The market price of a security is $46. Its expected rate of return is 10%. The risk-free rate is 4%, and the market risk premium is 9%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)

The new Market price =$28.75

Explanation:

According to the  Capital Asset Pricing Model CAPM, we have that  

Expected return= risk free rate+(beta X market risk premium)

10=4+ beta x 9

= 10- 4  = beta x 9

beta =6 /9 =0.666

IF  beta doubles with other variables constant

Expected return= risk free rate+(betaXmarket risk premium)

Beta= 0.666 x2 =1.3333

Expected return = 4+ 1.333 x 9

Expected return 4+ 12=16%

Price  =  Perpertual Dividend /Expected return

where Current Share price =$46

Dividend = $46 x 10%=4.6  

The new Market price =  Perpetual dividend/New Required return

= 4.6/16% =$28.75

So the new Market price =$28.75

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