An investor is evaluating a two-asset portfolio of the following two securities.

Question

An investor is evaluating a two-asset portfolio of the following two securities. a. If the two equity funds have a correlation of + 0.72, what is the expected risk and return for the following three portfolio weightings? Portfolio A: 75% British, 25% American Portfolio B: Investor has $10,000 and $5000 of them will be invested in British Stock Portfolio C: Investor will invest $2500 in British and $7500 in US

Security

Expected Return

Expected Risk ()

Correlation ()

British Equities

12.50%

26.40%

0.72

American Equities

10.80%

22.50%

Security

Expected Return

Expected Risk ()

Correlation ()

British Equities

12.50%

26.40%

0.72

American Equities

10.80%

22.50%

Explanation / Answer

Wa, Ra, SDa = American

Wb, Rb, SDb = Britan

Portfolio A

Wa = 0.25

Wb = 0.75

E(R) = 0.25*10.8% + 0.75*12.5% = 12.08%

SD = SQRT(0.252*22.5%2 + 0.752*26.4%2 + 2*0.25*0.75*22.5%*26.4%*0.72) = 24.17%

Portfolio B

Wb =5000/10000 = 0.5

Wa = 1-0.5 = 0.5

E(R) = 0.5*10.8% + 0.5*12.5% = 11.65%

SD = SQRT(0.52*22.5%2 + 0.52*26.4%2 + 2*0.5*0.5*22.5%*26.4%*0.72) = 22.69%

Portfolio C

Wb =2500/(2500+7500) = 0.25

Wa = 1-0.25 = 0.75

E(R) = 0.75*10.8% + 0.25*12.5% = 11.23%

SD = SQRT(0.752*22.5%2 + 0.252*26.4%2 + 2*0.75*0.25*22.5%*26.4%*0.72) = 22.11%

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