Questions tagged [modern-portfolio-theory]
A theoretical framework for analyzing investment portfolios based on their expected return and risk.
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Is this methodology for finding the minimum variance portfolio with no short-selling sound?
I have below here an excerpt from a book on (among other things) mean-variance analysis showing how to find the minimum variance portfolio (Risk and Portfolio Analysis: Principles and Methods, by Hult,...
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46 views
How do I maximize my expected utility of wealth?
Suppose I have a utility function say $U(p)=p^{1/2}$
and I bet on a basketball game.
I have my initial investment, payouts and probabilities of winning, how can I determine the maximum I need to bet ...
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1answer
45 views
Time varying weights in a portfolio
As I have seen in my portfolio theory class, we define the weights of some assets and quantify the risk and return of the whole portfolio. In this setup, the weights do not change in time. What if the ...
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48 views
portfolio return, sharpe ratio and value at risk
Can you please help me to confirm if my calculations are correct or need improvement, or (too simplistic...) :
- portfolio return,
- portfolio standard deviation,
- portfolio sharpe ratio
- ...
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1answer
31 views
How can we quantify time varying portfolios?
In portfolio management, it is assumed that the assets and the weights in the portfolio are static and do not change in time. By the help of this static structure of the portfolio, we can talk about ...
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22 views
Transform Hierarchical Correlation structure to Standard Form
In the standard portfolio risk setup, we have
$\sigma_{\Pi} = \sqrt{(w' B (VFV) B' w) + w'Dw}$
where
$w$ is our weight vector for N assets
$B$ is the Nxm factor beta matrix
$V$ is the factor ...
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0answers
25 views
Calculating R* in a two-asset world
In chapter 5 of John Cochrane's Asset pricing, we derive a state-space interpretation of the mean variance frontier by defining $R^*$ and $R^{e*}$. A little forward, we have this formulation:
$$R^* = \...
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1answer
77 views
Mean-Variance optimization with no short selling
I am wondering how I can find the vector of Lagrange multipliers $\mu$ for the non-negativity constraint of the following problem:
$$ L(w,\lambda, \mu) = w^{T}\Sigma w - \lambda(w -1) + \mu w $$
So ...
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1answer
52 views
Do Fama-French factor portfolios require optimization?
I am going to perform factor crowding analysis for my dissertation and I am struggling to build factor portfolios from the S&P 500 in r.
I built my dataset from the S&P 500 and I am able to ...
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1answer
66 views
Which riskfree rate to use for Maximum Sharpe Ratio Portfolio?
I am conducting out of sample backtests of the MV framework. But how exactly do I derive the Maximum Sharpe Ratio portfolio for this? The standard forumula of the Sharpe Ratio is given by:
$$\frac{(...
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0answers
67 views
Finding the Efficient Frontier in Tensorflow
I have two assets A and B. Asset A has an expected return of 0.92% with a standard deviation of 2.10. Asset B has an expected return of 1.39% and a standard deviation of 2.20. I want to find the set ...
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1answer
68 views
ESG Style Analysis
Hi all and thank you in advance.
Do you think that implementing a style analysis on ESG equity portfolios is feasible?
When I mean style analysis I refer to the seminal paper of Sharpe (1992) but I ...
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56 views
Portfolio construction in reality
I have a very basic knowledge of portfolio construction and optimization aside from the mean-variance efficient portfolio theory.
I am looking for a series of resources to dig more into the topic ...
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0answers
46 views
Do equities have spread duration?
I was reading a research article today that suggested that equities exhibit significant effective spread duration. I'm looking at this on an index level, not firm specific. I've tried several ways of ...
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1answer
146 views
Using Implied Volatility for Portfolio Optimization
Hello I am interested in portfolio optimization . Previously I when I have done portfolio optimization I would take the historical returns of a stock and use them to perform a mean variance ...
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1answer
86 views
Benchmark of a Dollar Neutral Strategy
A dollar neutral strategy invests the same amount of money long and
short without accounting for the volatility (risk) of either side.
Depending on volatility you either end up positively or ...
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1answer
57 views
Deriving investment amount for one asset of a two asset minimum-variance portfolio
Suppose I bought $100 worth of stock A and I want to hedge it by shorting stock B, they have correlation of rho and respective standard deviations. How do I know how much of Stock B to sell? that's ...
