Information in Financial Prices
The Market Pricing System - Hayek (1945)
• Information required to run economy is diffuse.
• No one individual has all the information or the ability
to understand it all if they had it.
• Instead, people specialize on the information most
important to them and rely on market prices otherwise.
• Market price aggregates the information of all those who
find the particular information important to to them.
Efficient Markets
The more efficient a particular market
• the more prices accurately reflect important supply and
demand information for a particular product.
• the fewer relatively knowledgeable people are specialized
in the market’s information. The highly-informed “dealers”
compete to beat others to the information while everyone
else simply observes prices and makes decisions based on
them.
Exercise: Bean Jar.
Example: Oil prices rise sharply.
Expert Dealer’s Response: gather information and decide
whether price rise is warranted (buy oil) or not (sell oil).
Most Consumers Response: use less oil.
Most Producers Response: produce more oil.
•The beauty of the market price system is that it economizes
on information and reduces the amount of resources spent on
gathering information.
• Only the most skilled dealers gather information because
prices so accurately reflect information that few can make a
profit at it and most are better off just reacting to prices and
avoiding the costs of gathering information.
Example: Technical Analysis - many stock investors simply
look at charts and follow price momentum.
Information Search
Stigler (1961)
• His main concern is how one ascertains price when it
changes frequently and when the underlying good
differs slightly across dealers due to service, location
and quality differences.
• Example: Brokerage commissions - payment for orders.
• Price dispersion is a measure of ignorance in the market.
• The more price dispersion, the more it pays to search for
and sample new dealers’ quotes.
• See bond broker websites (e.g., tradeweb.com,
bondhub.com).
• Markets and dealers provide a way to reduce price search
costs to most buyers and sellers as dealers compete with one
another by offering to buy (sell) for higher (lower) prices.
• Example: There is an ongoing debate about whether all
stock trades should go through a central market or whether
different dealers/markets should compete to execute orders.
• Economies of scale in information gathering and search
support large dealers/markets but not necessarily a
monopoly.
• Advertising prices and dealer reputation helps to reduce
price dispersion because it lowers search costs.
• See www.academic.nasdaq.com/headtrader - dealer game.
Information in Financial
Prices
• Asset prices and interest rates are used by consumers and
businesses to decide how much to consume, save and
invest in new productive capacity.
• Prices allow the consumption decision to be separated from
the production decision, i.e., consumers do not need
to know what producers are doing, interest rates
effectively provide the information relevant to each.
• Example: Suppose that producers have many highly
profitable investment projects. They bid up interest
rates which induces consumers to consume less and
save more. Consumers do not have to evaluate the
producers’ investments in making their savings
decisions.
Efficient Market Hypothesis
• The efficient market hypothesis states that all relevant
information on a firm’s financial prospects are
reflected in the prices of its securities.
• The most efficient markets have much available
information, low transactions costs and much
liquidity (can buy and sell without moving price).
• Many financial firms now specialize in providing
information.
• Examples: Briefing, Bloomberg, Thomson, Reuters,
Financial Engines.
• Question: If you are selling your house, how do you set
the price?
Extracting Information
Indirectly from Asset Prices
•A corollary to the efficient markets hypothesis is that
valuable information can be extracted indirectly from asset
prices.
• Simple Example: The ratio of stock price per share to book
value per share indirectly signals firms to expand (P/B large)
or contract (P/B small).
Information in the Term
Structure of Interest Rates
Yn = the nominal bond yield for a bond covering n years
rn = the expected "forward" yield for a one year bond
covering the one year period n.
NOTE: r2 is not the two year bond rate, it is the rate expected
on the one year bond next year.
(1 + Yn)n = (1 + r1)(1 + r2)...(1 + rn)
(1 + Yn) = [(1 + r1)(1 + r2)...(1 + rn)]1/n
This implies that any nominal long bond yield can be
expressed as a geometric average of one year rates.
From this formula, we can derive another formula for
computing the one period forward rate beginning at time t:
(1  Yn ) n
rn 
n 1  1
(1  Yn  l )
Example: Recently, the 29-year treasury bond yielded 6.1
percent and the 30-year bond yielded 5.9 percent. What is
the implied one-year rate for year 30? Is there anything
unusual about the answer?
(1  0.059 )
r 
 1  0.0026
(1  0.061 )
30
30
29
Information in Tax-Exempt
and Taxable Bond Yields
QUESTION: How do you know if its best to buy tax
exempt or taxable bonds?
YT = Taxable yield
YTE = Tax exempt yield
T = Tax rate
YTE = YT (1 - T) or,
=>
YT = YTE / (1 - T)
T = 1 - (YTE / YT)
If we know YTE and YT we can estimate the "indifferent" T implicit marginal buyer's tax rate. If your tax rate is larger
than T then buy tax exempt bonds.
Problem: Suppose that a Connecticut state bond is exempt
from federal and state income taxes. Its yield is 5 percent.
The fully taxable U.S. Treasury bond has a 6 percent yield. If
your federal tax rate is 30 percent and your state tax rate is 5
percent, should you buy the state bond or the Treasury bond?
