Question

The standard deviation of expected returns for investments X and Y equal 10.3% and 7.8%, respectively. The correlation between returns for X and Y is 0.30. How much risk reduction, that is diversification benefit in basis points, does the minimum risk portfolio provide?

a. 112 b. 134 c. 154 d. 178 e. 193

Answer 1

	Weights of a Minimum variance portfolio =
	wx=	(Sdy^2 - r x SDx x Sdy)/(SDx^2 +Sdy^2 - 2 x r x SDx x SDy)
		7.8^2 - 0.3/(10.3^2+7.8^2-2x0.3x10.3x7.8)
		0.309435
	Wy =	1- wx
		0.690565
	SDp=	Sq Root (Wx^2 x SDx^2 + Wy^2 x SDy^2 + 2 x Wx x Wy x Cov(x,y))
	Wx^2 x sdx^2 =			10.15813
	Wy^2 x sdy^2 =			29.01337
	2 x Wx x Wy x Cov(x,y) =			10.30047
				49.47197
	SDp =	Sq Root (1812.112)		7.034
	Weighted average sd =
	wx x sdx + wy x sdy =			8.574
	Diversification benefit =		8.574 - 7.034 =	1.540
	Diversification benefit (Basis point)=		1.54 x 100 =	154
				(answer c)