Question

How can investment correlation be used to reduce investment volatility while increasing invest return? Provide a simple example to illustrate your answer.

Answer 1

The reduction of investment volatility (measured by standard deviation of investment return) can be achieved through diversification of investment in assets with low or nil correlation (low correlation coefficient )

Diversified folios with low or nil correlation can reduce the risk and increase return.

If w1, w2 , w3 …wn are weight in the portfolio for assets 1, 2,3 ….n

Then,w1+w2+w3+……………………+wn=1

R1, R2,R3,…….Rn are the return of the assets 1, 2 , 3 ….n

S1, S2, S3……Sn are the standard deviation of the assets 1, 2, 3 …n

Portfolio Return=w1R1+w2R2+w3R3+…….+wnRn

Portfolio Variance=(w1^2)*(S1^2)+(w2^2)(S2^2)+………….(wn^2)*(Sn^2)+2w1w2*Cov(1,2)+2w1w3*Cov(1,3)+………+w(n-1)wn*Cov(n,(n-1)

Cov(1,2)=Covariance of returns of asset1 and asset2

If the correlation between the return of assets are zero,

Portfolio Variance==(w1^2)*(S1^2)+(w2^2)(S2^2)+………….(wn^2)*(Sn^2)

Portfolio Standard Deviation =Square root of Portfolio varianc

Suppose we have investment in asset A with mean return of 12% and standard deviation of 8%.

We can increase return and decrease volatility (standard deviation) in an uncorrelated asset B with Reurn 15% and standard deviation 10%

Return of assetA=Ra=12%

Return of assetB=Rb=15%

Standard deviation of asset A=Sa=8%

Standard deviation of asset B=Sb=10%

Correlation of asset Aand B=Corr(a,b)=0.1(low correlation)

Covariance(a,b)=Corr(b,2)*Sa*Sb=0.1*10*8=8

Assume for simplicity, equal amount is invested in asset 1 and asset 2

Hence, wa=wb=0.5

Portfolio Return;

0.5*12+0.5*15=13.5%

Return increased from 12% to 13.5%

Portfolio Variance=(0.5^2)*(10^2)+(0.5^2)*(8^2)+2*0.5*0.5*8=45

Portfolio Standard Deviation=Square root of Variance=(45^0.5)= 6.708204

Volatility measured by standard deviation decreased from 8% to 6.7%

The return will remain constant irrespective of the correlation.

The return, volatility (standard deviation) of the portfolio at different correlation between A and B are given below:

Correlation A,B	Portfolio	Portfolio
	Standard deviation	Return
0	6.4	13.5
0.1	6.7	13.5
0.2	7.0	13.5
0.3	7.3	13.5
0.4	7.5	13.5
0.5	7.8	13.5
0.6	8.1	13.5
0.7	8.3	13.5
0.8	8.5	13.5
0.9	8.8	13.5
1	9.0	13.5

If the correlation is higher than 0.5, there will not be any reduction in volatility(standard deviation)