Questions tagged [modern-portfolio-theory]

A theoretical framework for analyzing investment portfolios based on their expected return and risk.

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Can there be different Sharpe Ratios for the same index? [closed]

I am reviewing a fellow students paper, and it is argued in this paper that the Sharpe Ratio can differ based on which model is used to analyze the portfolio returns. Here a model based on the ...
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How does a mispricing affect CAPM/MPT statistical parameters?

In the CAPM/MPT context, would a mispricing affect the various statistical parameters? For instance, if Alpha is 2% and the CAPM E(R) is 10% (in equilibrium) and the E(Ra) = 12%, when calculating all ...
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Does it make sense to have an allocation to short term fixed income and a leveraged or unfunded position?

This may sound like a basic question but I have seen many large institutional investors have this as part of their asset allocation and am wondering why they do this? Does it make sense to have a ...
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Two specific questions about CAPM's assumptions and implications

I have two questions about the CAPM model: the first is theoretical while the second is related to observed market data. First question: let's say we have company A and company B and we want to ...
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Kelly Criterion for cash game poker (normally distributed returns)

I'm trying to apply the Kelly Criterion to poker. Poker players have been stuck using outdated bankroll management techniques for decades, and I want to change that. My goal is to graph the log growth ...
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Is CAPM + additions actually used in industry-level portfolio optimization? [closed]

I've been wondering how do institutional investors actually perform portfolio optimization, i.e., do the traditional methods work when combined together with superior data collections and quality, and ...
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2 votes
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Does a portfolio on efficient frontier also lie on CML(capital market line)?

I am trying to solve this question: Assume that CAPM is true. The risk-free rate is 3%, the expected return on the market portfolio is 10% and the standard deviation of the return on the market ...
1 vote
1 answer
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Can someone briefly explain me what's the difference between Exact Factor Model (EFM) and Approximate Factor Model (AFM)? [closed]

I'm reading De Nard et al. paper "Portfolio Selection in Large Dimensions" and the authors talk about these two models, but I don't have any background on these topics from university. Can ...
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Two approaches to optimizing quadratic utility

My understanding of the traditional Markowitz portfolio optimization process is as follows: Let’s say I have data from year 1 to year 10. At the end of year 10 (having information about year 10), I ...
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1 answer
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Covariance Between Two Frontier Portfolios

Based on the definitions of A, B, C, and D in "An Analytic Derivation Of The Efficient Portfolio Frontier" by Robert Merton (1972), how can I prove the following in a line-by-line derivation?...
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How to deal with benchmark timing in quantitative portfolio management?

In Grinold & Kahn (2000), the authors emphasized the separation of stock selection and benchmark timing in active portfolio management. So if we avoid benchmark timing, the optimal portfolio's ...
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Have more complex MVA-style models become obsolete?

Just reading a book about about portfolio optimisation. You hear left and right that MVA (Mean Variance Analysis of Markowitz) is out of date, creates suboptimal portfolios in practice and so on ...
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1 answer
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Why the portfolio return is defined as a weighted return?

After reading the modern portfolio theory, I am wondering why the portfolio return is defined that way. Suppose there are $n$ assets in a portfolio, the simple return of an individual asset $i$ at ...
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Why is the performance of a portfolio based on geometric means boosted by positive correlation?

https://qoppac.blogspot.com/2017/02/can-you-eat-geometric-returns.html The blog post above by Rob Carver discusses the use of geometric means to evaluate investments. The section "The ...
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What is industry best practice to combine alphas?

Say I have 100 different alphas that all have statistically significant returns in-sample. Is the best practice to use historical covariance matrix plus Markowitz portfolio theory to create an optimal ...
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1 answer
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Portfolio construction for almost identical assets

The problem I am looking at concerns the treatment of almost identical assets in portfolio construction. Let us assume that we have two assets, both with a standard deviation $\sigma=0.2$ and a ...
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Why weigh assets by market values in CAPM?

