Ec6012 Lecture10 The Equations of Finance

FROM THE LM CURVE TO THE FINANCIAL QUADRANGLE: SIMPLICITY AND REALISM IN FINANCIAL MARKET ANALYSIS

EJ Nell & Steve KinsellaNew School for Social Research & UL

TODAY

THEMES

• ‘The’ Rate of Interest in Economic Theory

• Institutional Realities

Short Long

Private

Public

Working Capital

Fixed Capital

Govt Current

Govt Capital

A Financial Quadrangle

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]

“THE FUTURE IS THE PRESENT SQUARED; THE PRESENT IS

THE SQUARE ROOT OF THE FUTURE.”

MARTINGALES & MARKIV PROCESSES

• Some Examples

present

expected future

P = F (F)

F = P (P)

P

F

Threshold

A REVISED KEYNESIAN SYSTEM

9 eqns,9 Unknowns:

Y, C, I, N, rF, K’, i, L, I

-Short-run Output function: Y = aN-Consumption function: C = wN-Expenditure equation: Y = C + I-Income equation: Y = wN + rFK

-MEC-CP interactionrF = MEC(i, Y, K’)rF = CP(i, Y, K’)

-Liquidity preference and money/credit supplyL =L(i, Y, K’) demand for liquidityL = M(i, Y, K’) supply of money and credit

-Investment: I = MEI(i, Y, K’, rF)

STRENGTHS & WEAKNESSES

default risk

JunkNon-Profit

ABAA

AAAMixed

MunicipalState

Federal

Private Short

time to maturity

Private Long

Public Short Public Long

d

m

iPS iPL

iGS iGL

Financial Quadrangle

Forex

re

Default Risk & Market Riskdefault risk

d

m

market risk

d

m

iPS iPL

iGS iGL

re

risk diagonal

d

m

mEmLmS

rEdE

dP

dG

i0

iGS

iPS

iGL

iPL

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:

• i = √(k2 + g2), and

• k = √(d2 + m2), so that

• i = √( d2 + m2 + g2)

IDEA

• Here we 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.

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.

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

• 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]

rE

dP

dG

mS mL

m

id

i0

rE

dP

dG

mS mL

m

i

d

i0

NEXT TIME

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