# Advaned Macroeconomics - Chapter 11: Financial markets€¦ · Financial markets: Introduction...

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Advaned MacroeconomicsChapter 11: Financial markets

Gnter W. Beck

University of Mainz

February 1, 2011

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 1 / 17

Overview

1 Financial markets: Introduction

2 The bond marketThe bond market: IntroductionThe bond market: The term structure of interest rates

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 2 / 17

Financial markets: Introduction

Financial markets: Introduction

Objective of financial markets:= Perform the essential function of channeling funds fromeconomic players that have saved surplus funds to those that have ashortage of funds.= Promotes economic efficiency by producing an efficientallocation of capital, which increases production (they allow funds toflow to people with the best investment opportunities).= Directly improves the well-being of consumers by allowing themto time purchases better.

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 3 / 17

Financial markets: Introduction

Financial markets: Introduction

Source: Mishkin (2009)Gnter W. Beck () Advaned Macroeconomics February 1, 2011 4 / 17

Financial markets: Introduction

Financial markets: Introduction

Structure of financial markets (categorization based on essentialfeatures of individual markets):

Debt and equity markets Primary and secondary markets Money and capital markets

Debt and equity markets: Direct funding is possible in two ways: By issuing a debt instrument or

equities. Debt: Debt can be short-term (maturity is less than a year) or

long-term (maturity is more than ten years). Most common debt instruments:

Bonds Mortgages.

Equity: In the broadest sense, equity means ownership.Gnter W. Beck () Advaned Macroeconomics February 1, 2011 5 / 17

Financial markets: Introduction

Financial markets: Introduction

Structure of financial markets (continued):

Primary and secondary markets:

A primary market is a financial market in which new issues of a securityare sold to initial buyers.

A secondary market is a financial market in which previously issuedstocks are traded.

Money and capital markets: Money markets deal in short-term debt instruments. Capital markets deal in longer-term debt and equity instruments.

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 6 / 17

Financial markets: Introduction

Financial markets: Introduction

Major money market instruments

Source: Mishkin (2009)

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 7 / 17

Financial markets: Introduction

Financial markets: Introduction

Major capital market instruments

Source: Mishkin (2009)

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 8 / 17

The bond market The bond market: Introduction

The bond market: Introduction

Credit market instruments: Simple loans: Lender provides the borrower with an amount of funds,

which must be repaid to the lender at the maturity date together withan interest rate payment.

Fixed payment loan: Lender provides the borrower with an amount offunds, which has to be repaid by making the same payment (interestand part of the principal) every period.

Coupon bond: Pays the owner a fixed interest payment (couponpayment) every year until the maturity date, when a specified finalamount (face value) has to be repaid.

Discount bond (Zero-coupon bond): Bought at a price below its facevalue, at the maturity the face value is repaid.

Yield to maturity: Interest rate that equates the present value of cashflow payments received from a debt instrument with its value today.

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 9 / 17

The bond market The bond market: The term structure of interest rates

The bond market: The term structure of interest rates

Consider a coupon bond with the following characteristics:

n: Number of years until maturity. Pn,t : Price of the coupon bond c: Yearly coupon payment. F = 1: Face value of the bond.

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 10 / 17

The bond market The bond market: The term structure of interest rates

The bond market: The term structure of interest rates

The price of this coupon bond is given by:

Pn,t =c

1+ Rcn,t+

c(1+ Rcn,t)

2 + . . . +1+ c

(1+ Rcn,t)n = (1)

= cn

i=1

1(1+ Rcn,t)

i +1

(1+ Rcn,t)n =

=1

1+ Rcn,tc

n1i=0

1(1+ Rcn,t)

i +1

(1+ Rcn,t)n =

=c

1+ Rcn,t

1 1(1+Rcn,t)

n

1 1(1+Rcn,t)

+1

(1+ Rcn,t)n =

=c

Rcn,t

(1 1

(1+ Rcn,t)n

)+

1(1+ Rcn,t)

n .

