3
votes
Calculating tangency portfolio weights with the given information? (2risky +riskfree asset)
The denominator $1^T \Sigma^{-1} U_e$ is a scalar number. First you multiply the inverse by $U_e$ giving a column vector which I will call $X$, then premultiplication of this vector by $1^T$ basically ...
- 10.9k
2
votes
Accepted
Derivation of optimal portfolio weights using Risk Budgeting approach
You are correct in your assumption, this is specified at the start of section 2.2.1 Definition of a risk budgeting portfolio.
We consider a set of given risk budgets $\{B_1,\dots,B_n\}$. Here
$B_i$ ...
- 1,736
2
votes
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. ...
- 21
2
votes
Accepted
Difference between Maximum Drawdown and Largest Individual Drawdown
From your (or rather Bacon's) description, it seems to me that
the "Largest Individual Drawdown" would more properly
be called a losing streak, or a run of negative
returns. Since you seem ...
- 3,186
2
votes
Accepted
Confusion about the formula for gain process in a financial market
@nbbo2 Thank you very much for providing this useful reference, I had a look into it and I think I understand now :)
For simplicity, let's take $A \equiv 0$, $\delta \equiv 0$ and $r(s) \equiv r$ (it ...
- 151
2
votes
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:
\begin{equation}
w_1 = \frac{\mu_1\sigma_2^2 - \mu_2\rho\sigma_1\sigma_2}
{\mu_1\sigma_2^2 - \mu_1\rho\...
- 569
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
...
- 1,009
1
vote
Accepted
Solving Equation for estimation risk averse parameter
You can think about it like this: given $\mu,\sigma,r$, a risk aversion parameter $\gamma$ will induce an optimal weight $w(\gamma)$, which in turn will induce some value at risk $VaR_{\alpha}$.
Hence ...
- 6,445
1
vote
Accepted
calculating portfolio weight for long short
The first one. Your net weight is zero. This is a self financing strategy. Think of it this way: if apple goes up by 10% and google goes down by 5% your return will be:
$r_p = 1 \times 10\% - 1 \times ...
- 8,062
1
vote
Calculating variance of long/short portfolio
I think your are really asking how to normalize the weights. For example,
$$
\begin{align}
w_\textrm{usd} &=
\begin{bmatrix}
100 \\ 50\\ -200\\ 51
\end{bmatrix},\\
&~\\
w^\prime &= \frac{...
- 206
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