Question

Ryan wishes to allocate his money between T-bills and the risky BJKHD fund. He expects there is a 20% chance of a recession, a 50% chance of normal growth, and a 30% chance of an expansion. On average, BJKHD has had returns of -5% in recessions, returns of 10% in normal growth periods, and returns of 15% in expansions. What is the standard deviation of a complete portfolio that has 60% of his investment dollars in the BJKHD and the remaining 40% of your investment dollars in T-bills yielding 2%?

Answer 1

BJKHD FUND
Situation	Probability	Return	Expected Return	(Return-Expected Return)	(Return-Expected Return)2*Prob.
			(Return*Prob.)
Recession	0.20	(5.00)	(1.00)	(13.50)	36.45
Normal	0.50	10.00	5.00	1.50	1.13
expansion	0.30	15.00	4.50	6.50	12.68
			8.50		50.25
			Expected Return BJKHD FUND		8.5
			Standard Deviation BJKHD FUND	√50.25	7.088
	T-BILLS
		Expected Return T-BILLS		2
		Standard Deviation T- BILS	√2	1.41
COMBINED STANDARD DEVIATION
			(A)	(B)	C= (A*B)
		Fund	Standard Deviation	weight	Standard Deviation* weight
		BJKHD	7.088	0.6	4.2528
		T-Biils	1.41	0.4	0.564
				Total	4.8168