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Note #1:
Asset Pricing and Market Reaction to Economic News

Prof. Lukasz A. Drozd

Spring 2015

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This note provides a review of major asset classes and uncovers the set of factors which influence their prices.

Introduction
Financial asset is something one can own, has value, and represents a contractual claim to future resources or payment of some sort. Depending on the asset class, the exact nature of the claim di↵ers and can be very simple or very sophisticated. Apart from commodities, financial markets primarily involve three basic asset classes: money, bonds and stocks. In what follows, we discuss the key characteristics of these three basic asset classes, the economics underlying the formation of their prices, and use the key insights how prices are formed to better understand the interaction between the (macro)economy and the financial markets.

Money
Money is the most basic financial asset, and it is independently important because it plays the role of a reference asset or a unit of account as well as the economy’s medium of exchange. By definition, money includes all assets that are widely accepted in making transactions and bear no interest. In the U.S. the definition includes currency in circulation (dollar bills and coins), and demand dollar deposits that bear no interest. 1

Unlike any other asset, money is not a contractual claim in a proper sense of this word. That is, its issuer does not promise any reward for holding money. Instead, its value is 1

While our definition is very concrete, and corresponds closely to the so called M1 monetary aggregate, we should mention here there are wider or narrower definitions of money. The exact dividing line between monetary and non-monetary assets is quite fluid.

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derived from a self-fulfilling belief that a transfer of resources will occur spontaneously when money is presented to virtually anyone. This aspect of money is very unique, as you will soon see.

Nominal Interest Rate
As already mentioned, one of the distinct features of money is that it o↵ers no reward for holding it. That is, money pays zero nominal interest rate. Clearly, by holding on to $100 dollar we always have only $100 in the future, no more no less.

Real Interest Rate and the Fisher Equation
The real return on holding money, i.e. the return earned in terms of goods one can buy next period by forgoing a purchase of one good today, however, crucially depends on what happens in the the economy. This is because how much one can buy for money at any point in time depends on prices of goods or the so called purchasing power of the dollar.

To calculate the real return or money (also referred to as real interest rate on money), consider a situation in which the prices of goods become more expensive by ⇡ e /100 percent next period. That is, for the sake of concreteness, if something costs $1 today, assume it will cost $1 + ⇡ e next period, where ⇡ e is just some unspecified number. Clearly, what this implies is that, if a certain amount of dollars purchase, say, X lb of sugar today, next period this same amount will purchase only

X
1+⇡ e

lb of sugar.

This is because the price of suger is expected to increase by ⇡ e /100 percent. Using an

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approximation2
X
⇡ X(1
1 + ⇡e

⇡ e ),

it is easy to see that by forgoing the purchase today, and instead investing in money, one approximately loses ⇡ e /100 percent in terms of goods one can purchase next period. Hence, the real return on money is negative and equal to

r⇡

⇡e.

The above expression is very useful to think about real returns on assets that are nominal, i.e. assets that involve nominal return. Define nominal return as the rate of growth each dollar invested in an asset grows on average (in dollars). That is, if today we invest $1, assume that asset that pays nominal interest rate i simply yields $(1+i) dollar next period. In the case of any such an asset, we can calculate the implied real interest rate by simply summing its nominal return and the real return on money. That is, the real return r on any nominal asset that pays nominal interest i is r⇡i

⇡e.

The above formula is referred to as the Fisher equation and it is very intuitive. It implies that while we may make money nominally on the asset itself, since we do so in monetary terms, in terms of goods we can buy less because money loses purchasing power at the rate ⇡ e . Hence, the overall return is the di↵erence between nominal interest rate and the rate at which we lose purchasing power.

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The approximation comes from the mathematical fact that:
(1 + x)
(1 + x)(1
=
(1 + y)
(1 + y)(1

y)
(1 + x
=
y)
(1

y xy)
(1 + x

y2 )
1

y)

=1+x

y,

as the terms xy and y 2 are very small whenever both x and y are small. Now express the fraction as 1+0
e
1+⇡ e and apply the formula assuming x = 0, y = ⇡ .

