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 ...
- 8,438
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 ...
- 516
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 ...
- 1,396
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 -...
- 11.4k
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 ...
- 9,332
4
votes
What can I use to measure of diversification?
You can also use the Herfindahl-Hirschman-Index (HHI) as a measure for concentration.
In portfolio analysis, you can calculate it as $$\frac{1}{N} \leq HHI(x) = \sum_{i=1}^N x_i^2 \leq 1$$ where $x$ ...
- 400
4
votes
What can I use to measure of diversification?
I use the 'implied correlation' defined as
$$
\rho = \frac{V^2_P-\sum V^2_j}{(\sum V_j)^2-\sum V^2_j}
$$
for $V_p$ the VaR (or volatility) of the portfolio, and $V_j$ the VaRs (or volatilities) of the ...
- 4,307
4
votes
Accepted
What can I use to measure of diversification?
In 2006 Choueifaty proposed a measure of portfolio diversification, called the Diversification Ratio (DR), which he defined as the ratio of the weighted average of the volatilities of ...
- 9,332
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 ...
- 10.9k
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 ...
- 367
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 ...
- 6,470
3
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, ...
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 ...
- 241
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
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) ...
- 3,186
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 ...
- 9,215
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 ...
- 9,332
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 ...
- 8,062
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-...
- 2,980
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 ...
- 2,880
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 ...
- 111
2
votes
Interpreting Statistically Significant (or Insignificant) Difference in Alpha Between Two Portfolios
No, your logic is not correct. As a disclosure note, I am an opponent of the method you are using.
Let us assume that you run a Frequentist regression of any kind on phenomena $A$ and $B$. You are ...
- 4,359
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 $(...
- 9,215
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 ...
- 968
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. ...
- 3,186
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 ...
- 106
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))(...
- 2,436
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 ...
- 801
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 ...
- 2,915
1
vote
Calculate Returns of Momentum Strategy (Overlapping Portfolios - Jegadeesh and Titman 1993)
In Jegadeesh and Titman, and the papers that follow it, the monthly return to the strategy for the month of March is found by averaging the monthly return for Tranche 1 in March, the avg return for ...
- 10.9k
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