Correlation Question

There are benefits to diversification as long as: A) there is perfect positive correlation between the assets. B) there must be perfect negative correlation between the assets. C) the correlation coefficient between the assets is 1. D) the correlation coefficient between the assets is less than 1.

D

xck2000 Wrote: ------------------------------------------------------- > D Could you please provide an explanation?

1 is perfectly correlated so assets move concurrently. -1 is perfectly negative correlated so assets move inverse. 0 has no correlation so assets do not more in patterns. Does that help?

This question may look too simple, but I just don’t understand why the answer is D. My thinking process is that if two assets are perfectly correlated (perfectly move together), then diversification should lower the risk of the portfolio and add benefits. What’s wrong with my thinking here?

If two securities move together perfectly (both go up 1% together and down 1% together…) then it wouldn’t matter if you owned one or the other security becase they do the same thing. As long as the correlation coeff. is <1, you are diversifying some of the risk away of just owning one security. Does that help?

everything. If two assets move perfectly together, then you have not diversified even a single bit. ie. If two assets move perfectly together, and you add those two assets, then why not simply pick one of those two cuz your return is going to be same, regardless of which asset you pick or you pick both of them, and the weights dont even matter here. You diversify by adding assets such that the correlation coefficient of the new asset with every other asset is less than 1.

Wrong. Moving together in the same direction could mean moving together toward dezaster. Remeber we’re talking about diversification benefits? what do we diversify? RISK. Moving perfectly in the opposite directions makes the positive returns of one asset being totally cancelled by the negative returns of the other, 0 return overall. As long as they don’t move in the same direction sholder to sholder, risk is reduced.

rlange Wrote: ------------------------------------------------------- > If two securities move together perfectly (both go > up 1% together and down 1% together…) then it > wouldn’t matter if you owned one or the other > security becase they do the same thing. As long as > the correlation coeff. is <1, you are diversifying > some of the risk away of just owning one > security. > > Does that help? That helps marvelously! Pepp, your explanation is also great, thank you guys

map1 Wrote: ------------------------------------------------------- > Wrong. > > Moving together in the same direction could mean > moving together toward dezaster. Remeber we’re > talking about diversification benefits? what do we > diversify? RISK. > > Moving perfectly in the opposite directions makes > the positive returns of one asset being totally > cancelled by the negative returns of the other, 0 > return overall. > > As long as they don’t move in the same direction > sholder to sholder, risk is reduced. Now I’m confused again! Could you be a bit clearer please?

Map1, don’t bother I get it now. I didn’t read it carefully. I think I REALLY need some sleep right now or i’ll just go crazy…night night

hmmm sorry i was heading home. k… i think you got it, so if you do. Ignore me. so instead of thinking of it in math terms. think of 2 stocks. Coke and Pepsi. Both move in similar motions due to economic environments and the same line of business. So are positively correlated BUT not at 1, because they are different companies with different risk. So they could never be perfectly correlated. For the sake of example let us say correlation of 0.9. Let say you own both companies equally. say pepsi suddenly lost their plant due to superman going in and went on a massive sugar high and etc etc. Pepsi’s stock dies to 0, and coke is still around because Superman hates Coke. Because you diversified, you only lost half your stock. however if you had 1 correlation, they become the same company, and any possible event that happens to one, will effect the other the same way. So despite having a strong correlation due to normal occurrences. one still is effected by risk associated with itself, therefore still benefit from diversification. OMG sorry… i think this was more confusing then if we did variance calculations… :(, i tried.

I agree more with map1… if D was correct we could build a portfolio with stocks, all of which are correlated >0 and <1. But that will not diversify it, since all of them still move in the same direction… i should say that though <1 diversifies the portfolios, <0 is something that does it better…

Here an easy explanation: (to make it easy I assume 50:50-mix and same variance) x Asset 1 y Asset 2 z= Portfolio value= 0.5x+0.5y VAR(z)=VAR(0.5x+0.5y)=0.25 [Var(x)+Var(y)]+ 2*0.5*0.5*r(x;y)*sx*sy) = 0.25 [Var(x)+var(Y)+2*r*sx*sy] if we assume (to make it easier) same variances: =0.25 * (2*Var(x)+ 2 * r(x;y)*sx^2) =0.5*VAR(x) * (1+r(x;y)) This term is only smaller than VAR(X) if r(x;y)<1 VAR(X) is the Variance of an undiversified portfolio with only Asset X or only Asset Y.

This can be proven for any number of portfolioassets with different or same variances

This is happening because the two stocks are different… two stocks with <1 correlation diversify, but the actual benefit comes when you have <0 correalation This is because both of them move in the same direction… if we have a portfolio of two similar technology stocks, they ll be more diversified than any single one of them but doesnt eliminate any negative impact on tech stocks… if we diversify to two different sectors, it might make them more diversified… if you are talking about variances, take two stocks such that one variance is much greater than the other… though the portfolio variance < the higher one, it is greater than the lower variance value… the portfolio is diversified but doesnt mean that the variance of portfolio < each of its assets…

D