 # portfolio standard deviation

Can someone explain this statement to me: When assets are positively correlated, there is no diversification benefit. I know that portfolio standard deviation is maximized when the assets are positively correlated, but what does this have to do with diversification? I must be missing something here.

in modern portfolio theory diversification is equivalent to volatility (stdev) reduction. The higher diversification - the higher stdev reduction. If you invest in assets that have high correlation to each other stdev is not reduced significantly - no diversification effect. another way to look at diversification - portfolio return is not very sensitive to any market/asset. If assets have high correlation and one asset loses a lot of money, most likely other assets are also losing a lot of money which means high loss for the portfolio (high sensitivity to individual market/asset behavior -> low diversification). If assets have low correlation to each other and one asset loses a lot of money hopefully other assets are going to compensate the loss or its portion (low sensitivity to individual asset behavior -> high diversification). I hope that helps.

I think the statement should be “When assets are PERFECTLY positively correlated, there is no diversification benefit.” i.e. when the correlation coefficient equals 1. whenever it is below 1 , there IS a diversification benefit. The closer it gets to -1, the bigger the benefit. Right?

YeahYeah, my understanding is that the original passage cited is accurate. If you own a portfolio consisting of two assets that are positively correlated, their returns will likely move together, which means that gains on one asset won’t offset losses on the other; they’ll both generate either a gain or a loss, but to what relative extent? If the assets are perfectly correlated, the standard deviation (risk) of portfolio returns will be maximized. If they’re positively correlated, but less than perfectly, the standard deviation is reduced but there’s still no diversification benefit until the correlation becomes negative, at which point gains on one asset should offset losses on the other to an extent. Anyway, that’s my caveman rationale.

I thought that as long as the correlation is less than positive one there is a diversification benefit.

Niblita75 Wrote: ------------------------------------------------------- > I thought that as long as the correlation is less > than positive one there is a diversification > benefit. Yea I thought so too. If you plot the graph of a portfolio of 2 assets, any correlation lower than p = 1 gives you a lower risk for any combination of those 2 assets.

The second “any” isn’t right. If the correlation is < 1 then there is some minimum risk portfolio that contains some of each security.

anerak321, I might not be correct but this is what I had understood when I was going through the Portfolio Management study Session’s. Friends, please correct me if I am wrong, as I am still in the process of learning and being from a tech background, it’s even more difficult to retain this voluminous material as ever page is new to me. Anyways, here’s what I think!! Consider a portfolio ‘P’ with 2 Risky Assets ‘A’ and ‘B’ If Returns (A) and Returns (B) are perfectly positively co-related i.e. Corr (A, B) = +1 1. Then a Loss of say \$10 in Stock A will also mean an exact same amount of loss in Stock B and the Overall Portfolio performance will be screwed. 2. There is 0 Diversification benefit in this case. If Returns (A) and Returns (B) are positively co-related i.e. Corr (A, B) > 0 but Corr (A, B) < +1 Ex Corr (A, B) = 0.6 1. Then a Loss in Stock A will mean a loss in Stock B but not to the exact same extent, so some risk has disappeared away due to not having perfect positive co-relation between the stocks in the portfolio. 2. There is some amount of diversification provided in this case If Returns (A) and Returns (B) are perfectly negatively co-related i.e. Corr (A, B) = -1 1. Then a Loss of say \$10 in Stock A will also mean an exact same amount of gain in Stock B and the Overall Portfolio performance will be very good 2. There is 100% Diversification benefit in this case If Returns (A) and Returns (B) are negatively co-related i.e. Corr (A, B) < 0 but Corr (A, B) > -1 Ex Corr (A, B) = -0.3 3. Then a Loss in Stock A will mean some gain in Stock B but not to the exact same extent. 4. There is some amount of diversification provided in this case From all the 4 cases we can conclude that, the portfolio will be diversified if the Correlation between the assets in the portfolio is NOT perfectly positively co-related with complete diversification provided when the assets are perfectly negatively correlated So any value of Correlation less than +1 will provide us some diversification benefits in some way or the other. So, the above sentence looks a bit incomplete to me. IT should have been When assets are perfectly positively correlated, there is no diversification benefit.

If the only way to get diviersification is by having perfectly negatively correlated assets, then diversification in practice is impossible, which is not true. You can still diversify all the way up to a perefctly positively correlated assets situation. Dreary

it would help if you look at diversification in terms of volatility reduction.

Thanks dinesh.sundrani. Your answer helped me clear my confusion. Thanks a ton.

Two assets dont have to be perfectly negatively correlated to obtain diversification…they only need not be perfectly positibvely correlated. Think about it in the simplest form: If you have two securities that are perfectly positively correlated, when one asset increases 5% the other will increase 5% as well. So what is the pt of holding both securities? Just as well off putting all your money in one of them - same result. However, if they are not perfectly positively correlated, they will not yield the same result…so you benefit from the additional security in some sense. If one secutity goes down 5% the other may decrease by 4.5%. You are better off having that second security in your portfolio rather than not having it and haveing twice as much of the first security. If two assets are perfectly negatively correlated…you have maximum diversification and your are perfectly hedged.

I believe that some of you are thinking about this wrong (or maybe I am)…Diversification benefits from non correlated assets arise when the whole (the portfolio) is greater than the sum of its parts (individual assets classes, stocks, bonds, etc). So you could have two assets that are perfectly positively correlated, but don’t move the exact same. For example, asset A goes up 10% and asset B goes up 5%…then asset A goes down 10% and asset B goes down 5%. Even though they don’t track each other exactly they are still perfectly correlated…+1. So if you had a portfolio of all asset A and you then added asset B you would reduced the overall volatility of the portfolio, but you didn’t really gain any diversification benefits. The whole is still equal to the sum of the parts. On the other hand if you added asset C which is has zero correlation with A and B, then the portfolio would show less volatility (or more gain for the same vol) than the sum of the individual assets. This is the basics of MPT here. If you go back to the formula for standard deviation of a two asset portfolio you can convince yourself of this. The third set of terms in that formula the key to understanding what I am pitifully trying to convey here. All that being said, anything less than +1 will give diversification benefits. I think that everything I am saying is correct, but would be happy to be corrected. Hope this helps.

Perfect!! I guess, Everyone’s’ beating around the same bush. Best way to think of diversification is to think of it as ‘volatility’ - Dinesh S