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So you have your bullet-shaped “efficient frontier”. There is no portfolio offering a better return for lower vol, assuming - of course - that your return assumptions and covariance matrix have perfect foresight? The textbooks habitually hint this; but this is not so. The hint is based on the supplementary assumption of zero cash, zero leverage, and no ...

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The problem that you have suggested minimizes the difference in the number of shares. If the share prices of the products that you are considering are very different, this could lead to undesirable outcomes. I would suggest that instead you minimize the difference in the dollars invested, which will give you the closest possible portfolio to your target. So ...

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I think approaches that you suggest are incompatible. Risk contribution (or risk parity/HRP) is portfolio construction method that takes the volatility and correlation of securities, along with a desired contribution to risk, and generates the weights of the portfolio. Black-Litterman is related to mean-variance optimization. In a simple form, it can take ...

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There is no exact answer to this problem, but there are a few different ways to approximate it. Here is my preferred approximation method: $k_i = log(1 + r_{p,i}) / r_{p,i}$ $c_i = \prod_{j=1}^i1 + r_{p,j}$ $t_i = log(c_i)/(c_i-1)$ where $r_{p,i}$ is the return on the portfolio and $i$ is time. The time series of contributions to returns is then given by: \$...

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If the numbers are contributions and not returns you should not calculate interest on interest but just add the contributions together.

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Contributions are not returns - they are breaking out the total gain for a portfolio into the gains associated with each component. So in your example, the portfolio goes up by 0.04 on day 1, 0.01 of which came from the gain in stock B and 0.03 came form the changes in stock A. On day 2, the portfolio goes up by 0.03, etc. Everything sums nicely ...

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I ended up figuring it out. Long story short, the annuity formulas (ordinary or due) can in fact get the job done, whether the share price or the capital value of the account itself compounds at the annual return rate makes no difference. But it's still helpful to see how the number of shares increase over n periods.

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This "market portfolio" is a chimera: very useful for basic reasoning and teaching, but that cannot be traded. Here are three reasons why the term "market" suggests that it is available on markets, but of course it is not: as you write in the question, you should invest in a lot of unlisted, hence not public, assets even if you restrict ...

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