 # Quick question in Portfolio theory

Schweser mentions that when we add an asset to an existing portfolio which has a correlation co-efficient of less than 1, it would reduce the risk of the portfolio. Isnt this dependent on the wt of the asset added? In case a new asset having a correlation of 0.3 is added to a portfolio and its wt is 10% of the portfolio, will it reduce the overall portfolio risk?

as long as the assets are not perfectly positively correlated (+1), then the overall portfolio will benefit in terms of risk. Assuming that weight is >0%

It also depends on the stdev of the individual assets. If you have 2 assets, with stdev(A)=1 and stdev(B) = 100, even if correl(A,B)=0, then adding too much of B will obviously increase the overall risk. However, if stdev(A)=stdev(B) and correl(A,B)<1, then adding B to A will reduce overall risk. 2 stock portfolio stdev = sqrt(wA^2*sA^2+ wB^2*sB^2 + 2*wA*wB*correl(A,B)*sA*sB)

Exactly. So adding a new asset will not ALWAYS reduce the risk of the portfolio, It is subjective.

Chrismaths, think of what you said, but backwards: Say you had Asset B to start with (with stdev=100) and add Asset A (stdev=1) when they have a correlation co-ef. of less then +1. The portfolio will benefit from diversification and overall risk will decrease relative to a certain rate of return. I haven’t read through all the CFA material, so I’m not sure if this is in there…but to better understand this draw the minimum-variance frontier for these 2 assets. Mez

A better example: Asset B (stdev=100) has a return of 10%. So your current portfolio is earning 10% with a stdev=100 Now you add Asset A (stdev=20) with a rate of return of 2%. And Corr(A,B)=+.5 What would happen to your new portfolio’s risk (stdev) if you still wanted to earn 10%? Logically it would decrease, so now you are better off than with your original portfolio with a stdev less than 100 and STILL earning 10%

If you have a two stock portfolio in which one stock returns 10% and one stock returns 2%, the only portfolio which returns 10% is the one concentrated completely in one stock. The Schweser statement means that if the correlation is less than 1 then there is always some minimum variance portfolio which has some of each stock in it.

Joey, even if with shortsales? Like I said, I’m getting all this knowledge from my finance courses and not the CFA material.

If the correlation is 0, there is no covariance between the 2 assets. Therefore, there is no reason to split the investment between the two assets, when it comes to risk. Just pick the asset with the smaller standard deviation of return and you will get decreased risk for your portfolio.

This is not right. ^

map1 Wrote: ------------------------------------------------------- > If the correlation is 0, there is no covariance > between the 2 assets. Therefore, there is no > reason to split the investment between the two > assets, when it comes to risk. Just pick the asset > with the smaller standard deviation of return and > you will get decreased risk for your portfolio. Better go read that section again…

Mez Wrote: ------------------------------------------------------- > Joey, even if with shortsales? > Like I said, I’m getting all this knowledge from > my finance courses and not the CFA material. Right even with short sales (althyough with leverage if it costs you less than 2% you have more degrees of freedom)

chrismaths [just clicked hide posts from Mez and map1] *clickety*