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3
votes
1answer
72 views

Why does Bloomberg's HRH test the simple returns for normality?

On a Bloomberg terminal, it is possible to use the HRH (Historical Return Histogram) function on individual assets. It basically generates a histogram of the (simple) returns and overlays them with a ...
0
votes
1answer
36 views

Should earnings be modelled normally or lognormally?

I am having difficulty deciding whether a company's earnings should be modelled normally or lognormally. If we consider two arguments: (i) The earnings of a company are the returns on the assets of ...
2
votes
2answers
104 views

The Distribution of Future Stock Price

In Hull, we are presented that $$\frac{\Delta S}{S_{0}}=\mu \Delta t+\sigma\sqrt{\Delta t}\cdot \varepsilon.$$ Following some algebra, $$ \begin{align*} \frac{\Delta S}{S_{0}} &=\mu \Delta ...
1
vote
2answers
92 views

Confidence Intervals of Stock Following a Geometric Brownian Motion

In preparation for my Options, Future's and Risk Management examination next week, I have been presented with a series of questions and their answers. Unfortunately, my lecturer, one of the less ...
1
vote
0answers
92 views

Monte Carlo simulation returns not normal distributed

I am generating 100,000 paths of SPX out to 1 year using Euler discretization. I look at how S is distributed for 100,000 paths at the 1 year point and I find it is lognormally distributed. I look at ...
0
votes
0answers
14 views

Use orthogonal decomposition to compute the optimal return for a CARA investor

Question from Back, 5.8. If all returns are joint normally distributed, then $R_p$, $e_p$, and ε are joint normally distributed in the orthogonal decomposition R= $R_p$ + $be_p$ + ε of any return R ...
2
votes
1answer
117 views

Portfolio choice problem of a CARA investor with n risky assets

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
1
vote
0answers
43 views

Stock prices and probability

Lets say that the current price of a security is £245 , $\mu =5%$ and $\sigma=32%$ Assume that the natural logarithm of $\frac{S_{t +\delta t}}{S_t}$ is approximately normally distributed with mean ...
-1
votes
1answer
75 views

Probability distribution and Stock Price Movement [closed]

How can we use normal distribution for finding the probability of a stock price offer where current price offer depends upon the last price offer. The price offer on some day can go 10% above (at the ...
2
votes
1answer
63 views

Variability in the Expected Shortfall estimator

Are there any results for calculating the variability in the Expected Shortfall measure. I am looking for Large sample confidence intervals under Normality for Expected Shortfall or calculation of ...
0
votes
1answer
67 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 ...
0
votes
0answers
12 views

Distribution of the differences of the inverse of the integral of a Gaussian Distribution

I have a time series, $P$, undergoing geometric Brownian motion, which varies between $1$ and $1000$. I difference it $P(t) - P(t-1)$ and can see the differences are distributed according to a ...
1
vote
1answer
96 views

Can Standardized unexpected earnings be considered a Z-score

According to this wikipedia: http://en.wikipedia.org/wiki/Earnings_surprise, the SUE score is a "standardized" difference between reported earnings and expected earnings. Therefore, can the SUE score ...
6
votes
2answers
291 views

Normally Distributed Returns Become Leptokurtic Due to Compounding

I was running a bunch of simple simulations in excel the other day in excel. Using the NORM.INV(RAND(),0,1) to simulate daily stock returns I noticed that the more compounded the returns, ie, the more ...
2
votes
2answers
867 views

An alternative to the Gaussian distribution to describe/fit market stock returns

After the financial crisis in 2008, many people (including me) don't really believe that stock returns can be described in terms of the normal distribution (Gaussian distribution). But besides the ...
0
votes
0answers
94 views

Stock Price Question

Can anyone show me how to answer this please? A stock has beta of 2.0 and stock specific daily volatility of 0.04. Suppose that yesterday’s closing price was 95 and today the market goes up by 3%. ...
0
votes
0answers
104 views

BS Implied Volatility under Normal returns

If I use theoretical prices under a normal valuation model, and I estimate their implied volatility using BLACK SCHOLES implied volatility, do I'll get corresponding log normal volatility?
2
votes
1answer
343 views

Interpretation of cross-correlation matrix when one sample distribution is not normal

I am looking at the variance of (log) price changes in securities vs. the amount of social media discussion about them. I'm not interested in building a model. I'm just looking to see if there is a ...
3
votes
1answer
235 views

What is the correct Stutzer index and Sharpe ratio relation, assuming a normal returns distribution?

Assuming the returns distribution is normal, then there is a relation between Stutzer index and Sharpe ratio. However, I found in the following paper 2 different equation: Paper I (page 10-11)‎ ...
3
votes
1answer
236 views

How to design back-testing (validation) for such modified Vasicek model?

Consider a classical Black Scholes model , $$\frac{dS}{S} = \mu dt + \sigma dW$$ , where $dW$ is a Brownian motion, that $W(t_1) - W(t_0) \sim N(0, t_1 - t_0)$. The back-testing strategy is ...
2
votes
1answer
74 views

Creditworthiness indicator for copula one-factor model

In this paper in equation 15 on page 261 dealing with one factor copula model, one is using creditworthiness indicator as one of a variables. It is defined as \begin{equation} Y_c = \sqrt{\rho_c} Z ...
4
votes
5answers
598 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 ...
3
votes
2answers
307 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 ...
2
votes
0answers
79 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?
1
vote
1answer
302 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 ...
2
votes
1answer
690 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 ...
8
votes
1answer
651 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 ...
1
vote
2answers
885 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: ...