Skip to main content
9 votes
Accepted

Why techniques for portfolio optimization do not take into account the non-fractionability of stock prices?

There are a few related reasons: The optimization becomes a lot harder when only discrete values are considered. Mean variance has a closed form solution for the continuous case but the case with ...
Bob Jansen's user avatar
  • 8,562
8 votes
Accepted

How are modern portfolio theory (MPT) and CAPM related?

CAPM states that the expected return of any given asset should equal $ER_i=R_f+β_i (R_m-R_f)$, with α being the error term of the previous equation. Now, as α has an expected value of zero, then only ...
MGL's user avatar
  • 516
5 votes
Accepted

average return Vs cumulative return interpretation

Consider these two simple portfolios: Portfolio 1 returns -10% in month 1 and 10% in month 2. Average arithmetic return is zero, and cumulative return is $(1-10\%)(1+10\%)=0.99$. Portfolio 2 returns -...
Helin's user avatar
  • 11.7k
5 votes
Accepted

Why did Markowitz not derive an equation for the efficient frontier?

It is surprising. What I think is: Markowitz became interested in the general problem when there are constraints (including inequality constraints) on the portfolio weights (in addition to the ...
Alex C's user avatar
  • 9,382
5 votes
Accepted

Question about quadratic form of f* in the Continuous Kelly Criterion

The Kelly Criterion aims to maximise the expected value of the logarithm of terminal wealth. The derivation starts off by assuming that there is a risky asset that is following a Geometric Brownian ...
Tim Wilding's user avatar
  • 1,406
4 votes

Why techniques for portfolio optimization do not take into account the non-fractionability of stock prices?

As correctly mentioned in an earlier answer, portfolio optimization is something used for books in hedge funds and other institutions. As a smooth utility function changes slowly near its maximum, ...
Michael Isichenko's user avatar
4 votes
Accepted

Literature about optimal number of stocks in a diversified portfolio

The first article on this was Fisher and Lorie "Some studies of variability of returns on investments in common stocks" JB April 1970. https://www.jstor.org/stable/2352105 The Statman ...
nbbo2's user avatar
  • 11.4k
3 votes

Is the portfolio return distribution a weighted combination of individual asset return distributions?

As @Martin has pointed out in his answer, of course it is. Let $X=\sum_{i=1}^N w_ix_i$ denote the return of a portfolio of $N$ assets with multivariate distribution $f(x_1,x_2,\ldots,x_N)$. The ...
Kermittfrog's user avatar
  • 6,663
3 votes
Accepted

Analyzing stock performance - keep companies after bankruptcy?

It could be useful to set ex-ante what is your investable universe. It is pretty typical that at any period of time you would track only names wich are part of a Benchmark (SP500, R1000, FTSE, Nikkei ...
NegativeJo's user avatar
3 votes

What is the meaning of Beta of an individual asset in relation to a portfolio, not the market?

Not directly answering your question, but is this theoretical or did you actually do this? If so, I hope you do know that beta is not stable over time, only measures a linear relationship and that the ...
AKdemy's user avatar
  • 8,934
2 votes

Determining the portfolio return distribution to calculate CVaR/ES

In the paper (Klaassen, 2002) the author propose a scenario generation method as well as a rule in order to precludes arbitrage opportunities. In the paper (Davari-Ardakani, et al. 2016) authors ...
Nick's user avatar
  • 253
2 votes

Dmat argument in solve.QP R function: Cov or 2*Cov?

Both approach gives same results for stocks weights but different results for lamda values Correct approach is multiplying the covariance matrix by 2 but you only need stocks weights so its the same
Manuel Guerra's user avatar
2 votes

Portfolio optimisation with conditional weight restrictions among asset

You could try a heuristic approach. The problem can be split into two nested optimisations: i) in the inner optimisation, given a set of selected assets, compute mean--variance efficient weights; ii) ...
Enrico Schumann's user avatar
2 votes
Accepted

Difference between constraining pre and post optimization

Consider the equation of two variables (basically your obj func): $$f(x,y) = x^2 + y^2$$ The unconstrained minimisation is $x=y=0$. If you now constrain this sum to be equal to one, post ...
Attack68's user avatar
  • 10.5k
2 votes
Accepted

Characteristic Portfolio for an Attribute

From b. we get $Vh = \lambda a$, so $h=\lambda V^{-1}a$ (assuming V is invertible). Using this to evaluate a. we get $h^Ta = \lambda a^T V^{-1}a=1$ (assuming $V^{-1}$ is symmetric). We can solve ...
Alex C's user avatar
  • 9,382
2 votes
Accepted

What is the return of risky asset in direct utility optimization probem?

