Question

	Security Returns if State Occurs
State of Economy	Probability of State of Economy	Roll		Ross
Bust	0.50	–19	%	12	%
Boom	0.50	19		5

Calculate the standard deviations for Roll and Ross by filling in the following table: (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 4 decimal places.)

(Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

(Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Standard Deviations

Roll%

Ross%

Answer 1

Roll

State of Economy	Probability (P)	Return(%)	Probability*Return	Deviation form expected return (D)	PD^2
Bust	0.5	-19	-9.50	-19.00	180.50
Boom	0.5	19	9.50	19.00	180.50

Expected return = Probability*Return

= -9.5+9.5

= 0%

Variance = PD^2

= 180.5+180.5

= 361

Standard Deviation = Variance

= 361

= 19.00%

*Deviation form expected return = Rate of return -  expected return​

Ross

State of Economy	Probability (P)	Return(%)	Probability*Return	Deviation form expected return (D1)	PD1^2
Bust	0.5	12	6.00	3.50	6.125
Boom	0.5	5	2.50	-3.50	6.125

Expected return = Probability*Return

= 6+2.5

= 8.5%

Variance = PD^2

= 6.125+6.125

= 12.25

Standard Deviation = Variance

= 12.25

= 3.50%

*Deviation form expected return = Rate of return -  expected return​