Portfolio Variance = Unrealistic theory??

[Jeffrey K.W. Lo]

With regards to the portfolio variance,

variance of the portfolio = (1/n)(avg. individual var) + [(n-1)/n][Avg Cov]

Is this purely a ?theoretical concept?? My natural instinct suggests that it is rather easy to find a very large sample n while maintaining an average covariance of 0, and then this equation will give a very small portfolio variance, but it will be inaccurate.

For example, i will
1) long HSBC in UK
2) short HSBC in HK
3) long temperature in new york
4) short temp in new jersey
5) long the weight growth of my dog
6) short the weight growth of my other twin dog

A portfolio like that will probably give me an avg cov of close to zero (I could be wrong here?). And if i use n=500 then the formula will give a VERY small portfolio variance, but will this small variance be accurate?

Thanks all in advance.

Jeffrey

 

[Yike Lu]

http://en.wikipedia.org/wiki/Arbitrage

 

[alain]

but will this small variance be accurate?

What exactly do you mean by that statement?