Question

Calculate the expected standard deviation on stock:

State of the economy Probability of the states Percentage returns

Economic recession 23% -5%

Steady economic growth 25% 10%

Boom Please calculate it 14%

Answer 1

Total probability should be equal to 100%.

Here they gave for recession and growth. So

Recession+growth+boom=100

23+25+Boom=100

Boom = 100-25-23= 52

Expected return= summation(probability * return)

-51014

=(0.23*-0.05)+(0.25*0.1)+(0.52*0.14)

Expected return (E) = 0.0863

Standard deviation = SQRT((summation(probability *(Return-E)^2))

=SQRT(0.23*(-0.05-0.0863)^2 + 0.25*(0.1-0.0863)^2 + 0.52*(0.14-0.0863)^2)

Standard deviation = 7.63%

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