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 4.8%. The probability distributions of the risky funds are:
expected return standard deviation
Stock Fund ( S )---------18%-------------38%
Bond Fund ( B )----------9----------------32
the correlation between the fund returns is .13

Standard deviation of optimal risky portfolio is 30.92%. If you were to use only the two risky funds and still require an expected return of 15% , what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimal portfolio in the previous problem. What do you conclude?

Answer 1

We know that
	15.00	`=	18xs	`+	9xb
	30.66	`=	38xs	`+	32xb
or,	5.00	`=	6s	`+	3b
	15.33	`=	19s	`+	16b
or,	95.00	`=	114s	`+	57b
	91.98	`=	114s	`+	96b
or,	3.02	`=	-39.00	b
	b	`=	-0.08
	s	`=	1.08
					hence, the pension fund manager should sell Bond Fund by 8% and on the same hand buy Stock Fund by 108% so as to get the optimal return of 15%