Lecture notes Week 1
Agenda: Chapter 14
1. Expected present discounted values
2. Bond prices and bond yields
3. Stock market and movements in stock prices
4. Risk, bubbles, fads, and asset prices
14.1 Expected present discounted values
Expectations about the future are important for economic activity today.
- To covert money in their present or future value you need the interest rates which
are determined in financial markets
Expected present discounted value of a sequence of future payments is the value today of
this expected sequence of payments.
Expected present discounted values are not directly observable but must be constructed from
information on the sequence of expected payments and expected interest rates.
1/(1 + it) → discount factor, i being the discount rate, which is used to compute the present
discounted value of one euro next year. [the higher the nominal interest rates the lower the
value today of a euro received next year.
Example: a firm to decide to undertake or not an investment decision.
- Firm has to compare the future expected revenue stream with todays costs Ct
- To convert the future expected revenue you need to use the expected present
disconunted value of the project
Present value computations
Note how the present dicoutned value depends positively on the size of payments and
negatively on the nominal interest rates
The present value of an expected value of streams can be computed using either nominal or
real terms
1
, (real interest rate)
Special cases:
For constant i and €z for n periods, we get the following expresion:
If i=0, then the present discounted value is just the sum of those expected payments
For constant i and €z for n periods but starting one period later, we get the following
For a constant interest rates i and constant €z forever (n→∞), we get the following formula:
→ For the firm to undertake the investment the €Vt>Ct must hold
14.2 Bond prices and bond yields
Price for a one-year bond
Price for a two year bond
2
,Bond Price Arbitrage
Arbitrage: for investors to be willing to hold both types of bonds, the (expected) return must
be the same
Maturity – of a bond is the length of time over which the bond promises to make payments
to the bond holder.
Yield to Maturity:
Another way to compare bonds is to look at the yield to maturity.
The yield to maturity on an n-year bond is the constant annual interest rate that makes the
bond price equal to the present value of future payments of the bond
The Yield Curve
The yield to maturity on a two-year bond is approximately:
Doing this calculation for bonds of different duration or maturities
we can obtain:
3
, Interpreting the yield curve
The yield curve provides information about what financial markets expect the 1-year interest
rate to be 1 year from now:
➢ An upward sloping yield curves means that long-term interest rates are higher than
short-term interest rates. Financial markets expect short-term interest rates to be
higher in the future.
➢ A downward sloping yield curve means that long-term interest rates are lower than
short-term interest rates. Financial markets expect short-term rates to be lower in
the future.
Yield to Maturity including risk:
Therefore, the two-year yield is:
Which is the average of the current and expected one-year rate plus a risk premium.
The US Yield Curve
• The blue yield line shows that expected future interest rates are below current
interest rates.
• Financial markets expect the central bank will lower interest rates in the future.
• This is because financial markets expect a recession and prompt the CB to help.
➢ The red curve expects the future interest rates to be higher than the current interest
rates.
➢ Financial markets expect that the central bank will increase interest rates in the
future.
➢ This is because financial markets expect the economy to recover and prompt the
central bank to raise interest rates.
14.3 stock market and movements in stock prices
Firms have 4 ways to finance: internal finance, external finance (bank loans), debt
finance (bond and loans), and equity finance (stocks or shares)
4
Agenda: Chapter 14
1. Expected present discounted values
2. Bond prices and bond yields
3. Stock market and movements in stock prices
4. Risk, bubbles, fads, and asset prices
14.1 Expected present discounted values
Expectations about the future are important for economic activity today.
- To covert money in their present or future value you need the interest rates which
are determined in financial markets
Expected present discounted value of a sequence of future payments is the value today of
this expected sequence of payments.
Expected present discounted values are not directly observable but must be constructed from
information on the sequence of expected payments and expected interest rates.
1/(1 + it) → discount factor, i being the discount rate, which is used to compute the present
discounted value of one euro next year. [the higher the nominal interest rates the lower the
value today of a euro received next year.
Example: a firm to decide to undertake or not an investment decision.
- Firm has to compare the future expected revenue stream with todays costs Ct
- To convert the future expected revenue you need to use the expected present
disconunted value of the project
Present value computations
Note how the present dicoutned value depends positively on the size of payments and
negatively on the nominal interest rates
The present value of an expected value of streams can be computed using either nominal or
real terms
1
, (real interest rate)
Special cases:
For constant i and €z for n periods, we get the following expresion:
If i=0, then the present discounted value is just the sum of those expected payments
For constant i and €z for n periods but starting one period later, we get the following
For a constant interest rates i and constant €z forever (n→∞), we get the following formula:
→ For the firm to undertake the investment the €Vt>Ct must hold
14.2 Bond prices and bond yields
Price for a one-year bond
Price for a two year bond
2
,Bond Price Arbitrage
Arbitrage: for investors to be willing to hold both types of bonds, the (expected) return must
be the same
Maturity – of a bond is the length of time over which the bond promises to make payments
to the bond holder.
Yield to Maturity:
Another way to compare bonds is to look at the yield to maturity.
The yield to maturity on an n-year bond is the constant annual interest rate that makes the
bond price equal to the present value of future payments of the bond
The Yield Curve
The yield to maturity on a two-year bond is approximately:
Doing this calculation for bonds of different duration or maturities
we can obtain:
3
, Interpreting the yield curve
The yield curve provides information about what financial markets expect the 1-year interest
rate to be 1 year from now:
➢ An upward sloping yield curves means that long-term interest rates are higher than
short-term interest rates. Financial markets expect short-term interest rates to be
higher in the future.
➢ A downward sloping yield curve means that long-term interest rates are lower than
short-term interest rates. Financial markets expect short-term rates to be lower in
the future.
Yield to Maturity including risk:
Therefore, the two-year yield is:
Which is the average of the current and expected one-year rate plus a risk premium.
The US Yield Curve
• The blue yield line shows that expected future interest rates are below current
interest rates.
• Financial markets expect the central bank will lower interest rates in the future.
• This is because financial markets expect a recession and prompt the CB to help.
➢ The red curve expects the future interest rates to be higher than the current interest
rates.
➢ Financial markets expect that the central bank will increase interest rates in the
future.
➢ This is because financial markets expect the economy to recover and prompt the
central bank to raise interest rates.
14.3 stock market and movements in stock prices
Firms have 4 ways to finance: internal finance, external finance (bank loans), debt
finance (bond and loans), and equity finance (stocks or shares)
4
