1. Fisher Separation Theorem
Chapter 1
Fisher Separation Theorem

2. A.Consumption and investment without capital markets
Assumptions
All outcomes from investment are known with certainty, i.e Ri=a1u1+a2u2+…+anun
No transaction costs, no exchange
No taxes
Two-period model

3. A.Consumption and investment without capital markets
Optimal consumption without capital markets
Consumption

4. A.Consumption and investment without capital markets
MRS: MRS decreasing:

5. A.Consumption and investment without capital markets
Production

6. A.Consumption and investment without capital markets
MRT: MRT increasing:

7. A.Consumption and investment without capital markets
Optimal consumption

8. A.Consumption and investment without capital markets
Optimal consumption for different investors
Individual 1 prefers consuming more at C1
Individual 2 prefers consuming more at C0

9. B.Consumption and investment with capital markets
Assumptions
All outcomes from investment are known with certainty.
Inter-temporal exchange rate of consumption bundles, r>0 is known. No transaction costs.
No taxes.
Two-period model

10. B.Consumption and investment with capital markets
Optimal consumption with capital markets
consumption

11. B.Consumption and investment with capital markets
Initial endowment, A:
Capital market line (CML)
Slope of u0 at A=-(1+ri)
Slope of CML=-(1+r)
, Invest more consume less at C0

12. B.Consumption and investment with capital markets
intercept slope
w (unchanged), u:u0→u1(↑)

13. B.Consumption and investment with capital markets
Production
A: Personal
B: Market
-(1+r)

14. B.Consumption and investment with capital markets
Optimal consumption

15. B.Consumption and investment with capital markets
Initial endowment, A(c0,c1)
Invest more at t=0
(or consume less at t=0)
A→B,

16. B.Consumption and investment with capital markets
Optimal consumption without capital markets,
ri>r
markets offer cheaper funds
invest less at t=0
consume more at t=0
borrow more to consume
B→C,
Optimal consumption with capital markets,

17. C.Implications Fisher separation theorem
“Given perfect and complete markets, the production is governed by an objective market criterion without regard to individual’s subjective preferences that enter into their consumption decision.”

18. C.Implications Complete market Basis Span, linear combination
Linear independent
Perfect market
No transaction costs, No taxes(Market frictionless)
No short sell restriction
Perfect competition, price takers
Perfect information, no information cost, asymmetric.

19. C.Implications
Optimal production, MRR=ri
Optimal consumption, ri= r

20. C.Implications Unanimity principle
Same production opportunity set, same investment portfolio,C

21. C.Implications
d.Individual delegates investment decision to managers(No individuals’ utility functions involved)
Investors’ required rate of return
=Market required rate of return
Maximization of investors’ wealth
Investors’ borrowing or lending according to their utility function
Managers made production decision without regard to the utility of the individual investor
Rf.DeAngelo[1981], Makowski[1983]