# Portfolio mngt-Corr

Schweser page 120 Q#9. Question states that SD btwn 2 risky assets are same and corr is less than +1. Will portfolio SD increase,decrease or remail same? In my views, the info given is not sufficient as we do not know whtr corr is +ve or -ve. But answer states the portfolio Sd will decrease. m confused. M i missing smthing?

that is the whole point of diversification. as long as the 2 stocks are not perfectly correlated, you are better off holding some of stock A and holding some of stock B…why? well, you get a higher return with lower volatility (st dev)…I’d def go over this material again. it shows up on level 2 in much heavier detail think about a concrete example, if you could buy an airline stock and an energy company, wouldnt you rather make a portfolio f these 2 stocks rather than putting all the mula in just one - when oil goes up, airlines will get crushed, but the energy company - since it is a PRODUCER of the commodity - will net higher profits, theoretically at least. so that is the gist of it. diversifty and uses correll to determine what assets you want to place into the porfolio…it goes beyond this, of course, but this should get you started

thanks daj.Very well explained…

but i still have sm confusion. If i understand it correctly, a +ve correlation would mean assets move in the same direction and will have some +ve covariance.n if it has +ve covariance, it will add to the risk of portfolio. In the question, it states corr of less than +1 which cud b +ve as well as -ve. so how come a +ve corr reduce SD of portfolio?( i understand a -ve corr will reduce risk n Sd of port.)

hks_3854 Wrote: ------------------------------------------------------- > but i still have sm confusion. If i understand it > correctly, a +ve correlation would mean assets > move in the same direction and will have some +ve > covariance.n if it has +ve covariance, it will add > to the risk of portfolio. In the question, it > states corr of less than +1 which cud b +ve as > well as -ve. so how come a +ve corr reduce SD of > portfolio?( i understand a -ve corr will reduce > risk n Sd of port.) Make up a two asset example - choose a standard deviation, and set both assets SD to that number. Then set correlation to +1. You will find that portfolio SD equals the SD of the indivual assets. Try it on excel so that you can vary the weights of the individual assets. You’ll see that the portfolio SD is the same as the individual SDs no matter the weights. You’ll also see that the covariance is the same as the variance of the assets. Now set correlation between 0 and 1. This will result in portfolio SD being less than the individual SDs. In addition, the covariance will be less than the individual variances. A perfect correlation means two assets move IN LOCKSTEP. IOW, they are effectively the same asset. So combining them results in no reduction in risk - adding asset B to asset A would be the same as adding Asset A to Asset A. But if correlation is < 1, there are somes states of the world where the two assets move in opposite directions (A has a low return, but B has a high one). In these cases, the combination of A and B goes down less than either asset by itself. Think of covariance as the weighted average cross-deviation in returns. In other words, it measures the extent to which the return on asset A is above it’s mean when asset B’s is above its mean (and the same for being below its mean). Correlation just scales covariance by standard deviations. One other thing - an asset’s variance is just it’s covariance with itself. So, the portfolio variance formula is just the weighted average of all the COVARIANCES in the portfolio. When correlation is < 1, the covariance of two assets will be less than the weighted average of the individual assets variances. So, the covariance lowers the weighted average (which is the portfolio variance). This isn’t as tight an explanation as I’d like, but I have 5 10-year old boys over for a sleepover with my son (part of his birthday), and they make a LOT of noise. So if this doesn’t make sense, let me know and I’ll clean it up later.

thnks busprof. i was actually missing simple mathmtical trick that corr btwn 0 and 1 will actually decrease portfolio SD(fraction alwys decreases the value).-ve corr will nywys decrease prot. SD.But ur explanation helped me grasp sm other imp points…thnks again n happy b’dy to ur son(it might b beleted coz of geographic timimg diff)

another query…in practical mkt situation, how does it work? What would a port. mangr prefer? A +ve corr in a portfolio or -ve corr? Would a -ve corr mean sacrificing on returns (i mean -1 corr. means if 1 asset is going up another is going down and hence thr can not b a possibility of a gain.Return will always b 0).

Pms strive for a mix of negatively correlated assets. you would never want all concentrated positions b/c the major tenet of finance is to diversify. maybe a HF mngr would make a serctor bet and concentrate, but they run an altogether different game than the Street.