# Tagged Questions

The normal-distribution tag has no wiki summary.

5answers
339 views

### In Black-Scholes, why is $\log{\frac{S_{t+\triangle t}}{S_t}} \sim \phi{((\mu - \frac{1}{2}\sigma^2)\triangle t, \sigma^2 \triangle t)}$?

Namely, I dont understand why the mean is $(\mu - \frac{1}{2}\sigma^2)\triangle t$ and not just $\mu \triangle t$. I am aware that it is supposed to represent a lognormal distribution, but I guess I'm ...
2answers
87 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 ...
0answers
69 views

### How to trade risk-adjusted returns?

Why does dividing daily returns by daily range eliminates fat tails and results in an (almost) gaussian distribution? And how could that distribution be exploited to enter trades?
1answer
126 views

### normalized accumulation distribution

I am looking for a way to take an accumulation/distribution indicator and normalize it so I can compare a bunch of stocks with stock prices that have no relationship with each other. EDIT: This ...
1answer
341 views

### a simpler test for normality given skewness, kurtosis and autocorrelation and size of time series

I typically do a JB (Jarque Bera) test and DW (Durbin Watson) tests for check for normality given skewness, kurtosis and autocorrelation of the data. However this requires a CHI distribution table ...
1answer
397 views

### Monte carlo portfolio risk simulation

My objective is to show the distribution of a portfolio's expected utilities via random sampling. The utility function has two random components. The first component is an expected return vector ...
2answers
511 views

### Whats the equation to calculate the area under the curve of a normal distribution, given an upper and lower standard deviation?

Lets say I want to find out the area under the graph of normal distribution curve, between X1=standard deviation of -0.5 and X2 = standard deviation of 0.5. Is there a formula for this? Case study: ...
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