Consider the following information: Rate of Return if State Occurs State of Econ
ID: 2766128 • Letter: C
Question
Consider the following information:
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
.15
.32
.42
.33
Good
.45
.19
.13
.12
Poor
.30
–.05
–.08
–.06
Bust
.10
–.16
–.28
–.09
Requirement 2:
(a)
What is the variance of this portfolio?
(b)
What is the standard deviation? (Do not round your intermediate calculations.)
Consider the following information:
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
.15
.32
.42
.33
Good
.45
.19
.13
.12
Poor
.30
–.05
–.08
–.06
Bust
.10
–.16
–.28
–.09
Explanation / Answer
It is being assumed that the weights of investment in Stock A , B & C are equal i.e. 1/ 3
Expected Return of A = .15*.32 + .45*.19 + .30 * -.05 + .10 * -.16 = 0.1025
Expected Return of B = .15*.42+ .45*.13 + .30 * -.08 + .10 * -.28 = 0.0695
Expected Return of C = .15*.33+ .45*.12 + .30 * -.06 + .10 * -.09 = 0.0765
Standard Deviation = Square root of [Sum of (Return - Mean) / n]
Standard Deviation: Stock A = square root of .147125/4 = .1918
Stock B = square root of .271011/4 = .2603
Stock C = square root of .271011/4 = .1677
Standard Deviation of portfolio = .1918/3 + .2603/3 + .1677/3 = 0.2066
Variance = (Standard Deviation)^2 = (.2066)^2 = 0.04268
Stock A Deviation Deviation2 Stock B Deviation Deviation2 Stock C Deviation Deviation2 0.32 0.2175 0.0473063 0.42 0.3505 0.1228503 0.33 0.2535 0.0642623 0.19 0.0875 0.0076563 0.13 0.0605 0.0036603 0.12 0.0435 0.0018923 -0.05 -0.1525 0.0232563 -0.08 -0.1495 0.0223503 -0.06 -0.1365 0.0186323 -0.16 -0.2625 0.0689063 -0.28 -0.3495 0.1221503 -0.09 -0.1665 0.0277223 Total 0.147125 0.271011 0.112509Related Questions
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