Monetary Macro-Economics | Lecture 1
Expected discounted - Importance future expectation
present value - Present value discount using interest rates
- Future stream revenue
z t , z t+1 , z t+2
- Expected
z t , z et+1 , z et+2
- Example of project
compare cost today with PV expected of
revenues valued today
Discount factor - 1/(1+it)
- Lower discount rate -> € higher -> for the same
revenue
- The discounted pv depends positively on the
size of the payment and negatively on the
interest rate
Nominal discounting - Cashflow discounted using nominal interest
rate and monetary amounts (interest rates in
currency (€, $...))
Real discounting - Cashflow discounted using real amounts and
using real interest rates
- Monetary amounts -> measured in currencies
(€zt)
- Real amounts -> real quantities (zt)
Present value - Borrow cost (ct) for investment or not?
comparisons - Compare (ct) with expected pv of the
investment
Special cases - Constant interest rate and constant €zt
- € V t=€ z∗1−¿ ¿
- When i=0
€ V t=n € z
- Payments last forever (n infinite)
€z
- € V t=
i
Bonds and Bond Prices - P 1bond=€ payment /(1+i 1 t )
e
- P 2bond =€ payment / (1+ i1 t )(1+i 1 t +1)
Bond price arbitrage - In reality
calculate the expected return
, - 1-year bond
€1 1€ x (1+i1t)
- 2-year bond
€1 1€ x (1/€p2t) x €pe1t+1
Bond arbitrage - For every euro you put in 1-year bonds, you
will get (1+i1t) euros next year)
- For every euro you put in 2-year bonds, you
can expect to receive €1/€p2t times €pe1t+1 next
year
- €p2t = todays price 2-year bond
- Bond arbitrage implies
(1 + it) = (€pe1t+1 / €p2t)
Yield to maturity - Express bond price in terms of a interest rate
2
Pbond 2 t= payment / ( 1+i 2 t )
- YTM, constant interest rate, makes PV equal to
price bond is traded for today
Pbond 2 t= payment / ( 1+i 1 t ) ( 1+i 1 t +1 )
e
-
( 1+i2 t ) = ( 1+ i1 t ) ( 1+ i1e t +1 )
2
-
Yield curve 1 e
- i 2 t ≈ (i 1t +i 1t +1 )
2
Upward sloping yield curve - Future i rates will be higher than today
Downward sloping yield - Future i rates will be lower than today
curve
ytm including risk - € P2t = payment / ( 1+i 1 t ) ( 1+i e1 t +1+ x )
- Risk premium reduces bond price
Stock pricing - Look at returns
- One year return stock:
Expected discounted - Importance future expectation
present value - Present value discount using interest rates
- Future stream revenue
z t , z t+1 , z t+2
- Expected
z t , z et+1 , z et+2
- Example of project
compare cost today with PV expected of
revenues valued today
Discount factor - 1/(1+it)
- Lower discount rate -> € higher -> for the same
revenue
- The discounted pv depends positively on the
size of the payment and negatively on the
interest rate
Nominal discounting - Cashflow discounted using nominal interest
rate and monetary amounts (interest rates in
currency (€, $...))
Real discounting - Cashflow discounted using real amounts and
using real interest rates
- Monetary amounts -> measured in currencies
(€zt)
- Real amounts -> real quantities (zt)
Present value - Borrow cost (ct) for investment or not?
comparisons - Compare (ct) with expected pv of the
investment
Special cases - Constant interest rate and constant €zt
- € V t=€ z∗1−¿ ¿
- When i=0
€ V t=n € z
- Payments last forever (n infinite)
€z
- € V t=
i
Bonds and Bond Prices - P 1bond=€ payment /(1+i 1 t )
e
- P 2bond =€ payment / (1+ i1 t )(1+i 1 t +1)
Bond price arbitrage - In reality
calculate the expected return
, - 1-year bond
€1 1€ x (1+i1t)
- 2-year bond
€1 1€ x (1/€p2t) x €pe1t+1
Bond arbitrage - For every euro you put in 1-year bonds, you
will get (1+i1t) euros next year)
- For every euro you put in 2-year bonds, you
can expect to receive €1/€p2t times €pe1t+1 next
year
- €p2t = todays price 2-year bond
- Bond arbitrage implies
(1 + it) = (€pe1t+1 / €p2t)
Yield to maturity - Express bond price in terms of a interest rate
2
Pbond 2 t= payment / ( 1+i 2 t )
- YTM, constant interest rate, makes PV equal to
price bond is traded for today
Pbond 2 t= payment / ( 1+i 1 t ) ( 1+i 1 t +1 )
e
-
( 1+i2 t ) = ( 1+ i1 t ) ( 1+ i1e t +1 )
2
-
Yield curve 1 e
- i 2 t ≈ (i 1t +i 1t +1 )
2
Upward sloping yield curve - Future i rates will be higher than today
Downward sloping yield - Future i rates will be lower than today
curve
ytm including risk - € P2t = payment / ( 1+i 1 t ) ( 1+i e1 t +1+ x )
- Risk premium reduces bond price
Stock pricing - Look at returns
- One year return stock:
