There is an old saying “Do not put all eggs in one basket”
Why?
Because risk is high.By keeping eggs in different baskets, we reduce risk
We try to do same thing through diversification.
By investing our capital in different assets , we try to reduce risk.
Diversified folios reduce the risk and also the ratio of Risk to reward.
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
Portfolio Standard Deviation =Square root of Portfolio variance
Risk of a stock is measured by standard deviation.
Hence reduction of standard deviation through diversification means reduction of risk.
We can take a simple example of two assets 1 and 2
Return of asset1=R1=15%
Return of asset2=R2=12%
Standard deviation of asset 1=S1=10%
Standard deviation of asset 2=S2=8%
Correlation of asset 1 and 2=Corr(1,2)=0.1
Covariance(1,2)=Corr(1,2)*S1*S2=0.1*10*8=8
Assume for simplicity, equal amount is invested in asset 1 and asset 2
Hence, w1=w2=0.5
Portfolio Return;
0.5*15+0.5*12=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
We can see, the risk of portfolio as measured by Standard Deviation has reduced significantly to
6,7 whereas the assets in the portfolio had standard deviation of 10 and 8
Risk / Return ratio of the portfolio=6.7/13.5=0.496
Risk/Return ratio of asset1=10/15= 0.666667
Risk/Return ratio of asset2=8/12= 0.666667
Risk return ratio of the portfolio is lower
WHY INVEST IN DIFFERENT INDUSTRIES TO DIVERSIFY?
Return of same types of assets are highly correlated. Suppose, if you invest in 10 different
Technology Companies, you may not be able to reduce risk, because all the companies will have
similar return and highly correlated.
We have seen in the equation of Portfolio Variance, one factor=2 w1*w2*Cov(1,2)
If there is high correlation between return of asset1 and 2, the Covariance(1,2) will be high .
Hence this factor 2w1w2Cov(1,2) will be high. As a result portfolio standard deviation will be
high and diversification will not serve any purpose.
Hence, in order to get benefit of diversification, we need to invest in different type of industries
so that the correlation between different assets are low. Consequently, the portfolio risk
(measured through standard deviation) is low.
Solution
There is an old saying “Do not put all eggs in one basket”
Why?
Because risk is high.By keeping eggs in different baskets, we reduce risk
We try to do same thing through diversification.
By investing our capital in different assets , we try to reduce risk.
Diversified folios reduce the risk and also the rati.
There is an old saying “Do not put all eggs in one basket”WhyBe.pdf
1. There is an old saying “Do not put all eggs in one basket”
Why?
Because risk is high.By keeping eggs in different baskets, we reduce risk
We try to do same thing through diversification.
By investing our capital in different assets , we try to reduce risk.
Diversified folios reduce the risk and also the ratio of Risk to reward.
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
Portfolio Standard Deviation =Square root of Portfolio variance
Risk of a stock is measured by standard deviation.
Hence reduction of standard deviation through diversification means reduction of risk.
We can take a simple example of two assets 1 and 2
Return of asset1=R1=15%
Return of asset2=R2=12%
Standard deviation of asset 1=S1=10%
Standard deviation of asset 2=S2=8%
Correlation of asset 1 and 2=Corr(1,2)=0.1
Covariance(1,2)=Corr(1,2)*S1*S2=0.1*10*8=8
Assume for simplicity, equal amount is invested in asset 1 and asset 2
Hence, w1=w2=0.5
Portfolio Return;
0.5*15+0.5*12=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
We can see, the risk of portfolio as measured by Standard Deviation has reduced significantly to
6,7 whereas the assets in the portfolio had standard deviation of 10 and 8
Risk / Return ratio of the portfolio=6.7/13.5=0.496
Risk/Return ratio of asset1=10/15= 0.666667
2. Risk/Return ratio of asset2=8/12= 0.666667
Risk return ratio of the portfolio is lower
WHY INVEST IN DIFFERENT INDUSTRIES TO DIVERSIFY?
Return of same types of assets are highly correlated. Suppose, if you invest in 10 different
Technology Companies, you may not be able to reduce risk, because all the companies will have
similar return and highly correlated.
We have seen in the equation of Portfolio Variance, one factor=2 w1*w2*Cov(1,2)
If there is high correlation between return of asset1 and 2, the Covariance(1,2) will be high .
Hence this factor 2w1w2Cov(1,2) will be high. As a result portfolio standard deviation will be
high and diversification will not serve any purpose.
Hence, in order to get benefit of diversification, we need to invest in different type of industries
so that the correlation between different assets are low. Consequently, the portfolio risk
(measured through standard deviation) is low.
Solution
There is an old saying “Do not put all eggs in one basket”
Why?
Because risk is high.By keeping eggs in different baskets, we reduce risk
We try to do same thing through diversification.
By investing our capital in different assets , we try to reduce risk.
Diversified folios reduce the risk and also the ratio of Risk to reward.
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
Portfolio Standard Deviation =Square root of Portfolio variance
Risk of a stock is measured by standard deviation.
Hence reduction of standard deviation through diversification means reduction of risk.
We can take a simple example of two assets 1 and 2
Return of asset1=R1=15%
3. Return of asset2=R2=12%
Standard deviation of asset 1=S1=10%
Standard deviation of asset 2=S2=8%
Correlation of asset 1 and 2=Corr(1,2)=0.1
Covariance(1,2)=Corr(1,2)*S1*S2=0.1*10*8=8
Assume for simplicity, equal amount is invested in asset 1 and asset 2
Hence, w1=w2=0.5
Portfolio Return;
0.5*15+0.5*12=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
We can see, the risk of portfolio as measured by Standard Deviation has reduced significantly to
6,7 whereas the assets in the portfolio had standard deviation of 10 and 8
Risk / Return ratio of the portfolio=6.7/13.5=0.496
Risk/Return ratio of asset1=10/15= 0.666667
Risk/Return ratio of asset2=8/12= 0.666667
Risk return ratio of the portfolio is lower
WHY INVEST IN DIFFERENT INDUSTRIES TO DIVERSIFY?
Return of same types of assets are highly correlated. Suppose, if you invest in 10 different
Technology Companies, you may not be able to reduce risk, because all the companies will have
similar return and highly correlated.
We have seen in the equation of Portfolio Variance, one factor=2 w1*w2*Cov(1,2)
If there is high correlation between return of asset1 and 2, the Covariance(1,2) will be high .
Hence this factor 2w1w2Cov(1,2) will be high. As a result portfolio standard deviation will be
high and diversification will not serve any purpose.
Hence, in order to get benefit of diversification, we need to invest in different type of industries
so that the correlation between different assets are low. Consequently, the portfolio risk
(measured through standard deviation) is low.