Can anyone help me understand as to why in CAPM's market portfolio investors will always have the assets in proportion to the market value? One of the intuitive reasonings that I have read explains ...
2 votes
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Marginal Risk Contribution Implementation Questions

Sorry if this is too obvious to you. The marginal risk contribution mentioned here is the same as in this post Marginal Risk Contribution Formula . I understand the concepts and derivation on the ...
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1 answer
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What is the APT trying to say?

I'm reading through Active Portfolio Management, and I can't get my head around the APT. As far as I can tell, the statement in equation 7.2 translates into: "If you can get better than consensus ...
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3 votes
1 answer
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Do managers information ratios exhibit autocorrelation? Ie. are they stable over time?

I'm reading through Active Portfolio Management, and I can't get my head around Information Ratio's real world applicability. In table 5.6 it lists some empirical infomation ratios: However, there is ...
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3 answers
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Why are monthly active returns averaged? Should they not be multiplied?

I'm looking at this video: https://www.youtube.com/watch?v=fZmuJ2A9TC8 @4:43 but the issue is more general. Here the speaker is taking monthly active returns and averaging them ...
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What does a portfolio risk of 20% mean?

From the book Active Portfolio Management there is a use of lingo I don't understand. Take this quote from pg. 100 "Why are institutional money managers willing to accept the benchmark portfolio ...
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Covariance Matrix by Multi-Factor Model

I have been trying to find literature for the derivation of the covariance matrix, following a multi-factor model. I have had no luck at all, every single article I have found on the web already ...
1 vote
1 answer
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Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions

Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions? During my engineer student days I saw the Markowitz theory for portfolio selection ...
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Tangency portfolio negative maximum Sharpe ratio

Suppose I have three assets: the market, factor A and factor B. The market is in excess returns of the risk free rate. The other two factors are long-short portfolios. I have net returns for these ...
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1 answer
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N asset covariance matrix vs N-1 asset covariance matrix

so I have been using a M-V framework to form M-V efficient portfolios. I have noticed that every time I make my investment universe smaller the minimum variance frontier moves to the right. This ...
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Why do we use half of the risk in objective function of markowitz portfolio theory

In some documents I have seen objective function of markowitz portfolio theory is as follows. minimize 1/2 * w'Σw where w is weights Σ is covariance matrix I could ...
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Risk Factors, Portfolio Optimization

I really need help with a project that I am working on, for my university.I study in Ecuador and the research material here is very limited. Nonetheless I have tried my best to start with the basics ...
2 votes
1 answer
156 views

Unexpected Inflation and Asset Allocation

If asset allocation decisions were made prior to the news of unanticipated inflation, how should asset allocators incorporate the fact the inflation is now 5% higher than the 2% inflation target? It ...
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2 votes
1 answer
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Correlation Matrix to Variance Covariance Matrix Portfolio STDEV

I have a correlation matrix that I wanted to convert into a variance covariance matrix. I also have the weights in a column in excel along with each assets standard deviation. What excel function can ...
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Mean-variance optimization and hedging

I've read--and have been able to replicate empirically--that mean-variance optimization will trade two positions against each other if assets are highly correlated. For example, if stocks $A$ and $B$ ...
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Portfolio Theory - Maximizing Expected Utility Function

I am trying to implement a portfolio selection tool based on utility functions. So, I should maximize the expected utility of a given utility function: $$ \begin{align} &\max_{w}\ E[u(W_0(1+w^TR))]...
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Can I invest in the market portfolio of modern portfolio theory? [closed]

According to the theory, the market portfolio is composed of all assets weighted by their market capitalization, and this is the portfolio one should own. Is there a way to build a portfolio close to ...
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Why the market portfolio is the tangency portfolio in the Mean-Variance Optimization model?

I read in an explanation that the tangency portfolio has all securities with weights proportional to their market value because supply equal’s demand. But I can't understand why supply equals demand ...
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Is finding the efficient frontier a max or min problem?