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60 views
Mean Semivariance Optimization VS PMPT
Mean Semivariance optimization defines semivariance, variance only below the benchmark/required rate of return, as:
$(1/T).\sum_{t=1}^{T} [Min(R_{it}-B,0)]^2$
where $B$ is the benchmark rate, $R_{i}$...
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1answer
45 views
Surface plots of the mean-variance efficient frontier
3d surface plots contain an X, Y and Z axis. For the mean-variance efficient frontier:
X axis is portfolio volatility ($\sigma_p$)
Y axis is portfolio expected return ($\mu_p$)
any ideas for what ...
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1answer
53 views
Benefit of better predicting the variance of portfolio daily returns while optimizing a portfolio?
Question
Is there a benefit of having lower gap between 'in-sample' variance of portfolio daily returns and 'out-of-sample' variance of portfolio daily returns? (= better estimates the out-of-sample ...
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1answer
160 views
Efficient frontier using Post Modern Portfolio theory
I have been trying to find a way to create the efficient frontier using Post Modern Portfolio Theory (PMPT), but have failed to come across a source that mentions how to do so. I know PMPT uses ...
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50 views
Pca for Portfolio Theory
given the fact that if you take the portfolio returns for different assets in a portfolio the first principle component represents the market exposure of the portfolio and the second principle ...
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1answer
88 views
Prove that the portfolio that maximizes utility lies on the efficient frontier
When maximizing mean-variance utility in a portfolio optimization framework
$max \{R - \lambda \sigma ^2\}$
where R is portfolio return, $\lambda$ is a risk aversion parameter, and $\sigma^2$ is ...
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1answer
292 views
Is my python solution good? : Global Minimum Variance portfolio with 'no-short sale' constraint
Question
Is my python code an answer (at least a close answer) to get the weight vector of the Global Minimum Variance portfolio problem? My codes are shown below after some explanations.
Details ...
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1answer
50 views
Economic term for “limited trade space”? Slots in car sales hall, oil bunker volume, warehouse size
Newbie here. Took the tour, and "financial engineering" was listed as viable questions, so I give this a shot despite being very basic. Please redirect me if there is a more suitable SE site for it.
...
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1answer
126 views
Portfolio Systematic Risk, Breaking it down into factor % contributions
I have a portfolio (p) of N equities, with let's say weights vector (m) at the start of the calculation period. Each equity has its own set of factors (like corresponding country, industry index, etc.)...
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1answer
283 views
Portfolio Optimization and Global Minimum Variance Portfolio (GMV)
I have few questions about classic mean-variance-optimization in general. I have a series daily returns of 15 assets and I want to combine these assets in a portfolio.
1) Do you think that 1 year of ...
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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 ...
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1answer
77 views
Expected Return on Stock
Suppose we have the following information on stocks $X$, $Y$, and $Z$:
Expected Returns: $E(R_X)=10\%$, $E(R_Y)=12\%$.
Standard Deviations: $\sigma_X=10\%$, $\sigma_Y=15\%$, $\sigma_Z=10\%$
Pairwise ...
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1answer
200 views
Quasi Random Monte Carlo in m.v. portfolio optimization
Not specifying a correlation matrix for the Monte Carlo Simulation's random returns is equivalent to assuming no correlation or a correlation coefficient of zero, which will seriously and adversely ...
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1answer
303 views
What on earth is an Alpha Model in the quantative investment process?
I am confused with the useage of the concept "Alpha Model" in quantative investment. According to Qian, Hua & Sorensen (2007), the first thing in the toolbox of quantative investment process is "...
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1answer
93 views
Optimal Weight of Risky Portfolio
"Suppose that the investor has a quadratic utility function. That is,
$$U \left[ W \right] = W - \frac{1}{250}W^2.$$
Assume the investor is maximizing its expected utility and is
considering in ...
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1answer
268 views
Monte Carlo (resampling) in m.v. portfolio optimization
The instability and high sensitivity of optimisation results can be augmented by adding another layer of quantitative methodology in the form of Monte Carlo Simulation. The name Monte Carlo alludes to ...
