P1.T1. Foundations of Risk Management - Reading 2 - Study Notes - Page 8

[Dr. Jayanthi Sankaran]

Hi David,

In the Study Notes of Reading 2 (Elton & Gruber) - on Page 8, a quick clarification - is the Risk-free rate of 3% given? The Example gives only Expected returns and Beta's. And, ask's us to compute Expected return of an asset with Beta = 2.0. The Market Risk Premium turns out to be 6%. But, how does one proceed from there, without information on the Risk-free rate? Am I missing, something here?

Thanks
Jayanthi

 

[ShaktiRathore]

Exp return=rf+beta*Riskprem.
E=rf+2*6=>E-12=rf when expected return is given we can find rf using the above eqn.r u doing this?
Thanks

 

[David Harper CFA FRM]

Thanks @ShaktiRathore ! @Jayanthi Sankaran By giving two asset returns and two betas, the problem sets up two unknowns and two formulas, as shown:

12% = Rf + 1.5*MRP
6% = Rf + 0.5*MPR

then it happens to solve initially for MRP, by subtracting the second formula from the first we get:

• on the left: 12% - 6% = 6%
• on the right: (Rf + 1.5*MRP) - (Rf + 0.5*MPR) = MRP

So MRP = 6%, and we can then retrieve Rf from either formula; e.g., 12% = Rf + 1.5*6%

We could also solve initially for Rf, we might multiply the second formula by 3 to get:
3*(6% = Rf + 0.5*MPR) --> 18% = 3*Rf + 1.5MRP, then do this subtraction:

18% = 3*Rf + 1.5MRP
- 12% = Rf + 1.5*MRP
= 6% = 2*Rf --> Rf = 3%
​

I hope that helps (I am on vaco for Thankssgiving, so I won't respond over the next few days!)

 

[Dr. Jayanthi Sankaran]

Thanks, David,

What a silly mistake to make - I can't believe I didn't see that! I was studying late at night, and somehow overlooked it! Have a great well-deserved Thanksgiving vacation

Thanks again
Jayanthi

 

[Dr. Jayanthi Sankaran]

Hi Shakti,

Thank you very much for clearing my doubt! Somehow, I overlooked it - studying late at night!

Jayanthi