 views
Portfolio Theory: Why is so much effort put into the reduction of estimation errors?
In MPT, very much effort by researchers is put into developing methods and techniques to handle the rather poor performance of the estimated means, variances and covariances. There are shrinkage ...
7
votes
2answers
521 views
Intuitive explanation of stochastic portfolio theory
Fernholz and Karatzas have published various papers about so called stochastic portfolio theory.
Basically they say that the return to be expected from a portfolio on the long run is rather the ...
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 - \...
7
votes
1answer
2k views
How modern portfolio theory(MPT) and CAPM are related?
1. Question
In what sense Capital Asset Pricing Model(CAPM) is related with Modern Portfolio Theory(MPT)?
Why do we need to check whether the current price of assets is overvalued or undervalued ...
7
votes
1answer
144 views
Finding a minimum variance portfolio when using a regulariser?
I am aware that the minimum variance portfolio of a market with $n$ securities can be shown to be:
\begin{equation}
w^* = (1^T_n\Sigma^{-1}1_n)^{-1}\Sigma^{-1}1_n, \\ s.t. \ \ 1^T_nw = 1
\end{...
6
votes
4answers
340 views
Why do anomalies disappear after they get detected?
In financial markets, anomalies refer to situations when a security or group of securities performs contrary to the notion of efficient markets, where security prices are said to reflect all available ...
6
votes
4answers
558 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 ...
6
votes
3answers
473 views
Most significant research articles for practical investors with research perspectives
I am an applied mathematician and recently I have decided to study the portfolio management theory. As a final objective, I want to manage my own portfolio and to try make some money on it using my ...
6
votes
2answers
403 views
Mean Variance Portfolio theory and real-world problem?
There are many assumptions on mean-variance portfolio theory and they seem to be very unrealistic, for example
1) investors have the same information at the same time:
calculating expected returns ...
6
votes
3answers
407 views
Generalized Mean Variance Portfolio
Utility based portfolio optimization deals with the problem of finding the optimal portfolio $x_T$ by maximizing the utility/objective function $O(x_T,x_0)$ where $x_0$ is the current portfolio.
In ...
6
votes
2answers
454 views
Maximum Certainty Equivalent Portfolio with Transaction Costs
Out of curiosity I tried to compute the portfolio weights of a maximum certainty equivalent allocation, however, by incorporating (quadratic) transaction costs. However, my result is not as intuitive ...
6
votes
2answers
339 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 ...
6
votes
2answers
1k views
Beta Constrained Markowitz Minimum Variance Portfolio - Closed Form Solution
This question is related to recent rule changes in the Quantopian Open.
I am trying to figure out a closed form solution to a beta constrained minimum variance portfolio problem but it doesn't seem ...
5
votes
2answers
2k views
Calculating alpha and its meaning
According to wikipedia, CAPM model is described by:
$E(R_{i})=R_{f}+\beta _{{i}}(E(R_{m})-R_{f})$
And according to website such as http://investexcel.net/jensens-alpha-excel/,
$\alpha = E(R_{i}) - ...
5
votes
1answer
7k views
Marginal Risk Contribution Formula
I am trying to understand and implement the standard 'marginal risk contribution' approach to portfolio risk and hoping to reconcile the formulae provided for its calculation in different sources. ...
5
votes
2answers
990 views
R package for portfolio
In the context of modern portfolio theory, one often wishes to minimise
$\mathbf{w}^{\mathrm{{\scriptstyle T}}}\boldsymbol{\Sigma}\mathbf{w}$
subject to $\mathbf{w}^{T}\boldsymbol{\mu}=c_{1}$, $\left\...
5
votes
2answers
776 views
Black-Litterman: Why should the views be independent of each other?
This question relates to this question.
In the Black-Litterman framework views of inverstors on the market are modelled.
These views have a covariance-matrix $\Omega$.
I always found it quite ...
5
votes
2answers
2k views
Black-Litterman, how to choose the uncertainty in the views $\Omega$ for smooth transitions from prior to posterior
In Black-Litterman we get a new vector of expected returns of the form:
\begin{align}
\Pi_{BL} = \Pi + \underbrace{\tau \Sigma P^T[P\tau\Sigma P^T+\Omega]^{-1}}_{\text{correction}}[Q-P\Pi]
\end{align}
...
5
votes
1answer
112 views
Alternative relative performance measure to Sharpe ratio for non-IID return
The Sharpe ratio is often used to compare the relative performance of portfolios despite its IID-assumption for the returns being violated.
I can find ample warnings about the consequences of ...
5
votes
3answers
1k views
How to apply the “Knapsack Problem” to minimise a portfolio's volatility?
Suppose I have a stock selection universe of 100 stocks.
I have estimated the covariance matrix of this 100 stocks.
I would like to create an equaly-weighted basket of 5 stocks which has the lowest ...
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 ...
5
votes
1answer
420 views
Rockafellar-Uryasev mean-CVaR optimiztion
In Rockafellar-Uryasev 2001 paper the mean-CVaR optimization can be written as a linear programming optimization problem as:
$$P_{\text{CVaR}} = \arg \min_w \text{VaR}_\alpha+\frac{1}{(1-\beta)S}\...
5
votes
1answer
491 views
Why did Markowitz not derive an equation for the efficient frontier?
Currently, I´m studying portfolio management and portfolio selection. The founder of the MPT is Harry Markowitz, of course. But reading his famous article from 1952 and his book from 1959 (actually, I ...
5
votes
1answer
446 views
Combining modern portfolio theory and Kelly betting?
I'm using modern portfolio theory to compute the frontier of efficient portfolios. I'd like to pick the best one in the spirit of Kelly betting, ie. maximising expected growth.
I'm looking for a ...
