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Consider the following scenario analysis Rate of Return Scenario Probability Stocks Bonds recession 0.20 -5% 14% Normal economy 0.60...

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Finance

Consider the following scenario analysis

Rate of Return

Scenario Probability Stocks Bonds

recession 0.20 -5% 14%

Normal economy 0.60 15 8

Boom 0.20 25 4

Is it reasonable to assume that treasury bonds will providehigher returns in recessions than in booms?

Calculate the expected rate of return and return and standarddeviation for each investment. (Do not round intermediatecalculations. Enter your answers as a percent rounded to 1 decimalplace.)

Answer & Explanation Solved by verified expert
3.9 Ratings (474 Votes)

Stocks Bonds
Expected rate of return 13.0% 8.4%
Standard deviation 9.8% 3.2%
Working:
Stocks: Bonds:
# 1 Calculation of expected return # 1 Calculation of expected return
Scenerio Probability Rate of return Scenerio Probability Rate of return
a b a*b a b a*b
Recession           0.20     -0.0500     -0.0100 Recession           0.20      0.1400      0.0280
Normal Economy           0.60      0.1500      0.0900 Normal Economy           0.60      0.0800      0.0480
Boom           0.20      0.2500      0.0500 Boom           0.20      0.0400      0.0080
Total      0.1300 Total      0.0840
# 2 Calculation of variance: # 2 Calculation of variance:
Scenerio Probability Rate of return Expected return Scenerio Probability Rate of return Expected return
a b c d=((b-c)^2)*a a b c d=((b-c)^2)*a
Recession           0.20     -0.0500      0.1300       0.00648 Recession           0.20      0.1400      0.0840    0.00063
Normal Economy           0.60      0.1500      0.1300       0.00024 Normal Economy           0.60      0.0800      0.0840    0.00001
Boom           0.20      0.2500      0.1300       0.00288 Boom           0.20      0.0400      0.0840    0.00039
Total       0.00960 Total    0.00102
# 3 Calculation of standard deviation # 3 Calculation of standard deviation
Standard deviation = Variance ^ (1/2) Standard deviation = Variance ^ (1/2)
=    0.00960 ^ (1/2) =    0.00102 ^ (1/2)
= 0.09798 = 0.032

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Transcribed Image Text

Consider the following scenario analysisRate of ReturnScenario Probability Stocks Bondsrecession 0.20 -5% 14%Normal economy 0.60 15 8Boom 0.20 25 4Is it reasonable to assume that treasury bonds will providehigher returns in recessions than in booms?Calculate the expected rate of return and return and standarddeviation for each investment. (Do not round intermediatecalculations. Enter your answers as a percent rounded to 1 decimalplace.)

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