Correlation and return

CFA Level I
#1

Hey guys!

There is an example in Schweser notes:

"Consider two risky assets that have variance of 0.0625 and 0.0324. Standard deviation are 25% and 18%.

Calculate standard deviation for equal-weighted portfolio when correlation 1; 0.5; 0 and -0.5.

The answer: standard deviations are 21.5%, 18.7%, 15.4%, 11.17%."

So the negative correlation gives us less risk.

Here is the question. What is the relationship between this correlation of variances and portfolio returns?

is there direct relationship between positive correlations and return, correlations -0.5 and return of portfolio and so on?

#2

The idea of adding stocks to your risky portfolio is the diversification. Adding stocks that have correlation of returns lesser than 1 with the others is a benefitial because it reduces risk but mantain return. If you diversify enough, you reduce your exposure to total risk to only systematic risk (which is lower than total risk). If correlation is negative somewhere, you will reduce total risk in a higher degree than having a positive correlation somewhere. So the relationship is, the lower the correlation of returns, the lower the portfolio risk; however risk is bounded to a floor risk equal to systematic risk. Hope I explained it clear enough.

#3

Thx! However I meant the relationship between correlation and return as profitability (not the relationship between correlation and risk). Is there any relationship?

For example, taking previous example, what will be overall return of portfolio if correlation =1, and what will be return of correlation =-0.5 ? Higher?

Intuitively I understand that the lower risk the lower profits. However I don’t get the direct relationship between correlations and profits (return).

#4

Nope, the level of return will only change if you change the weights of each stock inside the portfolio.

Expected Portfolio return = w1*R1 + w2*R2 + … + wn*Rn

where Ri = Expected return on stock “i”

As you see above, the portfolio return is not in function of correlation of returns. Thus, correlation does not affect portfolio return.

Portoflio risk (std dev of returns) = sq root [w1^(2)*var(R1) + w2^(2)*var(R2) + … + wn^(2)*var(Rn) + 2*w1*w2*StdDev(R1)*StdDev(R2)*Corr(R1,R2) + … + 2*wn-1*wn*StdDev(Rn-1)*StdDev(Rn)*Corr(Rn-1,Rn)]

As you see above, portfolio risk is in function of correlation of each pair of stocks. Thus, the lower the correlation between pair of stocks (negative even better), the lower the portfolio risk.

You are intuitively right, lower risk, lower profits; however you must not expect more profit for taking undiversified risk. I explained it in my previous response, diversification reduces total portfolio risk (systematic risk + unsystematic risk) to only systematic risk. You must relate portfolio returns with systematic portfolio risk, not total risk.

Hope this helps!

#5

Thx! Now it’s much more clear :wink:

#6

I am glad you could read my post in 3 minutes. Yeah!

#7

Lol

it was perfectly understandable :wink:

#8

I’m happy then :slight_smile: