CAPM and return on asset

[hthassan]

Hi dears,

I am reading the Elton and Gruber notes on CAPM model.

based on the Bionic turtle notes on page 9, there was this following Q
"Calculate the expected return on an asset with a Beta of 2.0
R1 = 6%
R2= 12%
B1= 0.5
B2 = 1.5"

The answer is on page 10, however, i did not know how to arrive to it

Would appreciate if someone can explain the method to me.

Appreciate your efforts

Thanks,
Hassan

 

[brian.field]

The CAPM says that the expected return on an asset E(R) is equal to the risk free rate + Beta*(Market Return minus the risk free rate) OR E(R) = risk free rate + Beta*(Market Risk Premium).

Let Risk Free Rate = X and Market Risk PRemium = Y.

Then we have 2 equations and 2 unknowns, as below.

0.06 = X + 0.50Y
and
0.12 = X + 1.50Y

Solve for X and Y to get X = 0.03 and Y = 0.06.

Then repeat the CAPM as E(asset with Beta = 2) = X + 2Y = 0.03 + 2(0.06) = 0.15.

 

[ShaktiRathore]

Hi,
you can also do it as Risk increases from B1= 0.5 to B2 = 1.5 that is by 1.5-.5=1 unit the return increases from 6% to 12% by 12%-6%=6% therefore for every 1 unit increases in Risk (beta) the return on asset increases by 6%.Thus increase in return for every 1 unit increases in Risk (beta) is 6%/unit of Risk.
As Risk increases from B1= 1.5 to B2 = 2 that is by 2-1.5=.5 units the return increases by=6%/unit of Risk.*.5 units=3%
Thus Return increases by 3% from 12%(B1= 1.5) to 12%+3%=15%(B2 = 2 ).
thanks

 

[hthassan]

Thank you guys for the informative reply.