Hi

@Bernardo,

your statement is partially correct: In the case of correlation coefficient = 0, then the portfolio std dev (sigma p) gets to zero the larger N (no of securities), however, as you can see the correlation coefficient is the critical point here in the portfolio std dev equation.

In any case where correl coefficient,

**rho **(ρ) is

**greater than 0**, portfolio std dev is positive (greater than zero).

In the case of perfect positive corre (

**rho = 1**), portfolio std dev equals the std. deviation of the securities (sigma)

1.) example: N = 50, sigma =

**0,14**, rho = 1

**sigma(p) **= 0,14 * sqrt [1/50 + (1-1/50)*1] =

**0,14 **
2.) example: N = 200, sigma =

**0,21**, rho = 1

**sigma(p) **= 0,21 * sqrt [1/200 + (1-1/200)*1] =

** 0,21**

1.1) example 1.) example: N = 50, sigma = 0,14, rho = **0.2**
**sigma(p) **= 0,14 * sqrt [1/50 + (1-1/50)*0.2] = **0,14 = 0.065**
**>>> The smaller rho becomes, the smaller the portfolio std dev. **
**And yes, portfolio std dev. is the product between the individual securities sigma and the term on the right-hand side involving the no. of assets (n) and rho.**
In addition, I have posted this over one year ago in the forum. Perhaps it is helpful:
https://www.bionicturtle.com/forum/...ariance-for-the-entire-stock-portfolio.10153/

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