Question

1. You are considering investing in a project with the following possible outcomes:

                                         Probability of     Investment

States                                  Occurrence          Returns

State 1: Economic boom         18%                  20%

State 2: Economic growth       42%                  16%

State 3: Economic decline      30%                   3%

State 4: Depression                 10%                 -25%

Calculate the expected rate of return and standard deviation of returns for this investment, respectively.

A) 8.72%, 12.99%

B) 7.35%, 12.99%

C) 3.50%, 1.69%

D) 2.18%, 1.69%

1. You are considering investing in a project with the following possible outcomes:

                                         Probability of     Investment

States                                  Occurrence          Returns

State 1: Economic boom         18%                  20%

State 2: Economic growth       42%                  16%

State 3: Economic decline      30%                   3%

State 4: Depression                 10%                 -25%

Calculate the expected rate of return and standard deviation of returns for this investment, respectively.

A) 8.72%, 12.99%

B) 7.35%, 12.99%

C) 3.50%, 1.69%

D) 2.18%, 1.69%

Answer 1

Expected rate of return

States	Investment returns	Probability	Probability weighted return (Probability x return)
State 1 : Economic boom	20%	18%	3.60%
State 2 : Economic growth	16%	42%	6.72%
State 3 : Economic decline	3%	30%	0.90%
State 4 : Depression	-25%	10%	-2.50%
Expected rate of return--> Sum of probability weighted return	8.72%

Standard Deviation of returns

States	Investment returns	Probability	Expected rate of return (refer above table)	Investment returns - Expected rate of return	Square of (Investment returns - Expected rate of return)	Probability x Square of (Investment returns - Expected rate of return)
State 1 : Economic boom	20%	18%	8.72%	11.28%	1.272%	0.229%
State 2 : Economic growth	16%	42%	8.72%	7.28%	0.530%	0.223%
State 3 : Economic decline	3%	30%	8.72%	-5.72%	0.327%	0.098%
State 4 : Depression	-25%	10%	8.72%	-33.72%	11.370%	1.137%
Step 1 : Sum of (Probability x Square of (Investment returns - Expected rate of return))	1.687%
Step 2 : Standard Deviation of investment returns---> Square root of Step 1	12.99%

Therefore Option A --> 8.72%, 12.99% is the right answer.

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