Question

The investor decides to diversify by investing $2,000 in Gryphon stock and $3,000 in Royal stock, which has an expected return of 8% and a standard deviation of 13.8%. The correlation coefficient for the two stocks' returns is 0.3. Calculate the expected return and standard deviation of the portfolio. Round your answers to 2 decimal places.

E(r)= 7.2

std. Dev. = 8.6

Enter your answers below.

E(rp) =

Answer 1

Total Investment = Investment in Gryphon Stock + Investment in Royal Stock

= $2,000 + $3,000 = $5,000

E(rp) = [w(Gryphon) * r(Gryphon)] + [w(Royal) * r(Royal)]

= [(2000/5000) * 7.2%] + [(3000/5000) * 8%] = 2.88% + 4.80% = 7.68%

S.D.(p) = [{w(Gryphon) * S.D.(Gryphon)}² + {w(Royal) * S.D.(Royal)}² * {2 * w(Gryphon) * w(Royal) * S.D.(Gryphon) * S.D.(Royal) * Correlation(Gryphon,Royal)}]^1/2

= [{(2000/5000) * 8.6}² + {(3000/5000) * 13.8}² + {2 * (2000/5000) * (3000/5000) * 8.6 * 13.8 * 0.3}]^1/2

= [11.8336 + 68.5584 + 17.08992]^1/2

= [97.48192]^1/2

= 9.87%