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How To Calculate Expected Value & Risk Adjusted Rate Of Return

by Emeka

Investment Scenarios Situation:

You have two alternative scenarios for investing $1,000,000.

Question: Which investment scenario is better?

Answer:

Scenario #1

U = 0.20*3.0+0.50*1.0+0.30*(-2.0) = 0.5
____________________________________________________
S = V 0.2(3.0-0.5)^2+0.50(1.0-0.5)^2+0.30(-2.0-0.5)^2 = 1.8

V = 1.8/0.5 = 3.6

Scenario #2

U = 0.60*1.5+0.10*1.0+0.30*(-0.2) = 0.94
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S = V 0.60(1.5-0.94)^2+0.10(1.0-0.94)^2+0.30(-0.2-0.94)^2 = 0.6

V = 0.6/0.94 = 0.64

Analysis on the two scenarios:

Scenario U S V
1 0.5 1.8 3.6
2 0.94 0.6 0.64

The expected return in scenario #1 is $500,000,
which is lower than scenario #2′s $940,000

Risk in scenario #1 is S = $1,800000
whereas in scenario #2, it is $600,000

Risk per expected return in scenario #1; 3.6 is a lot higher than
in Scenario #2; 0.64

The question of which is better depends on the investor,
some will take high risk with the expectation of high returns,
whereas some will go with lower risk with the expectation of a reasonable return.

As always higher ROI goes with Higher risk, but I am the risk taking type. However I do take calculated risk which goes with a calculated expected return.

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