New answers tagged modern-portfolio-theory
2
The Markowitz problem is an optimization problem of a series of
Gaussian distributions (symmetric) with a variance-covariance matrix
This is a common misunderstanding. Markowitz (mean-variance = MV) model do not require the Normal distribution of returns, even if such condition is optimal in some sense. The only necessary distributional condition is the ...
1
Hmm... some notable implicit assumptions made en passant here ;-) How persistent are these autocorrelations (ACs)? Let's unpick a little.
One obvious question is whether your AC process is strong enough to overcome transaction costs and slippage, if markets are almost-random. Then someone trying to trade that could easily just get their position sizes ...
0
Would it be appropriate to say that the scaling ($b$) on the weights ($w_{t,i}$) is irrelevant because you can just pick a scaling of $w_{t,i}$ that satisfies this requirement?
Furthermore, if $a \neq 1$ later in the paper they define $R^e_{t+1,i} = \beta_{t,i}F_{t+1} + \epsilon_{t+1,i}$ where $F_{t+1} = w_t^{\text{T}} R^e_{t+1}$ so we no longer have the $a$ ...
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Using some of @noob2 notation, if:
$x_i$: the initial dollar amount of asset i
$t_i$: the transacted dollar amount of asset i
$\theta$: the fee fraction (0.2%).
$w_i$: the desired post balancing weights
Then you have the minimisation problem:
$$ \min_{t}{f(t)} = \sum_i \left ( \frac{x_i + t_i -\theta|t_i|}{\sum_j x_j +t_j -\theta|t_j|} - w_i\right )^2 $$
...
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I do not think there is a closed form solution. I have applied a simple iterative method to your example problem. See below.
Let $N=4$ be the number of assets, indexed by $i$ ranging from 1 to $N$.
Let $x_i$ be the dollar allocations before rebalancing (in your example they are called "value (P*Q)").
Let $w_i$ be the desired post-rebalancing ...
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