Question

Rate of return		Zest	Croy
Bad	0.25	10%	13%
Decent	0.50	15%	13%
Better	0.25	20%	13%

There are two virtual programs Zest & Croy, what are the expected rate of return? Explain. What is the standard deviation for Zest? What is the standard deviation for Croy? Which is more risk averse? Which prefers risk? If there was two other programs to consider: Lex has 10% expected return & std dev of 2%. Pro has expected return of 12% and 5% std dev. Is Lex or Pro more risk averse? Explain.

Answer 1

Expected Return of Zest =0.25*10%+0.50*15%+0.25*20% =15%
Expected Return of Croy =0.25*13%+0.50*13%+0.25*13% =13%

Standard Deviation of Zest =(0.25*(10%-15%)^2+0.50*(15%-15%)^2+0.25*(20%-15%)^2)^0.5 =3.54%
Standard Deviation of Croy =(0.25*(13%-13%)^2+0.50*(13%-13%)^2+0.25*(13%-13%)^2)^0.5 =0%

Croy is more risk averse as standard deviation is 0. Zest prefers more risk.


Lex is more risk averse because coeffcient of variation of Lex is less than Pro.
Coefficient of Variation of Lex =2%/10% =0.2
Coefficient of variation of Pro =5%/12% =0.42