Financial Markets. A market is a place where goods and services are exchanged. A financial market is a place where individuals and organizations who want to borrow funds are brought together with those having a surplus of funds. We can classify markets. Based on: Underlying asset
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Based on: Underlying asset
financial, spot, secondary, capital
financial, money, primary
A firm’s selling its stock directly to
another firm/individual is an example of
Investment banking firm helps a company in the
design and sale of securities. The investment
banker is also called the underwriter.
The agreement between the firm and
underwriter can be of two types:
Examples of Investment Banking Firms:
Merrill Lynch, Salomon Smith Barney
Financial intermediaries get savings from individuals by
creating new financial products
For example, commercial banks open checking and
saving accounts, life insurance companies sell policies
and mutual funds sell new shares and are ready to buy
back outstanding shares.
Strengths offinancial intermediaries
Mutual funds differ in their investment objectives, e.g.
Ranking of Mutual Funds (US):
Auction market vs. Dealer market (Exchanges vs. OTC)
Exchanges can have continuous trading, call auctions
Mostly: Continuous-auction also contain opening call
How do they provide continuity: Limit Order Book
Liquidity: conversion to cash
quickly, with low cost, and
for reasonable transaction sizes
Members have seats (e.g. NYSE ≈1400 members)
Only members can execute transactions
Over-the-counter (OTC) market
Several dealers assigned to each stock
They quote bid/ask prices
Dealers hold inventory
except social, strategic policies capital is allocated
through a price system
debt capital: interest rate
equity capital: dividend yield
Four fundamental factors
rate = k* + IP + DRP + LP + MRP
k*: real risk-free rate
IP: Inflation Premium
DRP: Default risk premium
LP: Liquidity premium
MRP: Maturity risk premium
Government securities e.g. T-bonds have basically no DRP and
little LP. They are only subject to IP and MRP
Bond prices are negatively related to interest rates. In other words,
as interest rate rises, bond price will fall.
A security that has a single payoff of $110 in one year.
If the market price of this security is $100, what is the
If the market price of this security is $90, what is the
So a decrease in price increases return.
Interest rate (promised return)=10% and bond price=$920 now
I own this bond but I have just decided to sell it (I need cash).
If interest rate rises to 12% (market prices similar securities so
that their promised return rises to 12%), price of the bond will fall.
So I and other bondholders will have a loss due to a fall in price
when interest rates rise. This is called as the interest risk.
When I sell the bond at the new (lower) price, the buyer will have
a promised return of 12%.
The amount and the timing of payments made by the issuer of the
bond to bondholders are fixed. The market price is the only bond
feature that can change. So to raise the promised return from 10%
to 12%, the price of the bond has to fall.
For a given holding period, the interest rate risk as measured by the price change at the end of your holding period increases with the time to maturity of the bond.
So other things being equal, a bond with 20 year time-to-maturity will have larger MRP than that of a 10 year bond.
We will return to this discussion after we
cover the Time Value of Money concept.
Bond Rating Agencies:
Moody’s and S&P
Attributes associated with better ratings
TTM rate/year dealer-based markets
1 yr 8.0%
10 yr 11.4%
20 yr 12.7%
Maturity risk premium
Real risk-free rate
Years to Maturity
e.g. Yield Curve for Government securities (DRP=LP=0)
Yield Curve can be Upward sloping, Downward sloping, or
Consider the following two investment alternatives for an investor who has a two-year
Alternative 1: Buy a two-year zero-coupon instrument. (rate=s2)
Alternative 2: Buy a one-year zero-coupon instrument (rate=s1) and when it matures in one year, buy another one-year instrument.
Assume s1 8.000%
In a world of certainty (future interest rates are known) both of these strategies must
yield identical final payoffs. Otherwise, no one holds either the two-year bond or the one
Given the price of zero-coupon bond, you can find the interest rate from the following formula
The interest rate that would need to prevail in the second year to make the short
and long-term investments equally attractive, ignoring risk is called the forward
or exactly (1+s1)(1+f1,2)=(1+s2)2
when you know s1 and s2, you can calculate f1,2
f1,2=9.99% approximately or 10% exactly
Now consider the case of uncertainty where future interest rates are uncertain.
Assume that E(s12)=10% same as the forward rate
P1-year=$1000/1.08=$925.93 P2-year= $1000/(1.08*1.1)=$841.75
So 2-year security is priced using E(s12). Note that this is consistent with the
Consider a short-term investor who wishes to invest for one year
Under Alternative 2:the return is a riskless 8%
Under Alternative 1:the return is risky. If s12 turns out 10% as expected, the return
will be 8% since the bond price will be $1000/1.1=$909.09 in one year and
$841.75*(1.08)=$909.09. If s12 turns out different than 10%, the return will not be
Why should this investor buy the risky 2-year bond when its expected return is 8%,
no better than that of the risk-free one-year bond.