Your question is very confusing. But let's take it by parts: You say you have power utility so your utility is: $\frac{W_{t+1}^{1-\gamma}}{1-\gamma}$ You have a risk-free rate number You have an ...
phdstudent's user avatar
  • 8,381
2 votes

how to construct a diversified portfolio based on correlation

The maximum decorrelation portfolio can ensure your portfolio is not so correlated in one general asset class: min $\mathbf{w^{T} C w} $ subject to constraints that weights sum to 1 and are non-...
develarist's user avatar
  • 3,000
2 votes

Portfolio selection with no risk-free asset

There are a few reasons the authors may have only looked at risky assets. First, they are trying to find a faster way to solve a mean-CVaR optimization through relaxations. Therefore, they probably ...
kurtosis's user avatar
  • 2,900
2 votes

Quantatively identifying stocks to short when overall market starts to roll-over

my take would be -- short the index. I think when markets turn most people will sell the index and that will have been the best trade to be in. Not sure you can rely on historical/statistical beta ...
TickaJules's user avatar
2 votes

Analyzing portfolio returns using Fama-French Factors

It is very important to understand your end goal. FF regressions are used to understand return of portfolio which can be attributed to FF style factors. In this analysis I am assuming that you are ...
vaibhav's user avatar
  • 21
2 votes

Optimal weights in portfolio after rebalancing

It depends what your optimization problem is. The simplest would be return maximization: $$\max_{w \geq 0} w^\top x \text{ subject to } \mathbf{1}^\top w$$ This is a standard linear program, and the ...
msantama's user avatar
  • 151
1 vote
Accepted

Correlation between mean-variance efficient portfolios

Just divide covariance by the square roots of the two variances. In this case you would want $$ \frac{1/a}{\sqrt{\frac{1}{a}\frac{c}{b^2}}}, $$ which takes value $$ \frac{|1^{\top}\Sigma^{-1}\mu|}{\...
steveo'america's user avatar
1 vote

Portfolio selection with no risk-free asset

They just want to apply their technique to risky assets that actually have volatility. The risk-free asset has a volatility of $0$ so allocation towards it is treated as an after-thought since it's ...
develarist's user avatar
  • 3,000
1 vote

Country allocation -optimization 3 countries

Here's a thought. In 2-dim your score $(x, y) \in [-4,4]^2$ is best characterised as the minimal distance from the line $y=x$, along which your portfolio is balanced. I.e. wherever $y=x$ either at $(...
Attack68's user avatar
  • 10.5k
1 vote

Dealing with stochastic results of Machine Learning Models

The best bet for you is to use Ensemble Learning, as someone experienced with Kaggle competitions, the best way to replicate good performance on Private Learderboard is to ensemble as many algorithms ...
Dhruv Mahajan's user avatar
1 vote

Dealing with stochastic results of Machine Learning Models

Stochastic solutions are an unavoidable property of stochastic methods, in particular optimisation methods. See for instance section 3 in A Review of Heuristic Optimization Methods in Econometrics. ...
Enrico Schumann's user avatar
1 vote

Dealing with stochastic results of Machine Learning Models

Have you tried to choose an arbitrary number of model, let say 20, each one having its own seed? Then you run your twenty models and use the median of your 20 results as signal. One advantage of that ...
SachaTheBrave's user avatar
1 vote

How would you equally distribute the risk of each stock in a portfolio?

We're going to assume that we have $N$ assets in our portfolio with weights $w$ and prices $x$. The variance of your portfolio is given by: \begin{equation} V\left( w'x \right) = w' E\left((x-E(X))(...
Stéphane's user avatar
  • 2,476
1 vote
Accepted

Measuring liquiduity of a portoflio of bonds

It does not take into consideration the fact that liquidity is not symmetric, also in Fixed Income markets. Indeed, there is much more liquidity pressure on the downside than on the upside. I suggest ...
Vitomir's user avatar
  • 821
1 vote

Portfolio optimization of unequal length back-tests

First of all: The issue is classic, but by no means trivial. Your "First" option is probably the easiest. You just adjust your dataset by thorwing away the data points that are not present in all ...
vanguard2k's user avatar
  • 2,915

Only top scored, non community-wiki answers of a minimum length are eligible