First lecture of two on the equations for finance.

1. FROM THE LM CURVE TO THE
FINANCIAL QUADRANGLE:
SIMPLICITY AND REALISM IN
FINANCIAL MARKET ANALYSIS
EJ Nell & Steve Kinsella
New School for Social Research & UL

2. TODAY

3. THEMES
• ‘The’ Rate of Interest in Economic Theory
• Institutional Realities

4. A Financial Quadrangle
Short Long
Working Fixed
Private
Capital Capital
Govt Govt
Public
Current Capital

5. PRESENT & FUTURE
present = f(expected future), f ’>0
expected future = φ(present), φ’>0
CP: the future is the square root of the present multiplied by
the growth rate appropriately compounded.CP the future is
the square root of the present multiplied by the growth rate
appropriately compounded.: F = (1+g)n √P
MEC: P = √F [(1+g)-n]

6. “THE FUTURE IS THE PRESENT
SQUARED; THE PRESENT IS
THE SQUARE ROOT OF THE
FUTURE.”

7. MARTINGALES & MARKIV
PROCESSES
• Some Examples

8. expected future
P = F (F)
F = P (P)
present

9. F
Threshold
P

10. A REVISED KEYNESIAN SYSTEM
-Short-run Output function: Y = aN
-Consumption function: C = wN
-Expenditure equation: Y = C + I
-Income equation: Y = wN + rFK
9 eqns,
-MEC-CP interaction 9 Unknowns:
rF = MEC(i, Y, K’) Y, C, I, N, rF, K’, i, L, I
rF = CP(i, Y, K’)
-Liquidity preference and money/credit supply
L =L(i, Y, K’) demand for liquidity
L = M(i, Y, K’) supply of money and credit
-Investment: I = MEI(i, Y, K’, rF)

11. STRENGTHS & WEAKNESSES

12. default risk
Junk
Non-Profit
AB
AA
Private Short Private Long
AAA
Mixed
Municipal
State
Federal
Public Short Public Long
time to maturity

13. d
re
iPS iPL
iGS iGL
Forex
m
Financial Quadrangle

14. default risk
Default Risk & Market Risk
d
risk diagonal
rE
dE
iPS iPL
dP
d
iGS iGL
dG
market risk
m m
i0
mS mL mE
d
re
iPS iPL
iGS iGL
m

15. A DERIVATION
• Now let i be a rate of interest, k a rate of generalized risk, d
the rate of default risk and m the rate of market risk, with g
representing the rate of net interest (we choose ‘g’ because
we will argue later that the rate of net interest should reflect
the rate of growth). Then we have:
= √(k2 + g2), and
•i
= √(d2 + m2), so that
•k
i = √( d2 + m2 + g2)
•

16. IDEA
• Herewe see that we have defined a distance function, D.15
The basic idea is that the risk factor is a vector the length of
which measures the distance from the point of zero risk.

17. STRUCTURE OF THE
QUADRANGLE
• Structure of the Quadrangle: we want to examine the
relationships between the markets, and between risks and
returns.
• First
we need to define the rates of interest in the four
submarkets, the overnight market and the stock market. Then
we will relate these rates to the real economy; this will give us
the structure in which economic activity takes place. At that
point we can turn to behavioral equations and determine
employment and output, the debt equity ratio and the overall
holding of securities in portfolios.

18. CENTRAL BANK & RATE
STRUCTURE
• Some simple equations can be written, starting with one for
the Fed setting the overnight interbank rate, then moving to
the short-term market for Treasuries:
• i0 = D(0, 0, i0*)
• iGS = D(0, mS, gN)
• over the cycle:
• iPS
= D(dS, mS, gN) where gn is the rate of growth of
capacity employment

19. • Now we can write equations for the long-term market, for
corporate and government fixed capital
• iGL = D(dG, mL, gY)
• iPL = D(dP, mL, gY)
• Next we turn to equity markets
• re = D(me. rF), [this is a vector combination]

20. i
d
rE
dP
i0
dG
m
mS mL
i
d
rE
dP
i0
dG
m
mS mL

21. NEXT TIME
• Effects
of changes on risk, working capital & endogenous
money, and the final equations for finance