1) Many Investors, all price takers

 2) Investors plan for 1 period

 3) Investors limited to publicly traded assets

4) Investors can borrow or lend at risk free rate

5) There are no taxes or transaction costs

 6) All investors are rational mean-variance optimizers

 7) Investors have homogeneous expectations

1. All investors will hold the market portfolio, M
2. The CML is the best attainable capital allocation line
3. The risk premium on the market portfolio is proportional to risk and degree of risk aversion : E(r_M) - r_f = Aσ_M²
4. Risk Premium on individual assets in proportional to the risk premium on M and beta. E(r_i) - r_f = β_i *[E(r_M) - r_f],               β_i = Cov(r_i,r_M)/σ_M²

what is beta under CAPM?

ß

ß = Cov(r_i,r_j)/σ²_M

CML vs SML

Capital Market Line and Security Market Line

CML = graphs of risk premiums over σ

SML = graphs risk premiums of individual assets vs ß

CAPM vs Single Index

α

α assumed to be zero in CAPM

Single Index assume average α

is zero, but individual nonzeros are possible

used to relax the unlimited risk free portfolio assumption

E(r_i) = E(r_z) +ß_i*[E(r_m)-E(r_z)]

2 such examples:

1) Human Capital

2) Privately held businesses - if they are really different risks, owners will seek traded hedge assets, bidding up their price (-α)

material impact

1 option is avoid purchasing shares in employer

E(R_i)=E(R_M) *

[Cov(R_M,R_i)+P_H/P_M *Cov(R_i,R_H) ]/

[σ_m² + P_H/P_M *Cov(R_M,R_H)]

P_H = value of agg human capital

P_M = market value of traded assets

If investment risk is constant and no opportunities change, CAPM = ICAPM

More likely, new risks

1)changes in parameters that describe investments opp. in particular, change in economic conditions.

2)Changes in the prices of consumption goods

E(R_i) = β_iME(R_M) +∑ß_ikE(R_k)

ß_ik beta on ith hedge portfolio