# Tag Info

Accepted

### Why does the Markowitz mean-variance model require the assumption of normality?

it doesn't require normality. What it requires is that the investor's decisions are determined by mean and variance. A normal distribution is determined by mean and variance, so if you assume joint ...
• 6,983
Accepted

### Why is it so rare for finance theory to depart from the normal distribution?

The Geometric Random Walk: The Starting Point Let me begin by being a little more specific. The simplest, yet relatively sound model of asset prices that we have is this one: ln S(...
• 2,486

### Is there a closed-form solution for the following integral?

Thanks to Gordon's help, we have that \begin{eqnarray*} F=exp\Big\{d + \frac{{c}^2}{2}\Big\}\Big[ \Phi\Big(\Phi^{-1}\Big(1+b\Big)-{c}\Big)- \Phi\Big(\Phi^{-1}\Big(a+b\Big)-{c}\Big)\Big] \end{eqnarray*}...
• 419
Accepted

### Show that $(W_t, \int_0^t W_s ds)$ has a normal joint distribution

Note that \begin{align*} \int_0^t W_s ds &= tW_t -\int_0^t sdW_s \tag{1}\\ &= \int_0^t (t-s)dW_s. \end{align*} Then, for $\lambda_1, \lambda_2 \in \mathbb{R}$, \begin{align*} \lambda_1 W_t + \...
• 21.2k
Accepted

### Reconciling Two Claims About Volatility Under Fat Tails

I don't think the claim that "Lévy alpha-stable distributions are better descriptors of returns" is universally accepted. While Mandelbrot (and others before him) has correctly identified ...
• 233
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### Quantile normal and lognormal

Quantiles are preserved under monotonic transformations, hence the quantile for $Y$ is simply the exponential of the quantile of $X$, no need for corrections whatsoever (see here for instance). Put ...
• 14.7k
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• 2,432

### Portfolio Theory: Why is so much effort put into the reduction of estimation errors?

In MPT investors maximize ex ante expected return for a given level of ex ante variance. Gaussian-ity or iid-ness of returns are not requirements. The problem is estimating these ex-ante quantities ...
• 4,337

### If equity returns are normally distributed, why are average equity returns not zero

Well there are two misconceptions in your assessment of how returns behave. 1) Returns can be normally distributed or not; 2) Even if they are normally distributed it does not mean that returns ...
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### If equity returns are normally distributed, why are average equity returns not zero

It's news to me that in today's world anybody really believes that equity returns are normally distributed. For instance in US Senate testimony by a Goldman Sachs CFO, under assumptions of Gaussian ...
• 169

### What is the Probability Distribution of Max-Drawdown?

I think the answer you're looking for is very similar to this question Expectation of maximum draw down in the Brownian motion case. just like your assumption that return is normally distributed with ...
• 609
Accepted

### Why can we assume that asset return rates are normally (or lognormally) distributed?

In the colloquial sense of the word "justified," it is not justified. I will describe why it is justified mathematically and under what circumstances and in what case it is not justified. ...
• 4,299

### Transforming non-normally distributed interest rates for OLS regression

You do not need to transform the variables into normally distributed data in order to use them in a regression. That is not a requirement of ordinary least squares. If the error terms are normally ...
• 4,299

### Asset return distribution

In the Black Scholes (1973) model, the stock price is assumed to follow a geometric Brownian motion $\mathrm{d}S_t=S_t\mu \mathrm{d}t + S_t \sigma \mathrm{d}W_t$. If you solve the SDE, $(S_t)$ is log-...
• 16k

### Simulating covariance matrices with nonzero correlation

I will just clarify Point 2 in StackG excellent answer. (It's really a comment, but it's too long and has too much math symbols to fit in the comment field.) Suppose you're given a covariance matrix \$...
• 12.5k