Question

Options for the second blank are (expected return or standard deviation)

Consider the expected outcomes of Projects A and B: State of Nature Probability of Occurrence Project A Return Project B Return Recession 0.25 0.06 -0.20 Average Growth 0.50 0.03 0.08 Prosperity 0.25 -0.06 0.40 Project Bis than Project A because the is higher riskier safer You can check your answer i more times before the question is hoed

Answer 1

Expected return E(r) of each Project =  $\sum$ p(s)*r(s),

where p(s) is the probability of each outcome,

and r(s) is the expected return of each outcome.

Variance $\sigma$ ²  = $\sum$ p(s)*[r(s) - E(r)]²

where [r(s) - E(r)]² is the squared deviation from the expected return.

Standard deviation =  $\sqrt{}$variance

1 State 2 Recession 3 Average 4 Prosperity 5 E('r) 6 Variance 7 Standard deviation C D E F Project A Project B Project A Project B Probability Return Return p(s)*[r(s) |p(s)"[r(s) p(s) r(s) r(s) - E(1)1 - E(1)1? 0.25 0.06 -0.20 0.000506 0.021025 0.50 0.03 0.08 0.000113 0.25 -0.06 0.40 0.001406 0.024025 0.015 0.090 0.002025 0.0451 4.50% 21.24%

ECO 1 State 2 Recession 3 Average 4 Prosperity 5 E('r) 6 Variance 7 Standard deviation Probability p(s) 0.25 0.5 0.25 Project A Return r(s) Project B Return r(s) 0.06 -0.2 0.03 0.08 -0.06 0.4 -SUMPRODUCT(B2:B4,C2:04) -SUMPRODUCT(B2:34,02:04) Project A p(s)*[r(s) - Project B p(s)*Ir(s) ECO)? =B2*(C2-$C$5)^2 =B2*(D2-$D$5)^2 =B3*(C3-$C$5)^2 =B3*(D3-$D$5)^2 =B4*(C4-$C$5)^2 =B4*(D4-$D$5)^2 =SUM(E2:E4) =SQRT(E6) =SUM(F2:F4) =SQRT(F6)

Project B is riskier than Project A because the standard deviation is higher

The risk is measured by standard deviation, and not by expected return