hello everybody! I have a question which I was hoping you could help me with.
let’s say that we have portfolios A,B,C,D with known expected returns and standard deviations(we know the exact numbers for all 4 portfolios).We also know that A and C lie on the efficient frontier and that borrowing and lending is permitted.
How can we find the risk free rate based on this information?
Thank you!
If that’s all you know, then you do not have enough information to determine the risk-free rate.
If you know that A and C lie on the CML (i.e., the efficient frontier when the risk-free asset is included), then you do have enough information to determine the risk-free rate:
Slope of CML = [E(RA) − E(RC)] / (σA − σC)
So,
[E(RA) − rrf] / σA = [E(RA) − E(RC)] / (σA − σC)
E(RA) − rrf = [E(RA) − E(RC)]σA / (σA − σC)
rrf = E(RA) − [E(RA) − E(RC)]σA / (σA − σC)
= {E(RA)(σA − σC) − [E(RA)σA − E(RC)σA]} / (σA − σC)
= [E(RA)σA − E(RA)σC − E(RA)σA + E(RC)σA] / (σA − σC)
rrf = [E(RC)σA − **** E(RA)σC] / (σA − σC)
Thank you very much for your reply, it was really helpful!!!
My pleasure.