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Consider the following information:    Rate of Return if State Occurs   State of Economy Probability of State of Economy Stock...

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Finance

Consider the following information:

  

Rate of Return if State Occurs
  State of EconomyProbability of State of EconomyStock AStock B
  Recession.10.03–.20
  Normal.70.08.14
  Boom.20.13.32

Calculate the standard deviation for stock a and b.

Answer & Explanation Solved by verified expert
4.5 Ratings (757 Votes)

Stock A Stock B
Standard deviation 2.69% 13.43%
Working:
# 1 Calculation of expected return of both stock:
Stock A Stock B
State of Economy Probability of State of Economy Rate of return Rate of return
a b c=a*b d e=a*d
Recession           0.10 0.03       0.0030 -0.2     -0.0200
Normal           0.70 0.08       0.0560 0.14      0.0980
Boom           0.20 0.13       0.0260 0.32      0.0640
Expected return       0.0850      0.1420
# 2 Calculation of variance of both stock:
Stock A Stock B
State of Economy Probability of State of Economy Rate of return Expected return Rate of return Expected return
a b c d=((b-c)^2)*a e f g=((e-f)^2)*a
Recession           0.10 0.03       0.0850 0.000303 -0.2      0.1420 0.011696
Normal           0.70 0.08       0.0850 0.000017 0.14      0.1420 0.000003
Boom           0.20 0.13       0.0850 0.000405 0.32      0.1420 0.006337
Variance 0.000725 0.018036
# 3 Calculation of stnadard deviation :
Standard deviation = Variance ^ (1/2)
So, Standard deviation of:
Stock A = 0.000725 ^ (1/2) = 0.026926
Stock B = 0.018036 ^ (1/2) = 0.134298

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Transcribed Image Text

Consider the following information:  Rate of Return if State Occurs  State of EconomyProbability of State of EconomyStock AStock B  Recession.10.03–.20  Normal.70.08.14  Boom.20.13.32Calculate the standard deviation for stock a and b.

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