Question

Fund BIOTECH with the following performance: Down 50% in Year 1, Up 60% in Year 2. Average arithmetic return is 5% per year with higher than average volatility that is expected to persist in the future. Fund UTILITIES with the following performance: Down 1% in Year 1, Up 2% in Year 2. Average return is 0.5% with lower than average volatility that is expected to persist in the future. Based on your analysis of the two funds' performance and riskiness, which fund would you select and why?

Answer 1

Biotech
Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability* D^2[D*D]
					0.5	-0.5	-0.25	-0.55	0.15125
0.5	0.6	0.3	0.55	0.15125
Expected Return = Sum of Probabilty*Return		0.05	Variance =Sum of [D^2]	0.3025
			Standard Deviation =Variance^1/2	0.55

Co Efficient of Variation = Standard Deviation/Expected Return = 0.55/0.05 = 11

Utilities
Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability* D^2[D*D]
					0.5	-0.01	-0.005	-0.015	0.0001125
0.5	0.02	0.01	0.015	0.0001125
Expected Return = Sum of Probabilty*Return		0.005	Variance =Sum of [D^2]	0.000225
			Standard Deviation =Variance^1/2	0.015

Co Efficient of Variation = Standard Deviation/Expected Return = 0.015/0.005 = 3

Co Efficient of Variation is RISK PER UNIT OF RETURN. Therefore, as UTILITIES has LOWER RISK PER UNIT OF RETURN, it should be chosen.