Solution to Risk - Return Problem

Both products have identical expected cash flows, but there is less risk associated with Product 2, relative to Product 1.

Product 1            
Outcome p x px x-E(x) (x-E(x))2 p(x-E(x))2
Pessimistic 10% -$2,199 -$219.9 -$4,299 18,481,401 1,848,140
Moderate 60% $2,116 $1,269.6 $16 256 153.6
Optimistic 30% $3,501 $1,050.3 $1,401 1,962,801 588,840.3
  100% E(x) = 2,100.0   variance = 2,437,134
          standard deviation = $1,516.132
             
Product 2            
Outcome p x px x-E(x) (x-E(x))2 p(x-E(x))2
Pessimistic 20% -$500 -$100 -$2,600 6,760,000 1,352,000
Moderate 40% $2,000 $800 -$100 10,000 4,000
Optimistic 40% $3,500 $1,400 $1,400 1,960,000 784,000
  100% E(x) = $2,100   variance = 2,140,000
          standard deviation = $1,462.874