Question

1. TRUE OR FALSE The two assets A and B have expected returns and volatilities: E(Ra), SD(Ra) and E(Rb), SD(Rb). Suppose we construct an equally weighted portfolio using these two assets. Then,SD(Rp)<12SD(Ra)+12(SDrs) to diversification benefit.

Answer 1

Ans - Yes it is true that standard deviation of portfolio is less than the standard deviation of individual stocks. This happens because of correlation. Correlation tells us about the relationship between two variables.

In portfolio when securities have negative correlation i.e the movement between is opposite to each other, that provides the diversification benefits.

Let just understand by an example- Mr A wants to invest 10000 in equity. He can choose one option in which he selects to invest full amount in one stock say X and on the other and he has option to invest equally in two stocks X and Y. And there is negative correlation of 0.5 which means if price of X rises by 10%, the price of stock Y falls by 5% and vice versa.

Due to economic slowdown the price of X falls by 10% and price of y rise by 5%

Case 1 - If Mr.A wants to invest in only X stock where the price falls by 10%

10000 *10%

= 1000

In this case there is a loss of 1000

Case 2 - If Mr.A wants to invest equally in X and Y where the price of X falls by 10% and prices of Y rises by 5%

then,

X = 5000*10%

loss = 500

Y = 5000*5%

profit = 250

Net loss = 250

From above example we can conclude that due to diversification benefits we can reduce the risk of portfolio by investing

in securities that have negative correlation. The optimal portfolio is that portfolio in which there are risky assets with risk free assets to have zero correlation benefits.

Equation of portfolio standard deviation

σ_P = (w_A²σ_A² + w_B² σ_B² + 2w_Aw_Bσ_Aσ_Bρ_AB)^1/2

^where w_{A =} weight of one security

w_B= weight of other security

ρ_AB= correlation between securities

σ_{A =} standard deviation of one security

σ_B=standard deviation of other security