Question

SolarSun Corporation is evaluating asset A. The annual rate of return and probabilities associated with Asset A are as follows: RATE OF RETURN PROBABILITY 10% 13% 16% 10% 20% 70% ASSET PRIMARY POST Question 1 . Calculate the expected return, the standard deviation, the coefficient of variation and the range of retums for Asset A. Carry all values out 2 decimal places-ex. 3.45% 1) EXPECTED RETURN 2) STANDARD DEVIATION 3) COEFFICIENTOF VARIATION- 4) RANGE OF RETURNS= 68% 95% 99% 2 FT 5 8

Answer 1

Details provided as per the question are summarised below.

Asset A Rate of Return Probability 10% 13% 16% 10% 20% 70%

Answers to the respective questions are as follows,

1.

EXPECTED RETURN

The expected return is calculated by using the below formula

Where R1, R2, R3 are the Rate of returns  of the Asset A in different scenarios

P1, P2, P3  are the Probabilities of generating that return

Expected Return = (0.1*0.1) + (0.13*0.2) + (0.16*0.7)

= 0.1480 i.e. 14.80%

So, Expected Return is equal to 14.80%

2.

STANDARD DEVIATION

The Standard Deviation is calculated as per the below formula

$\sigma = \sqrt{P_{1}(R_{1}-E_{R})^{2}+P_{2}(R_{2}-E_{R})^{2}+P_{3}(R_{3}-E_{R})^{2}}$

where P_n represents the probabilities in different stages,

R_n represents the Returns of the Asset A in different stages, and

E_R represents the Expected Return of the Asset A as calculated in part 1 of the question

$\sigma = \sqrt{0.1(0.1-0.148)^{2}+0.2(0.13-0.148)^{2}+0.7(0.16-0.148)^{2}}$

= 0.0199 i.e. 1.99%

3.

COEFFICIENT OF VARIATION

The formula for calculating the coefficient of variation is as below

COV = (Standard Deviation of Asset / Expected Return of Asset)

COV = (0.0199 / 0.148) = 0.1345

So, the value of COV is 0.1345

4.

RANGE OF RETURNS

For calculating the Range of returns we first assume that the returns are following the Normal Distribution.

After this assumption, we proceed with the calculations

68%

For 68% confidence interval the values fall between the 1SD of the mean, i.e. (-1SD <= X <= 1SD)

So, 68% Confidence Interval = (Expected Asset Return) +/- (1* SD of Asset)

= 14.80 +/- 1.99%

= 12.81% to 16.79%

So with 68% confidence, the Asset A returns will range from 12.81% to 16.79%

95%

For 95% confidence interval the values fall between the 1.96SD of the mean, i.e. (-1.96SD <= X <= 1.96SD)

So, 95% Confidence Interval = (Expected Asset Return) +/- (1.96* SD of Asset)

= 14.80 +/- (1.96*1.99%)

= 10.90% to 18.70%

So with 95% confidence, the Asset A returns will range from 10.90% to 18.70%

99%

For 99% confidence interval the values fall between the 2.58SD of the mean, i.e. (-2.58SD <= X <= 2.58SD)

So, 99% Confidence Interval = (Expected Asset Return) +/- (2.58* SD of Asset)

= 14.80 +/- (2.58*1.99%)

= 9.67% to 19.93%

So with 99% confidence, the Asset A returns will range from 9.67% to 19.93%