Question

Calculate mean and standard deviation for the following asset.

Economic State Return Probability

Recession -16% 35%

Normal 15% 30%

Boom 36% 35%

Answer 1

• Probability Weighted Return = Return x Probability
  • Recession Probability Weighted Return = 35% x -16% = -5.6%
  • Normal Probability Weighted Return = 30% x 15% = 4.5%
  • Boom Probability Weighted Return = 35% x 36% = 12.6%
• Mean or Expected Return = sum of Probability Weighted Return      
  • Expected Return = -5.6%+4.5%+12.6% = 11.50%
• To calculate variance and standard deviation we need to calculate the probability weighted squared deviations or P(X - Expected return of R)^2
  • Recession Probability weighted squared deviations = 35% x (-16-11.5)2= 2.646875%
  • Normal Probability weighted squared deviations = 30% x (15-11.5)2= 0.03675%
  • Boom Probability weighted squared deviations = 35% x (36-11.5)2 = 2.100875%
• Variance = Sum of Probability weighted squared deviations
  • Variance = 2.646875 + 0.03675 + 2.100875
  • Variance = 4.785%
• Standard deviation = Square root of variance          
  • Standard deviation = Square root of 4.785%
  • Standard deviation = 21.873%