Assume that both Spark and Vodafone plot on the Security Market Line (SML). Spar

Question

Assume that both Spark and Vodafone plot on the Security Market Line (SML). Spark has a beta of 2.6 and an expected return of 21.2%. Vodafone has a beta of 0.9 and an expected return of 9.3%. The expected return on the market portfolio is 12%, and the risk-free rate is 4% Spark 2.6 Vodafone Market Portfolio Risk-free Asset Beta Expected Return | 21.2% | 0.9 9.3% 1.0 12.0% 0.0 4,0% a) If you wish to hold a portfolio consisting of Spark and Vodafone and have a portfolio beta equal to 1.5, what proportion of the portfolio must be in Spark? (2 marks) (2 marks) b) What is the expected return on this portfolio?

Explanation / Answer

Lets Assume Weight of Spark = X and Weight of vodafone = 1-X

Beta of portfolio = 1.5= (X*2.6)+(1-x)*.9

1.5 = 2.6X+.9-.9X

1.5-.9 = 2.6X-.9X

.6 = 1.7X

X = .6/1.7 X = .352 = .35 = 35%

Weight of Spark = 35%

Weight of vodafone = 1-.35 = .65 = 65%

Expected return on portfolio = (Weight of spark*expected return on spark)+(weight of vodafone*expected return on vodafone)

(.35*21.2)+(.65*9.3) = 13.465 = 13.47%

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