I'm trying to understand where the efficient frontier comes from. What I understand about the efficient frontier I understand the efficient frontier is essentially a subset of the boundary of the ...
2 votes
1 answer
436 views

Kelly Criterion for Multiple Simultaneous Correlated Bets [closed]

I am looking for an equation for the optimal fractional bet sizing for N number of simultaneous correlated bets. I am looking specifically for an equation for binary bets, but an equation for bets ...
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1 answer
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Why additivity assumption holds in CAPM and factor models? (Screenshot of a textbook included) [closed]

All the excerpts are from the book investment, written by Bodie. At the bottom of this post, I attached pages of the the book that show a related part of my question. Question 1. Why the variance of ...
3 votes
2 answers
419 views

How to derive this mathematical equation from the perspective of the mean-variance portfolio optimization?

Question I found a simplified inequation to decide whether the new asset A should be added to my current portfolio B. If the following inequation is satisfied, the new asset A should be added to my ...
2 votes
2 answers
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Best books on portfolio construction?

I am a master of finance student and although I understand the basics and the theory of portfolio construction I am still struggling when it comes to the practical side of things, i.e. building a real-...
2 votes
1 answer
289 views

Carhart 4-Factor Model intercept interpretation

I've been following studies such as Kempf & Osthoff (2007) and Statman & Glushkov (2009) in building a methodology measuring ESG portfolio performance centred around the Carhart 4-Factor Model....
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Consensus expected excess return from Active Portfolio Management

In the book Active Portfolio Management, when discussing components of expected return (page 92 in edition 2), the authors mention that the consensus expected excess return $\beta_n\mu_B$ is the ...
1 vote
1 answer
162 views

Optimal portfolio with only n assets (with n less than total assets)

Given a time series of a set of N assets (let's say 100), how can I find the optimal portfolio, with the constraint that only n<N assets (let's say 10) can be in the portfolio? With 'optimal ...
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1 answer
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Active portfolio management - characteristic portfolios derivation

In the book Active Portfolio Management by Grinold and Kahn, on page 30, when it derives the characteristic portfolio $h_a$ for some characteristic vector $a$, the problem is set up as $$\min h^TVh$$ ...
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Interaction between raw position signals and portfolio optimisation methodologies [closed]

I'm trying to get my head around how the various aspects of constructing a final position generally interact and wonder whether anyone could expand on my (tentative) understanding currently. As I see ...
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1 vote
1 answer
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How to deal with securities that has short historical data when performing mean-variance portfolio analysis?

I am trying calculate expected return and risk (stdev) based on historical data using Mean Variance Analysis framework. Let's say the portfolio has 10 stocks, 9 of them have more than 10 years history ...
1 vote
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Strange efficient frontier, when I try to calculate BTC & ETH ratios using MPT(Modern Portfolio Theory) [closed]

The 10k Monte-carlo simulations all fall on the same line, instead of a proper scatter plot.. Not sure what I'm doing incorrect. It all works fine, if I include Monero in the mix. Any pointers ? I'm ...
1 vote
0 answers
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How to prove that the return criteria for adding an investment A to an existing portfolio can be represented using Sharpe Ratio Approach

How can I prove that the return criteria for adding an investment A to an existing portfolio can be represented as the below inequality using the Sharpe Ratio Approach for risk adjusted returns as ...
1 vote
1 answer
227 views

annualized vs annual returns

For the purposes of MPT, to compute return of an asset, one typically uses the daily log return of the assets and then anualizes it and the same goes for stddev ...
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Sub-portfolio correlation

I am trying to reduce correlation matrices into sub portfolios. For example, I have a covariance matrix $\Sigma$ and weight-vector $w$ of two line items which I blend together into a sub-portfolio $\...
1 vote
1 answer
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Equivalence of Standard Deviation and Variance as a risk measure - WRONG?

In Modern Portfolio Theory, I often see that people seem to view Standard Deviation and Variance as equivalent. Example from Markowitz himself: "Thus far I have used the standard deviation ...

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