This requires the 2-year bond to sell at a price lower than the $841.75
Suppose all investors have short-term horizons and therefore are willing to hold
the 2-year bond only if its price falls to $819.
At this price, this year’s expected return on this bond is 11% ($909.09/$819=1.11).
This means a premium of 3% compared to the risk-free one-year bond.
In this environment, the forward rate f12 no longer equals E(s12). s2 now equals
10.5%((1000/819)1/2=1.105) and f12=13%.
The change in s2 by 1.5% (10.5%-8.995%) denotes a positive MRP. It is the risk
premium given for holding long term bond.
We can also imagine a scenario in which long-term bonds can be perceived by
investors to be safer than short-term bonds.
Suppose all investors have long-term horizons (2-year). In this case, investing in
two-year bond is riskless and investing in one-year bond has reinvestment rate risk.
This would cause E(s12) to be more than f12.
In this case, we will have a negative MRP.
try to explain the shape of yield curve
e.g. Pure Expectations Hypothesis
Long-term rates are an average of current and expected
future short-term rates. For example:
definition of f12 s2=(s1+f12)/2 f12=2 s2-s1
definition of f23 s3=(2s2+f23)/3 f23=3 s3-2s2
Plug into the first expression
s3=(s1+2 s2-s1+3 s3-2s2)/3= s3
PEH says s3=(s1+E(s12)+E(s23))/3 since E(s12)=f12 and E(s23)=f23
Also note that:
definition of f12 2s2=(s1+f12) f12=2 s2-s1
definition of f23 3s3=(2s2+f23) f23=3 s3-2s2
definition of f13 3s3=(s1+2f13) 2f13=3 s3-s1
1 year 6.0%
2 years 6.2%
3 years 6.4%
4 years 6.5%
5 years 6.5%
Upward sloping yield curve
If PEH holds, what does the market expect will be the
interest rate on one-year securities, one year from now?
Three-year securities, two years from now?
6.2% = (6.0% + x%) / 2
12.4% = 6.0% + x%
6.4% = x%
PEH says that one-year securities will yield 6.4%, one year from now.
6.5% = [2(6.2%) + 3(x%)] / 5
32.5% = 12.4% + 3(x%)
6.7% = x%
PEH says that three-year securities will yield 6.7%, two years from now.
In the calculation above we relied on the expression E(s25)=f25
Equivalently, we can use the fact that long term rate is arithmetic average of short term rates
three-year securities two years from now
recall that s2=(s1+f12)/2
If MRP≠0 and PEH is not correct
Recall definitions of s1 and s2
s2=k*+IP2+MRP2 and s1=k*+IP1 assuming MRP1=0
E(s12)=k*+IP12 so IP2=(IP1+IP12)/2
since f12= 2s2 - s1 then
If yield curve is upward sloping i.e. s2>s1, then since 2s2=s1+f12
it must be f12>s1
So it is not necessarily true thatE(s12) >s1,i.e. it can be that
E(s12) <s1 but E(s12)+2MRP2>s1
Assume that the real risk free rate is 3% and that
inflation is expected to be 8% in year 1, 5% in year 2,
and 4% thereafter.
Assume that all treasury bonds are free ofdefault risk.
If 2-year and 5-year treasury bonds both yield 10%,
what is thedifference inmaturity risk premiums on the
Assuming that real risk free rate and MRP stay constant over time
MRP5 = 10% - 8% = 2%.
MRP2 = 10% - 9.5% = 0.5%.
MRP5- MRP2 = (2% - 0.5%) = 1.5%.
Exact solution :
4-6 The real risk free rate is 3 percent. Inflation is expected to be 3 percent this year, 4 percent next year, and then 3.5 percent thereafter. The maturity risk premium is estimated to be 0.0005*(t-1), where t= number of years to maturity. What is the nominal interest rate on 7-year Treasury note?
MRP1= 0.0005*(1-1)=0, MRP2= 0.0005*(2-1)=0.05%
4-12 The 5-year bonds on Cartwright Enterprises are yielding 7.75% per year. Treasury bonds with the same maturity are yielding 5.2 percent per year. The real risk free rate has not changed in recent years and is 2.3 percent. The average inflation premium is 2.5 percent, and the maturity risk premium takes the form: MRP=0.1%(t-1), where t= number of years to maturity. If the liquidity premium is 1 percent, what is the default risk premium on Cartwright’s corporate bonds?
Treasury bonds: k*+IP5+ MRP5 =2.3%+2.5%+0.4%=5.2%
Cartwright’s corporate bonds k*+IP5+ MRP5 +LP+DRP
LP+DRP=7.75%-5.2%=2.55% so DRP=1.55%