Question

A mutual fund manager has a $40.00 million portfolio with a beta of 1.00. The risk-free rate is 4.25%, and the market risk premium is 6.00%. The manager expects to receive an additional $29.50 million which she plans to invest in additional stocks. After investing the additional funds, she wants the fund's required and expected return to be 13.00%. What must the average beta of the new stocks be to achieve the target required rate of return? Do not round your intermediate calculations. (show the work)

	a.	2.08
	b.	2.18
	c.	2.60
	d.	1.66
	e.	1.87

Answer 1

- Required return of new Fund = 13%

Calculating the new Fund's Beta:-

where, rf = Risk free return = 4.25%

Rmp = Market Risk Premium= 6%

13% = 4.25% + Beta(6%)

Beta = 1.4583

So, New Fund's beta = 1.4583

- Old Fund's Portfolio Investment is $40 million and beta is 1

Additional Investment = $29.5 million

Total Investment in new Fund = $40M + $29.5M = $69.5 million

Calculating the Beta of Additional Investment:-

New Fund's beta = (Weight of Old Fund)(Beta of Old Fund) + (Weight of Additional Investment)(Beta of Additional Investment)

1.4583 = ($40M/$69.5M)(1) + ($29.5/$69.5M)(Beta of Additional Investment)

1.4583 = 0.5755 + 0.424460(Beta of Additional Investment)

Beta of Additional Investment = 2.08

So, the average beta of the new stocks be to achieve the target required rate of return is 2.08

Option A

If you need any clarification, you can ask in comments.    

If you like my answer, then please up-vote as it will be motivating