Questions tagged [modern-portfolio-theory]

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

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3k views

Problem with determining weights in tangency portfolio (2 risky assets)

I use the following well known formula in order to determine the weight of asset i in the tangency portfolio (in the case of two risky assets): $w_{i,T}=\frac{\sigma[r_2]^2E[R_1]-\sigma[r_1,r_2]E[R_2]...
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1answer
2k views

How to calculate the global minimum variance portfolio in R?

I am attempting to use the globalMin.portfolio command to calculate the global minimum variance portfolio in RStudio. My code is as follows (note that several ...
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1answer
299 views

Black Litterman: Is it possible to have multiple views (from different sources) on the same asset?

From the basics of Black Litterman I understand that each view on a stock is implemented via the pick matrix P with the expected value of the views in Q. I have read several papers where each stock ...
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2answers
931 views

Derivation of the tangency / maximum Sharpe ratio portfolio in Markowitz Portfolio Theory? (2 risky assets)

I’m looking for a nice & detailed explanation for how to derive the formula for the weight of asset 1 in the tangency / maximum Sharpe ratio portfolio in Markowitz portfolio theory in a world with ...
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5k views

Tangency portfolio and CML - Why does it have the highest sharpe ratio?

In the book that I am studying, the tangent portfolio was defined as the regular efficient portfolio in the case with $n$ risky assets and 1 riskfree asset with the extra requirement that the ...
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1answer
54 views

How to determine portion of portfolio's risks from components?

Say I have a portfolio of 3 stocks $A,B,C$ with $\mu_A = 5%$, $\mu_B = 10%$, $\mu_C = 15%$ and volatility $\sigma_A = 10%$, $\sigma_B = 15%$, and $\sigma_C = 25%$. Let us also say that correlations ...
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1answer
801 views

how can we know the residual return will be uncorrelated with the market return

I was reading that if we know a portfolios beta we can break the excess return on that portfolio into a market component and a residual component. ...
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76 views

Portfolio Theory: Must VarCovar Matrix be based on return var/covar?

I am trying to estimate the minimum variance portfolio where the assets are currency derivatives. In the specific case it does not make sense to base correlations or variance on asset returns. I am ...
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1answer
56 views

given someone's past investing history, is there a way to calculate his risk aversion?

given someone's past investing history, is there a way to calculate his risk aversion? Say, we know this client's investment history for example his past return, is there a way to calculate his risk ...
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61 views

How to Rank assets in Portfolio? [closed]

I am working on active equity Portfolio. I have total 30 securities in my Portfolio. Can someone please guide me how can I rank those assets in my portfolio. ...
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3answers
67 views

How to compute the foreign exchange volatility within a portfolio

Suppose I have a portfolio of 5 assets. Assets 1 and 2 have foreign exchange exposures and therefore foreign exchange volatility. How can I calculate the marginal contribution to the total portfolio ...
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136 views

Interpreting different factor models w.r.t. correlation matrix and min variance portfolio weights

Background In Eric Zivot's analysis of factor models he uses three models The sample (.sample) Single index model (.si) Barra factor industry model (.ind) PCA model (.pca) You can download his ...
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2answers
624 views

Dealing with a constraint which is the square root of a quadratic form

I'm trying to maximize my portfolio, but don't know how to deal with the constraint which is on the form max $2u^Tx-x^T \Sigma x$ Subject to $e^Tx = 1$ $u^Tx - m (x^T \Sigma x)^{1/2} >= c $ ...
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1answer
285 views

Mixing Portfolio Strategies

Given a set of $N$ assets, the amount of strategies proposed in literature to diversify the investors wealth in order to find the 'optimal' portfolio is overwhelming. However, for example DeMiguel et ...
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3answers
676 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 ...
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1answer
126 views

Portfolio optimization

first I just hope that this question is in the right place. I have started working on portfolio optimization and the formulation of the problem and their solution : For example in the Markowitz ...
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1answer
309 views

Portfolio with lots of subportfolios

An account manager has $N$ distinct, equally-sized pots of money, which will be used to make $N$ distinct subportfolios, each of which is drawn from a slightly different (but potentially overlapping) ...
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3answers
532 views

Interpretation of portfolio standard deviation

I have computed an efficient frontier using quadratic optimization algorithm for some stock data and then plotted it. However, I have troubles understanding how to interpret standard deviation of ...
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38 views

Change in portfolio when IPO announced

I'm wondering whether there would be a change to my answer of the change in portfolio when there is a new stock introduced. My investment strategy is to maximise expected return such that my standard ...
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1answer
254 views

Calculate mean variance portfolio

I am trying to calculate the mean variance portfolio using the plug-in approach. First I generate some artificial data: x <- replicate(10,rnorm(1000)) Then I ...
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1answer
184 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 ...
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1answer
395 views

Mean variance efficient portfolios and target returns

If I use mean variance optimisation to create an efficient portfolio with a target expected return of 20% in a year's time and find that the actual return at the end of the year was 24%, what explains ...
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2answers
525 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 ...
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3answers
2k views

How to estimate variance-covariance matrix of assets with different length of historical data? [duplicate]

Consider you have 4 assets A, B, C and D, where Asset <...
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1answer
166 views

How to calculate a hypothetical minimum-variance point?

