# Diversification - Correlation - Covariance **DOESN'T MAKE SENSE**

Adding securities that are highly correlated reduces the number of stocks you need to achive diversification? WHAT HECK is this? This is from the CFAi books…

What if the correlation among stocks is higher than 0.30? Suppose an investor wanted to be sure that his portfolio variance was only 110 percent of the minimum possible portfolio variance of a diversified portfolio. How many stocks would the investor need? If the average correlation among stocks were 0.5, he would need only 10 stocks for the portfolio to have 110 percent of the minimum possible portfolio variance. With a higher correlation, the investor would need fewer stocks to obtain the same percentage of minimum possible portfolio variance. What if the correlation is lower than 0.30? If the correlation among stocks were 0.1, the investor would need 90 stocks in the portfolio to obtain 110 percent of the minimum possible portfolio variance.

That section is very poorly written, so it’s not surprising that you don’t follow what they’re trying to convey.

If the average correlation of returns is +0.30, then you’ll get some level of diversification benefit. If the average correlation of returns is +0.80, you’ll get a smaller level of diversification benefit.

What they’re saying is that when the average correlation of returns is +0.80, it may take 5 stocks to get 90% of the maximum (smaller) diversification benefit, while if the average correlation of returns is +0.30 it may take 10 stocks to get 90% of that (larger) diversification benefit.

It’s an unusual comparison, but that’s what they’re saying.

S2000magician - Thank you! I still don’t get it because… Portfolio1 = Apple, google, samsung (assuming they are all in the same industry) Portfolio2 = GE, Apple, Toyota I would argue that Portfolio 2 is more diversified given the same # of securities. So, the lower the correlation the more diversification benefits you get. CFAi - still doesn’t make sense

Portfolio 2 is more diversified.

They’re not saying that portfolio 1 is more diversified.

They’re saying that for portfolio 1 the greatest diversification benefit you can get is a reduction of 0.5% in standard deviation of returns, and that you can get, say, 90% of that reduction with only three stocks. For portfolio 2 you can get a reduction of 4.5% in standard deviation of returns, and that to get 90% of that reduction you’ll need eight stocks.

Wouldn’t it be otherwise? I think that Portfolio 1 needs fewer stocks to get the 90% diversification benefit. The Portfolio 2 as having highly correlated stocks it will need much more quantity of stocks to obtain the 90% diversification benefit, other stocks that are less correlated with the previous 3 of course.

Portfolio 1 has highly correlated stocks as they are all in the same industry!

Portfolio 2 contains stocks of different industries.

CFAi is saying that for a portfolio of highly correlated stocks you need less # of stocks to achieve diversification versus portfolio 2 which has lower correlation…so you’ll need more stocks to achieve diversification.

There has to be a better way to explain this

But what they’re _ not _ saying is that you achieve _ the same amount of diversification _. That’s the key.

For your portfolio 1, at best you’re going to get very little diversification benefit, while for portfolio 2 you’re going to get a lot of diversification benefit.

All they’re saying is that if there’s not a lot of diversification benefit to be had (portfolio 1), you can get most of it with only a few stocks; if there’s a lot of diversification benefit to be had (portfolio 2), it takes more stocks to get most of that.

With 3 stocks in portfolio 1 you get nearly all of the potential diversification benefit, which is very little. With 3 stocks in portfolio 2, you’ll get more diversification benefit than you get in portfolio 1, but you’ll get a smaller percentage of your potential diversification benefit, because the potential is much greater.

Thank you Magician!

That makes sense now!

Whew!

I meant Portfolio 2 and Portfolio 1 respectively. Sorry.

Hey Harrogath,

How many people in Peru take the CFA exams?

Hey Harrogath,

How many people in Peru take the CFA exams?

Hi Rasec,

About 300 people for the Level I 2014 December exam. Was nice to see some people from other countries too who took the exam in Lima

Regards

Entonces el CFA esta de moda en Peru? Yo soy Peruano y trabajo en Washington DC.

Desde que la SBS reguló que las áreas que manejan activos de inversión o fondos del público tengan empleados con una certificación internacional en finanzas, ya sea CFA, FRM, CAIA, etc ahora se ha puesto más de moda incluso, ya no es tanto un grado diferenciador, ahora se convierte poco a poco en un standard y un requisito para ingresar a ciertos puestos. Eso me parece bien, el mercado financiero peruano es reconocido por su acertado manejo del riesgo y la prevención de crisis, además celebramos de tener el mejor banquero central del mundo

Saludos Rasec, y qué gusto ver peruanos exitosos en el WDC. Un abrazo.

Ahora ya no basta que tengas un titulo universitario de una buena uni? Ahora quieren un CFA charter? Pasu!

Te mando mi correo para mantenerdos en contacto. Quiero conocer mas Peruanos que trabajan en el campo de finanzas.

Perea.cesar [arroba] G M A I L PUNTO COM

-Cesar