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 MarketsThe 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 SearchStigler (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 RatesYn = 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:

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?

rY

Ynn

n

n ln

( )

( )

1

111

0026.01)061.01(

)059.01(29

30

30

r

Information in Tax-Exempt and Taxable Bond YieldsQUESTION: How do you know if its best to buy tax

exempt or taxable bonds?

YT = Taxable yieldYTE = Tax exempt yieldT = 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 SpreadsYn = 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 PricesProblem: 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 gallonFebruary $1.00March $1.11April $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 gallonFebruary $1.11March $1.00April $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 gallonFebruary $1.30March $1.20April $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 PricesCall 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 VolatilityWe 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 100A 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 Premium

770 43

775 39

780 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 VolatilitiesLike 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 wasExpiration Implied Volatility Incremental VolatilityDec 1990 .187 ---Jan 1991 .205 .218Feb 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)