Markovitz portfolio and change of cach system:

Consider a Financial market in which NN risky assets are listed. We note RR the vector of its return, E\mathcal{E} the vector of RR's means and Λ\Lambda the matrix of RR's covariances. We suppose that Λ\Lambda is not invertible and that the means of returns are not all equals.

Let PminP_{\text{min}} be the portfolio in which we invest 1$1\$ at t=0t=0 and having a minimal variance. We do the following change of cach: instead of calculating the prices of an asset or a portfolio in dollars, we will evaluate the price in numbers of PminP_{\text{min}}. For instance, if an asset costs 1$1\$ at t=0t=0 it costs 1010 in the new cach (we suppose that we have only two dates t=0t=0 and t=0t=0).

We note RminR_{\text{min}} the vector of assets's returns in the new cach PminP_{\text{min}}, Emin\mathcal{E}_{\text{min}} the vector of RminR_{\text{min}}'s means and Λmin\Lambda_{\text{min}} the matrix of RminR_{\text{min}}'s covariances.

Explain why the matrix Λmin\Lambda_{\text{min}} is not invertible (its rank is N1N-1).

Note by Mountassir Farid
5 years, 7 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link]( link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


There are no comments in this discussion.


Problem Loading...

Note Loading...

Set Loading...