Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.2%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	13%	42%
Bond fund (B)	6%	36%

The correlation between the fund returns is 0.0222.

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

For minimum Variance portfolio

Weight of (S) = ((Standard Deviation of B)² -correlation * Standard Deviation of S * Standard
Deviation of B)/((Standard Deviation of S)² + (Standard Deviation of B)² - 2 * correlation * Standard Deviation of S * Standard Deviation of B) = ( 36%² -0.0222*42%*36%)/(42%² + 26%² -2 * 0.0222*42%*36%) = 42.18%

Weight of S = 42.18%
Weight of B =1-42.18% =57.82%

Expected Return =Weight of S* Expected Return of S+Weight of B* Expected Return of B =42.18%*13%+57.82%*6% =8.95%

Standard Deviation = ((Weight of S * Standard Deviation of S)² + (weight of B * standard Deviation of B)² + 2* Weight of S * Standard Deviation of S* weight of B * standard Deviation of B * correlation)^0.5
​= ((42.18*42%) + (57.82%*36%) + 2* 42.18*42% * 57.82*36% * 0.022)^0.5 = 27.63%