Information in Yield Spreads
Yn
= Yr + I + P
where Yn is the nominal yield,
Yr is the real yield - yield on U.S. Treasury
inflation-indexed bonds (see WSJ),
I is the expected inflation rate over the life
of the bond - regular Treasury yield
minus inflation-indexed yield,
P is the risk premium - bond yield minus same
maturity U.S. Treasury yield.
P widens during recession and narrows in expansion. It
can be measured by the difference (spread) between the yield
on a risky bond and a risk-free bond (U.S. Treasury Bond).
Risk Spread - Baa Corporates
Minus10-Year Treasury Bonds
Question: Why is this spread large in 1991 and 1999 and
relatively small during 1995 through 1998?
Relative Risk Spread - Baa
Minus Aaa Corporate Bonds
Banks can use spread such as this one to set rates on loans
to customers with different business risk levels.
Inflation Spread -30-Year
Treasury Minus 3-Month TBill
Question: Why did this spread increase sharply during the
early 1990’s and fall in the late 1990’s?
Information in Federal Funds
Futures Prices (Rates)
• The Federal Funds (FF) rate is the rate at which banks lend
funds to one another. When banks have excess (little) funds
to lend, the FF rate falls (rises). The Federal Reserve Board
controls the FF rate by buying (selling) Treasury securities
from banks, which decreases (increases) their excess funds.
Therefore, futures prices for FF should reflect the market’s
expectation of the probability of an FF rate change.
• Example: Suppose the current FF rate is 6 percent and the
FED may raise rates by 0.25 percent next month. If one
month FF futures are at 6.15 percent, what is the futures
market’s expectation of the probability that the FED will
raise rates. (FF futures actually quoted in price discounts e.g.,
6 percent = 94)
6.15 = p (6.25) + (1-p)(6.00) => p = .60
Information in Futures Prices
Problem: Suppose your company delivers oil to customers at
a fixed price of $1 per gallon. You have an inventory
of 1 million gallons and storage capacity for 2 million
gallons. Your customers will be using 0.5 million
gallons per month over the next four months. It is
January 1 and you observe the following set of prices
for spot oil and oil futures.
Spot
$0.90 per gallon
February
$1.00
March
$1.11
April
$1.23
What is your strategy for purchasing the oil you will need? If
there are many firms in your situation, how might spot and
futures prices change in the near-term?
Problem: Assume everything above but you observe a
new set of prices for spot oil and oil futures.
Spot
$1.23 per gallon
February
$1.11
March
$1.00
April
$0.90
What is your strategy for purchasing the oil you will need? If
there are many firms in your situation, how might spot and
futures prices change in the near-term?
Note: Futures prices signal information to market
participants and different price patterns can induce
different behaviors from participants.
Problem: Assume everything above but you observe a
new set of prices for spot oil and oil futures.
Spot
$1.40 per gallon
February
$1.30
March
$1.20
April
$1.10
What is your strategy for purchasing the oil you will need? If
there are many firms in your situation, how might spot and
futures prices change in the near-term? (something like this
happened in New England in January 2000.)
Redo each problem and assume that you have 2 million
gallons in inventory.
Information in Options Prices
Call Option: The right to purchase 100 shares of a security at
a specified exercise price (Strike) during a specific period.
EXAMPLE:
On October 23, 1987, a January 60 call on
Microsoft had a premium of 7 1/2. The stock
price at the time was 53.
This means the call is good until the third Friday of January
and gives the holder the right to purchase the stock from the
writer at $60 / share for 100 shares.
cost is $7.50 / share x 100 shares = $750 premium or
option contract price.
Question: Is this option a good buy?
Measuring Implicit Volatility
We can use options prices to get the market’s prediction of
the volatility of a company’s stock price over the life of the
option.
1. Choose an option with an exercise price (E) equal to the
discounted stock price.
E = Se-rt
where S=stock price, e is the exponential function, r=the
risk-free rate, and t is the option maturity time in years.
2. Get the implied standard deviation () using
 = C(2).5/S(t).5
where C is the call’s market price and  = 3.1416.
Volatility Index on S&P 100
A widely followed index of overall stock market volatility is
the VIX - the standard deviation of the S&P 100 implied by
one-month index option premiums. See www.cboe.com.
Suppose we have the following set of 3-month call option
premiums for the S&P 100:
Exercise Price
770
775
780
Premium
43
39
34
Assume that the risk-free rate is 6 percent and the S&P 100
index is trading at 786. To find the implied volatility, select
the option that has a exercise price closest to E = Se-rt which
in this case is the 775 strike (E = 786e-(.06)(.25) = 774.4). Then
 = C(2).5/S(t).5 = 39(2*3.1416).5 /786(.25).5 = 98/393 = .25
Term-Structure of Implied
Volatilities
Like interest rate term structure, you can get a term structure
of stock market volatilities by getting the implied volatilities
from options of different maturities. For example, on
December 3, 1990, the implied volatilities for S&P 100
options of various maturities was
Expiration
Implied Volatility
Incremental Volatility
Dec 1990
.187
--Jan 1991
.205
.218
Feb 1991
.257
.344
Question: Does this pattern make sense given that Iraq was
given until January 15, 1991 to leave Kuwait?
• One could do the same with interest rate options or
individual stock option (say around earnings announcements)