Question

22. Stock A has a beta of 1.25 and an expected return of 14%. Stock B has a beta of 0.75 and an expected return of 10%. Now, if you construct a portfolio of stock A and Treasury Bills that has the same risk as the market index, what will be your portfolio’s expected return? Assume all stocks are fairly priced.

Answer 1

Solution :-

As per CAPM

ER = Rf + Beta ( Rpm )

Stock A

14% = Rf + 1.25 ( Rpm ) ..........(i)

Stock B

10% = Rf + 0.75 ( Rpm ) .............(ii)

Now

On Deducting (ii) From (i)

4% = 0.50 Rpm

We get Rpm = 8%

And If Rpm 8% then Rf =

14% = Rf + 1.25 ( 8% )

Rf = 4%

Therefore Return of Treasury Bond = 4%

Now we need to Portfolio of Treasury Bill and Stock A with Beta 1

And Beta of Treasury Bill = 0

Let Weight of Stock A be X

and Weight of Treasury Bill = ( 1 - X )

( X * 1.25 ) + ( 1 - X ) * 0 = 1

X = 0.80

Therefore Weight of Stock A = 0.80

And Weight of Treasury Bill = 1 - 0.80 = 0.20

Now Portfolio Return =

= ( Wa * ERa ) + ( Wrf * Rf )

= ( 0.80 * 14% ) + ( 0.20 * 4% )

= 11.2% + 0.80%

= 12%

Therefore portfolio’s expected return = 12%

If there is any doubt please ask in comments