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Who Supplies Money and Why?
Money in the economy is derived from currency (dollar bills and coins), which is exclusively supplied by the the Federal Reserve System. The Federal Reserve System, or simply the Fed, is the central bank of the United Sates. The Fed has the exclusive right to print currency (dollar bills and coins) and e↵ectively decides how much money there is in circulation. The Fed injects currency into circulation by buying other assets, such as government bonds, and holding them. Its mandate is to manage the economy’s money supply, which needs money to facilitate transactions. The statutory goal of the Fed is to stabilize the economy, i.e. ensure price stability and full employment. The amount of money in circulation typically exceeds the amount of currency (dollar bills and coins). Nonetheless currency is the seed of all money in the economy. The reason why this is the case is because banks cannot allow people to write more checks unless they hold sufficient reserve of currency in their vault. They need these reserves to cover any possible cash withdrawals by the depositors. However, since banks typically do not hold all deposited currency, and instead loan out the excess amount, the banking system as a whole actually does create extra money. We will discuss money creation later in more detail.

Exchange Rates
Most countries have a distinct currency. Hence, there are markets in which currencies can be traded for other currencies. This markets are referred to the Foreign Exchange Markets (in short, Forex). The relative price of one currency in terms of another currency is called exchange rate, and it is the amount of foreign currency that one can acquire in the forex market in exchange for one unit of the home country currency (one dollar). We denote current spot exchange rate by ✏.

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Bonds
Bonds are representative of an important class of securities3 called fixed income securities. This class of securities includes all assets that generally oblige the issuer to make a monetary payment on some a priori defined schedule. Because of the a priori defined nature of payments, this asset class is often referred to as debt, and the use of such instruments to raise funds by corporations is referred to as debt financing (as opposed to equity financing).

Here we exclusively focus on zero-coupon bonds. Such bonds are characterized by a contractual promise of a fixed payment at a specified future date. The payment is referred to as the face value of a bond and the date at which the payment is meant to take place is referred to as the maturity date of a bond. The face value of a bond as well its maturity date are specified a priori and are both printed on the face of the bond, together with the name of the issuer. The bond simply obliges the issuer to pay the face value to whoever holds the bond at that time of maturity. It is initially sold in the primary market and before it matures it is traded by third parties in the secondary markets.

$F

$P
Purchase
Price
Today
(t)

Face value
Future 
period
(t+1)

time

Figure 1: Cash flow associated with a purchase of a zero-coupon bond. 3

A security is generally a fungible, negotiable financial instrument representing financial value. Securities are broadly categorized into: debt securities (such as banknotes, bonds and debentures), equity securities, e.g., common stocks; and, derivative contracts, such as forwards, futures, options and swaps. The company or other entity issuing the security is called the issuer. A country’s regulatory structure determines what qualifies as a security. For example, private investment pools may have some features of securities, but they may not be registered or regulated as such if they meet various restrictions. Source: Wiki.

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In many ways a bond resembles a loan. Note that the issuer of a bond e↵ectively borrows funds (money) from investors who purchase the bond from in the primary market. The amount borrowed is equal to the price of the bond (P), which clears the market; that is, at which demand for this bond equals the supply. The amount borrowed that has to be repaid is the face value of the bond F, and the repayment is due when the bond matures (at maturity date). The di↵erence between the price at which the bond is purchased and the face value of the bond, both known a priori, e↵ectively define the “interest rate” that the investors (lender) charges the issuer of the bond (the borrower) for the funds (money) that she obtains for this time period. The key di↵erence between bonds and loans, however, is that bonds can be traded in the secondary markets (i.e. between third parties), and loans typically are not.

While a bond o↵ers a legally binding contract that requires its issuer to pay the face value of the bond upon maturity, it is important to remember that the issuer may still renege on this legal obligation by filing for bankruptcy protection in court. In such a case, the bond is exchanged for the right to seize any assets that the issuer has. The bankruptcy court will consider the claim associated with bonds as senior to equity (stocks). That is, bond holders will be paid first and some bonds may be senior to other bonds. However, the borrower’s assets may still be insufficient to pay o↵ all bond holders – which typically is the case. In addition, in case the debtor does not meet its payments on bonds voluntarily and does not file for bankruptcy, bond holders have the right to put debtor into bankruptcy and initiate bankruptcy process. Equity holders do not have this right.

