All Questions
Tagged with normal-distribution distribution
10 questions
6
votes
2
answers
685
views
Transformation to reduce standard deviation without changing median
Consider some negative skew and high kurtosis return time-series $X_t$. I do not know the functional form of the pdf of $X_t$ and have about 150,000 data points.
Suppose that I was to create an ...
- 61
4
votes
1
answer
231
views
Reconciling Two Claims About Volatility Under Fat Tails
I have read the Wikipedia article on volatility, and Nassim N. Taleb's Incerto, and found two statements attributed to Mandelbrot's views, which appear to be in contradiction.
Taleb (who was mentored ...
- 153
2
votes
1
answer
542
views
Quantile normal and lognormal
Let's assume we have a normal distribution $X\sim \mathcal{N}(\mu,\sigma^2)$. In a normal distribution the quantile can be calculated as follows:
\begin{equation}
\Phi_X ^{-1}(p)=\mu +\sigma {\sqrt {...
- 123
2
votes
2
answers
232
views
Problem with obtaining densities
For my research I need to obtain a series of densities, however, I am encountering some problems.
The first problem is perhaps very simple, but the answer eludes me. Let's say I have an observation ...
- 491
1
vote
1
answer
599
views
Value at Risk (VaR): Normal distribution with gamma distributed volatility
If I was to do a 99% VaR calculation on a portfolio with normally distributed returns $\mathcal{N} (\mu,\sigma)$, the 99% VaR would be $\mu - 2.33\sigma$.
Instead of having a constant volatility, let'...
1
vote
1
answer
477
views
Creating the histogram for the distribution of the portfolio returns
Given log returns for some stocks $A$ and $B$, which are the constituents of our hypothetical portfolio in equal weights, how does one actually come up with a distribution of the log returns of the ...
- 305
0
votes
2
answers
504
views
Log normal price simulation
I'm trying to figure out a spreadsheet I have which simulates 50000 returns in excel using the following function:
LOGNORM.INV(RAND(),0,0.35)-1
Question:
How ...
- 83
0
votes
1
answer
663
views
Theoretical distribution of (geometric) Brownian motion (with drift)
I am working on a simulation study which focuses on both the Brownian motion with drift (1) and the geometric Brownian motion (2). I denote them by $X_t$.
What are the theoretical distributions of ...
- 31
0
votes
1
answer
73
views
Quantile with periodic investing
Short Version
Can I get a quantile of such an expression?
\begin{equation}
\sum_{k=1}^{n} A_k\exp(\mathcal{N}(t_k\mu-\sigma\sqrt{t_k}/2,\sigma)))
\end{equation}
I know I can do it for one part of ...
- 123
0
votes
1
answer
115
views
Is the value also log-normally distributed?
My book assumes many times that $log(1+R)$ is normally distributed, so R is log-normal. But does this also mean that the value process is log-normal? Since $V=V_0(1+R)\rightarrow V/V_0=1+R$, and since ...
- 253