With regard to diversification, if two investments are correlated in their response to economic conditions, then they are not providing diversification. So, for diversification purposes, the less correlated two investments are, the better. Is it therefore also the case that anticorrelation is to be avoided to achieve diversification? For example, it seems pointless to invest in both a strengthening dollar fund and a weakening dollar fund. So, for diversification it is ideal to avoid both correlation and anticorrelation, and to seek zero correlation between two investments? If so, what about owning both equities and bonds? Are they not anticorrelated? I would like to understand diversification better.

The idea underlying diversification is to achieve a desired expected rate of return at the smallest possible risk. If there are two investments that are perfectly negatively correlated, then by investing in both you could achieve a rate of return that is the average expected rate of return of the two investments without risk. For example, suppose investments A and B yield the following rates of return:

{A=10%, B=0%} 1/3 of the time

{A=5%, B=5%} 1/3 of the time

{A=0%, B=10%} 1/3 of the time

Investments A and B are perfectly anticorrelated, and both have an expected rate of return of 5%. If you invest half of your money in each, you will get 5% rate of return with no risk.

In an alternative example, suppose investments C and D yield the following rates of return:

{C=10%, D=-10%} 1/3 of the time

{C=5%, D=-5%} 1/3 of the time

{C=0%, D=0%} 1/3 of the time

Investments C and D are also perfectly anticorrelated, but C has an expected rate of return of 5% and D has an expected rate of return of -5%. If you invest half of your money in each, you will get 0% (=(5%+(-5%))/2) rate of return with no risk. In fact, this case illustrates the case you mention about simultaneously investing in a strengthening-dollar fund and a weakening-dollar fund.

What the above examples show is that perfect anticorrelation allows you to obtain a riskless portfolio, which is something impossible to get with investments (or investment portfolios) which are not perfectly anticorrelated.

In the real world, arbitrage makes it highly unlikely that you will find assets that are perfectly anticorrelated and allow you to obtain a riskless rate of return higher than the rate at which you could borrow funds. If such a situation arises, say you could borrow at 2% to invest in a risk-free portfolio giving you a 5% rate of return, then you should borrow as much as possible because you would get $3 for each $100 borrowed (i.e., you would get $3 "for free" because you are not investing any of your own money, so that's a "free lunch"!!!). Clearly, if you borrow and invest large amounts, either the 2% at which you borrow will go up, or the 5% return on your investment portfolio will go down, or both, until you are no longer able to get $3 of “free” money for each $100 borrowed.

So the typical situation is one where diversification is done with assets that are not perfectly correlated (which could include both less-than-perfectly-correlated and less-than-perfectly-uncorrelated), so as to achieve the desired balance between risk and expected rate of return.