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 11 / 17

The bond market The bond market: The term structure of interest rates

The bond market: The term structure of interest rates

For a zero-coupon bond (c = 0) we obtain:

Pn,t =c

Rcn,t

(1 1

(1+ Rcn,t)n

)+

1(1+ Rcn,t)

n = (2)

=1

(1+ Rcn,t)n =

1(1+ R0n,t)

n .

An n-period coupon bond can be considered as a collection of n-1zero-coupon bonds (due in periods 1, 2, . . . , n 1) with face value cand one zero-coupon bond with face value 1+ c (due in period n).

Then, we can write:

Pn,t =c

1+ R01,t+

c(1+ R02,t

)2 + . . . + 1+ c(1+ R0n,t)n . (3)Gnter W. Beck () Advaned Macroeconomics February 1, 2011 12 / 17

The bond market The bond market: The term structure of interest rates

The bond market: The term structure of interest rates

To compute the yields to maturities of the involved zero-couponbonds (denoted by R0i ,t , with i = 1, 2, . . . , n) we proceed as follows:

If the holding period is only one period we have:

P1,t =1+ c

1+ R01,t. (4)

= Equation determines R01,t . If the holding period is two periods we have:

P2,t =c

1+ R01,t+

1+ c(1+ R02,t

)2 . (5)= Equation determines R02,t .

Repeating this steps allows to solve for the remaining zero-couponinterest rates.

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 13 / 17

The bond market The bond market: The term structure of interest rates

The bond market: The term structure of interest rates

If one buys a n-period bond today (t) and sells it in the next period(t+1) the rate of return is given by:

1+ hn,t+1 =Pn1,t+1

Pn,t=

1(1+R0n1,t+1)

n1

1(1+R0n,t)

n(6)

Taking logs of this equation, observing that ln (1+ a) a (for smallvalues of a) and using pn,t = lnPn,t one can write:

hn,t+1 pn1,t+1 pn,t = nRn,t (n 1)Rn1,t+1. (7)

Given that no-arbitrage opportunities exist the expected return hn,t+1must be equal to the interest rate on a risk-free bond (st) plus a riskpremium, n,t , i.e., we must have:

Ethn,t+1 = st + n,t . (8)Gnter W. Beck () Advaned Macroeconomics February 1, 2011 14 / 17

The bond market The bond market: The term structure of interest rates

The bond market: The term structure of interest rates

Combining the two expression for hn,t+1 we can write:

hn,t+1 = nRn,t (n 1)EtRn1,t+1 = st + n,t (9)(n 1) (EtRn1,t+1 Rn,t) = (Rn,t st) + n,t ,

where (Rn,t st) denotes the term spread. Solving this equation for Rn,t yields:

Rn,t =n 1

n EtRn1,t+1 +1n (st + n,t) (10)

For Rn1,t+1 we obtain:

Rn1,t+1 =n 1

n Et+1Rn2,t+2 +1n (st+1 + n1,t+1) (11)

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 15 / 17

The bond market The bond market: The term structure of interest rates

The bond market: The term structure of interest rates

Plugging the so obtained expression for Rn1,t+1 into the equation forRn,t and repeating these two steps for Rn2,t+2, ... we obtain:

Rn,t =1n

n1i=0

Et (st+i + ni ,t+i ) . (12)

= Interpretation?

The nominal interest rate on the risk-free bond is given by:

st = rt + Ett+1 (13)

(Fisher equation). Plugging this expression into the just derived equation for Rn,t yields:

Rn,t =1n

n1i=0

Et (rt+i + Ett+i + ni ,t+i ) . (14)

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 16 / 17

The bond market The bond market: The term structure of interest rates

The bond market: The term structure of interest rates

Yield curve: A plot of the yield on bonds with differing terms tomaturity but the same risk, liquidity and tax considerations is called ayield curve.

A yield curve can be

upward-sloping, i.e. long-term rates are above short-term rates. flat, i.e. short- and long-term rates are the same downward-sloping (inverted), i.e. long-term rates are below short-term

rates or shaped more complicated (very rare).

Gnter W. Beck () Advaned Macroeconomics February 1, 2011 17 / 17

Financial markets: IntroductionThe bond marketThe bond market: IntroductionThe bond market: The term structure of interest rates