Question

Berger Paints’ stock has an expected return of 10.5% and a β of 1.45. Mr. Manzoor invested $145,000 in a portfolio that includes stocks of Berger Paints and SPL only. The β of SPL stocks is 0.85. The expected return on Mr. Manzoor’s portfolio is 8.75%. The risk free rate is 3.5%. How much money did he invest in Berger Paints’ stocks?

Answer 1

Berger Paints

Expected Return =

10.5% = 3.5% + 1.45(Rm - 3.5%)

10.5% = 3.5% + 1.45Rm - 5.075%

10.5% = 1.45Rm - 1.575%

Rm = (10.5% + 1.575) / 1.45

Rm = 8.33%

Expected Return of SPL =

= 3.5% + 0.85(8.33% -3.5%)

= 7.61%

Let the Weight of Berger Paint be X

Weight of SPL will be 1-X

Return of Portfolio = 8.75%

Return of Berger Paint * Weight of Berger Paint + Return of SPL * Weight of SPL = 8.75%

10.5% * X + 7.61% * (1-X) = 8.75%

10.5% X + 7.61% - 7.61% X = 8.75%

2.89% X + 7.61% = 8.75%

X = (8.75% - 7.61%) / 2.89%

X = 39.45%

Amount Invested in Berger paints = 39.45% * 145000 = $ 57203

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