The U.S. government bonds are almost free from the risk of default. However, corporate bonds, municipal bonds or bonds of some other countries are not. In fact, while rare, defaults do take place (including government debt, e.g. Greece recently). The default risk is what ultimately determines the rating of a bond (given by rating agencies such as Moody’s, Standard & Poor’s or Fitch). Figure 2 illustrates how yield on an essentially identical type of bonds issued by a di↵erent parties reflects the implicit default risk (the

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resulting di↵erence in price of otherwise similar bonds is for this reason referred to as default premium). Note that the default premium is time-varying, and usually goes up during recessions. This is especially visible during the financial crises, such as the Great Depression (1929-1933) or the recent financial crisis. (Note: Depression is a very deep and prolonged recession.)

Figure 2: Default premia in the bond markets.
The key question that we ask in this lecture is how bond prices are determined in the market? It turns out that they are largely determined by the current and expected future policy of the Fed, and showing it is the goal of what follows. Those of you who read business press regularly probably know that, in fact, the Fed formulates it policy in terms of “nominal interest target.” To implement its target, the Fed buys or sells bonds in exchange for currency, adding or subtracting money from the economy.

Yield to Maturity
To relate bond prices to Fed’s policy, we must first define the nominal interest rate associated with an investment in a bond. We will look at a particular interest rate that

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assumes that the bond is held until its maturity data, which we refer to as yield to maturity.4
To see how yield to maturity is calculated, consider the investment strategy illustrated in Figure 1. This strategy assumes an investment in period t (today) in an n periods to maturity bond which costs $Pn,t to purchase today and which pays $F (face value) upon maturity (arrow down means payment made by the holder, arrow up means payment to the holder), which takes place n periods from t (today). Since the bond costs $Pn,t dollars to purchase – the market price of the bond – and pays $F dollars upon maturity (n-periods from now), it should be clear that every dollar invested in this bond on average yields F/Pn,t dollars upon maturity. Hence, in nominal terms, the rate of growth of invested money in this bond, in , can be easily calculated from the growth relation5 :

(1 + int )n = F/Pnt ,
and hence is equal to
int = (

F 1
)n
Pnt

1.

(1)

The formula is defined for any n, including n < 1 or positive number. However, when n < 1 or when it involves a fraction of a year one has to bear in mind that our definition is a bit di↵erent from the one reported by major news outlets. The news outlets report an approximate yield. We will note make this distinction in class, but it an important one to properly read financial data6 .

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For those of you who are not familiar with this terms, the interest rate is the average growth rate of invested funds. That is, interest rate i is paid when invested funds grow in dollar terms at a per period rate i. That is, if one invests $1, after one period one has (1 + i), after two periods one has (1 + i)(1 + i) = (1 + i)2 , after two periods one has (1 + i)(1 + i)(1 + i) = (1 + i)3 , etc. 5

The left-hand side is the implied final amount one has when a dollar invested grows at per period rate in . To see why, note that after one period $1 that is invested and grows at rate in per period yields (1 + in ) after one period, (1 + in )(1 + in ) after two periods, (1 + in )(1 + in )(1 + in ) = (1 + in )3 after three periods etc... The right-hand side is the final amount we get out of each $1 invested in a bond that costs P today, pays F upon maturity, and matures after n periods. 6

One can easily calculate the yield to maturity for any value of n, but the calculation becomes cumbersome when n¡1 (or a fraction). Since the most heavily traded bonds involve maturities n < 1, traders

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As is clear from the formula, yield to maturity and bond prices are (inversely) related, i.e. the higher the yield is the lower price of the bond is and vice-versa. It is also clear that bond prices can be easily recovered from the information about bond yield, its face value and its time to maturity. Hence, by describing a bond by a yield instead of its price, we do not lose any information. In practice, yields are more informative than prices and are often used in place of prices.

Finally, it is important to bear in mind that yield to maturity does not always equal the nominal return (or yield at a di↵erent time horizon) one may earn on an investment in a particular bond. If a bond is s...

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