Tutorial 5#

1) Definitions#

  • Government Bonds: future payment obligation issued by government for funds

  • Principal: amount to be payed at end

  • Coupon: Interest

Interest Rate (of zero-coupon bond):

\[ i = \frac{ Principal }{price_{market}}-1 \]

2) Fiscal Budget#

\[ T+\Delta B = G+ iB \]

leads to: equilibirum debt ratio

\[ b^* = \frac{ g-t }{y-r} \]

This determines the position and equilbrium here:

img

3) Sovereign Default#

Interest:

\[ i = \frac{ i_0+w }{1-w} \]

Why is it equilibrium and true?

  • safe bond: \(price_{safe}=\frac{ payoff_{safe} }{1+i_0}\)

    • so safe : \(1+i_0 = \frac{ payoff}{price}\)

  • if return on bond is too high:

    • if \(i > \frac{ i_0+w }{1-w}\) means

    • expected return of risky investment > expected return of safe investment

  • investors would react