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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 ...
• 9,144

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 ...
• 151

Asset rate (elasticities ?) of substitution

Your language needs to be more clear. What do you mean by a shock to asset 2? A decrease in price of asset 2, should not change your allocation and have no spillovers (since the expected return of ...
• 8,441

"Risk Matters Hypothesis" - does it really?

I didn't read the referenced paper, but I did try to replicate your numbers. I agree with your calculations for the individual Sharpe ratios for the two portfolios. However, I do not agree with your ...
• 6,642

How do I show that there is no tangency portfolio?

Any point on the efficient frontier is the sum $$Z +\lambda X, \qquad \lambda\in\mathbb{R},$$ where $Z$ is the minimum variance fully invested portfolio and $X$ is an efficient zero-cost portfolio. ...
Accepted

Interpretation of optimal weights in portfolio for risk-adjusted return maximization

With regards to your question about the denominator, if we expand the denominator, it becomes: w_1 = \frac{\mu_1\sigma_2^2 - \mu_2\rho\sigma_1\sigma_2} {\mu_1\sigma_2^2 - \mu_1\rho\...
• 1,564
1 vote
Accepted

How can this problem be defined formally?

The event that the second stock price is less than a constant $K$ at the time $h$ is mathematically described by $\{S_2(h)< K\}$. The first stock price, at the time $t\in [T,H]$, given the event is ...
• 1,033
1 vote

Reverse optimization: How to generate the expected portfolio returns given the weights and a series of constraints on those weights?

This is not yet an answer, but too long for a comment. Let's start without the box constraints and solely impose $\sum_iw_i=1, i.e. w^T\mathbf{1}=1$:  \begin{align} \max_w\quad & w^T\mathbf{\mu}-...
• 6,927
1 vote

Help me understand super replicating portfolio

I'm not familiar with super-replicating portfolios, but what I've gathered is that the idea is to find a static hedge that is greater than or equal to the asset with probability 1, ie find $a, b$ such ...
• 635
1 vote
Accepted

Value-at-Risk of a portfolio with a stock after recent IPO

You may be able to use a multi-factor model for the VaR, if allowed by whoever needs to approve/validate your VaR methodology. In summary, assume that there are a only few indices, and that every ...
• 12.6k
1 vote
Accepted

Standard deviation of large equal-weighted portfolios

This is incorrect at the step where you evaluate the double summation: $Var(R_P)=\sum_{i=1}^n\sum_{j=1}^n\frac{1}{n^2} Cov(R_i,R_j)$ You then have to consider two cases $i=j$ and $i \neq j$. For $i=j$,...
• 1,769
1 vote
Accepted

Why not inequality constraint in mean-variance portfolio optimization?

I'm not sure if I understand your question correctly. I'll try to answer, but you ay want to clarify what you're asking. I'll review portfolio optimization and constraints. Typically, you have a ...
• 12.6k

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