Question

you would like to create a portfolio that is equally invested in treasury bills and three stocks. one stock has a beta of 1.04 the second stock has a beta of 1.68 what does the better of the third stock have to be if you want the portfolio to have a beta 15% greater than the overall market show all work

Answer 1

Solution :-

Beta of the Market = 1

Therefore Required Beta of Portfolio = 1 * ( 1 + 0.15 ) = 1.15

Weight in Treasury Bills ( W TB ) = 25%

Weight of Stock 1 ( W S1 ) = 25%

Weight of Stock 2 ( W S2 ) = 25%

Weight of Stock 3 ( W S3 ) = 25%

Now Beta of Treasury Bill ( Risk Free ) = 0 ( Always )

Beta of Stock 1 ( B1 ) = 1.04

Bets of Stock 2 ( B2 ) = 1.68

Beta of Stock 3 = ( B3 ) = ??

Now Required Return = ( W TB * Beta of TB ) + ( W S1 * B1 ) + ( W S2 * B2 ) + ( W S3 * B3 ) = 1.15

( 0.25 * 0 ) + ( 0.25 * 1.04 ) + ( 0.25 * 1.68 ) + ( 0.25 * B3 ) = 1.15

0.25 B3 = 1.15 - 0.26 - 0.42

0.25 B3 = 0.47

B3 = 1.88

Therefore Beta of third Stock = 1.88

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