If we have $N$ assets which are uncorrelated, but have the same mean return of $\mu$ but the variances are different where $\sigma_i^2$ is the variance of each asset $i = 1, 2,...,N$ how can you write ...
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29 views

Market portfolio [closed]

If I create portfolio consisting of three stocks and build efficient frontier for this portfolio and if there is a risk free rate for treasury bills and then I draw tangent line from risk free rate on ...
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2answers
416 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 ...
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2answers
887 views

Basic question on Portfolio Theory

I was revising my stuff about portfolio theory and I noticed that every single time, expected return and corresponding variance or covariance are given! (not calculating ourselves). So I'm just ...
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3answers
10k 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 ...
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1answer
38 views

Can adding an uncorrelated high vol strategy to a low vol portfolio result in a portfolio with even lower volatility?

Let's say I have fund A with 20% annualized volatility and portfolio B with 15% annualized volatility. If A and B have 0 correlation, can the combination of these funds have volatility < 15% ? Are ...
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272 views

Finding mean vector and covariance matrix for annual returns given quarterly returns

I am currently trying to calculate a vector for the mean annual returns of 4 different asset classes along with their 4x4 covariance matrix in excel. However, I am having problems since the data I ...
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2answers
2k views

Difference between Sharpe Ratio and Information Ratio

I am finding it difficult to understand the difference between the sharpe ratio and the information ratio and the relationship between the two, and cannot find a decent reference that breaks it down ...
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1answer
394 views

Definition of sharpe ratio maximising and variance minimising portfolios

In this paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2226985, in the derivation of the mean variance efficient portfolio using lagrangians in the appendix, on page 29, the two portfolios ...
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1answer
92 views

Understanding portfolio weights and purchasing stock in modern portfolio theory

Recently I've been learning about the markowitz algorithm. It's pretty interesting, but I'm curious how we apply this in practice. Lets say I have some optimal portfolio: $R_p = x_aR_a + x_bR_b$ ...
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1answer
77 views

calculating portfolio volatility [closed]

Given: vector of portfolio weights $W = [w_1 w_1 ]$ correlation matrix $C = \left( \begin{array}{ccc} a & b \\ d & e \end{array} \right) $ standard deviation of the asset returns $S = [s_1 ...
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1answer
376 views

What Exactly is Expected Return

Consider the following plot, courtesy of this page: Regarding the $y$-axis, how does this "expected return" relate to the "instantaneous expected return" in a geometric Brownian motion (GBM)? E.g., ...
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1answer
245 views

Reference Request: Horse Race for Portfolio Allocation

Probably the most popular horse race study for portfolio strategies is Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?, with DeMiguel, L. Garlappi and R. Uppal. ...
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262 views

Residual Covariance Matrix, and MVO for Residual Variance and Alpha

My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$. We know the equation for residual variance ...
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2answers
236 views

When to adjust portfolio weights?

In portfolio allocation literature there is lot of effort made in obtaining 'better' portfolio weights, for example via improving parameter estimates, introducing Bayesian approaches, incorporating ...
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1answer
453 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 ...
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1answer
127 views

Calculating Fees (Kane, Marcus, and Trippi)

Having read a chapter in Bodie, Kane and Marcus' Investment, I came across a formula I do not quite understand. It states that the percentage fee in excess of what an index fund would charge on active ...
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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 ...
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2answers
261 views

Expected Utility and $\log$

I've just started reading about expected utility and utility functions and have the following question. $\textbf{Question:}$ An investor has an initial wealth of 100 and a utility function of the ...
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1answer
583 views

Markowitz portfolio optimization question

I am studying the Markowitz portfolio optimization theory, and I just wanted to ask if I understood this correctly. For a stock portfolio we distinguish two kinds of risks: an unsystematic risk, which ...
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2answers
994 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\...
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2answers
747 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 $\Sigma$ ...
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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 ...
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2answers
707 views

Calculate efficient frontier using fPortfolio with incomplete set of returns

I want to calculate the efficient frontier for a set of 140 assets using returns from the past 10 years. However, some of these assets came into existence only more recently, so for some assets I have ...
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0answers
58 views

Investing in all assets with positive expected return and allowing for positive correlation

How does the answer to this question Risk minimization by investing in all assets with positive expected return change if assets can be positively correlated (but not perfectly) and short sales are ...
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0answers
477 views

Tangent portfolio weights without short sales?

Consider a mean-variance investor in a world with a risk-free asset. Let $R_f>0$ be the return of the risk-free asset, $\mathbb{E}(R_i)>R_f$ the expected return of the risky asset $i$ and $SD(...