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# Ec6012 Lecture10 The Equations of Finance

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First lecture of two on the equations for finance.

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### Ec6012 Lecture10 The Equations of Finance

1. 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. 2. TODAY
3. 3. THEMES • ‘The’ Rate of Interest in Economic Theory • Institutional Realities
4. 4. A Financial Quadrangle Short Long Working Fixed Private Capital Capital Govt Govt Public Current Capital
5. 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. 6. “THE FUTURE IS THE PRESENT SQUARED; THE PRESENT IS THE SQUARE ROOT OF THE FUTURE.”
7. 7. MARTINGALES & MARKIV PROCESSES • Some Examples
8. 8. expected future P = F (F) F = P (P) present
9. 9. F Threshold P
10. 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. 11. STRENGTHS & WEAKNESSES
12. 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. 13. d re iPS iPL iGS iGL Forex m Financial Quadrangle
14. 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. 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. 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. 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. 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. 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. 20. i d rE dP i0 dG m mS mL i d rE dP i0 dG m mS mL
21. 21. NEXT TIME • Effects of changes on risk, working capital & endogenous money, and the ﬁnal equations for ﬁnance