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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