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1answer
166 views
Why the weight vector of 'global minimum variance' the 'eigenvector' with the minimum eigenvalue?
Question
Why is it the case that the weight vector of the global minimum variance portfolio the eigenvector of the covariance matrix with the smallest eigenvalue?
Question with more details
I ...
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24 views
Adjust the Capital Market Line For Margin Interest
Modern Portfolio Theory assumes unlimited borrowing and investing at the risk-free rate. Of course, this is not realistic; margin interest costs several multiples of the RFR, especially for portfolios ...
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1answer
46 views
Show that the variance of the market portfolio is the weighted average of the ovariances between each constituent and the market portfolio itself
Let us assume that the market portfolio consists of n assets.
Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
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1answer
101 views
Naive question: how do factor models inform portfolio construction?
I have read plenty on the topic of factor modelling, but, in the end, after one has decided upon the factors to include in a model, how do all the Betas how tell one how to weigh each asset in a ...
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1answer
307 views
How is the Fama French 3 factor model used for portfolio construction?
In which ways is the Fama French 3 factor model used by practitioners to construct portfolios?
I understand that the betas can be calculated for a portfolio of stocks or for single stocks. Are the ...
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2answers
259 views
Max allowable return in Markowitz model
The Markowitz model solves the following problem: The portfolio with the smallest variance among attainable portfolios with expected return µV.
Here we have to choose µV to get the optimal portfolio ...
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0answers
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Continuous formula for the price of an asset paying one terminal dividend?
I have been trying to come up with ways to come up with an answer for a question we got in my class of "Asset Pricing Theory". The question is as follows:
"Write the price of the asset at time t in ...
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2answers
457 views
How to calculate optimal portfolio using sector constraints in python
I'm looking into CVXPY at the moment.
Main goal would be to be able to calculate the optimal portfolio, which in my opinion would mean that we need to maximise
(expected return - risk free) / ...
3
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2answers
330 views
Widely accepted methods for coming up with the co-variance matrix of assets?
Question
What are the widely accepted ways for coming up with co-variance matrix of assets
after the Markowitz's modern portfolio theory?
Question explained in more detail
After Modern portfolio ...
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1answer
91 views
Average portfolio correlation vs. external metric
I am coming across a problem I can't seem to wrap my head around, and I am not sure I am using the right words so cannot find much info in it!
I have a portfolio of assets, with data on historical ...
3
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1answer
142 views
Mean-variance portfolio optimization: methods for superior estimates of returns
Leaving aside the aspects related to the estimation of the variance component (all the latest techniques to compute a stable covariance matrix of a given set of assets such as simple shrinkage, Ledoit-...
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49 views
Tangency portfolio with constraints
Hello to everyone I am trying to implement a version of MV optimization with constraints as UB and LB, it seems to work fine but now i was trying to figure out a simple way to derive a CML in the same ...
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0answers
79 views
Jacobs and Levy: Enhanced Active Equity Strategies
Hello to everyone I am writing because I am having a bit of tough time figuring out how to replicate the constraints for a Portfolio Optimization using the set up from Jacobs & Levy 2006 - '...
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1answer
65 views
Is it possible to create an instrument on the amount of beds sold within the real-estate market
I have been doing some research on the PBSA (purpose-built student accommodation) market around the globe. The market is growing year on year there is an index on this market the cbre.
What ...
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Show that the variance of the portfolio market portfolio is function of the betas of its consituents [closed]
Let us assume that the market portfolio consists of n assets.
Given that the return of the market portfolio can be written as $r_m = \sum_{j=1}^{n} w_jr_j$, we have that $\sigma^2_m = E(\sum_{j=1}^{n} ...
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1answer
147 views
Convert Geometric Direct Alpha PME to Arithmetic Excess IRR (PME Alpha / Implied Private Premium)
As a followup to this old question, Private Equity: Direct Alpha vs Excess IRR, I have a new one.
In automating PME calculations, the Direct Alpha (DA) approach is computationally simpler and ...
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1answer
102 views
What is the purest way to get exposure to Jump risk premia, is there a jump swap
So to get exposure to Variance risk premia one could use variance swaps, is there a equivalent security for jumps. Hedging against jump but not diffusion risk could allow one to take targeted exposure ...
