By Rodney Lewis,2014-04-11 16:44
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How Do Expectations Affect Asset Prices?

    An asset is expected to provide a stream of future payments to the owner. Putting aside speculative bubbles, an asset’s value (its price) at any moment in time is the expected present discounted value of the

    stream of future payments. Putting aside risk, the expected real return on all assets should be the same; otherwise, investors would be willing to hold only the asset with the highest expected return. Since asset prices depend on expectations about the future, they are greatly affected by new information that changes these expectations. Likewise, the more unexpected an economic evente.g., a monetary policy decision

    the greater its effect on asset prices.


    At present, apart from the obvious topical interest in finance, the discussion of expectations and financial markets seems a bit of a sideshow. Chapter 16 will link asset prices and the real economy by introducing relationships between consumption and wealth and between investment and stock prices. Other chapters will discuss the possibility that a fall in asset prices can lead to a financial crisis, with repercussions for the real economy. In this context, Chapter 22 discusses the Great Depression and Japan's poor economic performance since the collapse of Japanese stock prices in the early 1990s.


1. Tools and Concepts

    i. Arbitrage refers to the notion that (ignoring risk) expected returns on two assets must be the same. If two assets have different expected returns, investors will purchase the asset with the higher return and sell the one with the lower return, thereby increasing the relative price (and reducing the relative expected return) of the asset with the higher return. The process continues until expected returns on the two assets are equalized.

    ii. A bond's maturity is the length of time over which it promises to make payments to the holder. A bond's yield to maturity is the constant interest rate that makes the present discounted value of future payments on the bond equal to the price of the bond today. The yield curve (also called the term

    structure of interest rates) is the relation between the yield to maturity and the maturity of a bond.

iii. The chapter introduces a significant amount of basic financial vocabulary.

    iv. The fundamental value of a stock is the expected present discounted value of future dividends. A rational speculative bubble occurs when the stock price exceeds the fundamental value because investors expect the price to increase.



1. Bond Prices and the Yield Curve

    Bonds are assets that (typically) promise a sequence of fixed nominal payments. Ignore default risk, so that the promised payments actually occur. The price of a bond is the present value of these payments.

For example, the price of a bond that promises to pay $100 in one year is given by

     $P=$100/(1+i). (15.1) 1t1t

    The numeric subscript on the price and the nominal interest rate indicates a one-year bond. Note that the price of the bond varies inversely with the interest rate.

    Likewise, the price of a bond that promises to pay $100 in two years (i.e., a two-year bond) is given by

     e $P=$100/[(1+i)(1+i)]. (15.2) 2t1t1t+1

    Note that price of the two-year bond (the present value of $100 received in two years) depends on the expected one-year interest rate next year.

    An alternative derivation of the two-year bond price relies on arbitrage, the principle that expected returns on all assets (in positive supply) must be the same. If investors do not care about risk, as is assumed throughout most of the chapter, then no one would be willing to hold an asset with an expected return below the expected return on other assets.

    Suppose investors choose between holding one- and two-year bonds. The one-year (gross) return on a one-year bond is 1+i. To derive the expected one-year (gross) return on a two-year bond, note that at the end 1teof one year, the two-year bond will become, effectively, a one-year bond, with expected sale price $P. 1t+1eDivide this sale price by the original price to arrive at the expected one-year (gross) return of $P/$P. 1t+12t

    Equating the expected returns from the two assets and rearranging gives

     e $P=$P/(1+i). (15.3) 2t1t+11t

    The expected sale price of a one-year bond next year is simply the present value of the bond proceeds next year, or

     ee $P=$100/(1+i). (15.4) 1t+11t+1

    Substituting equation (15.4) into equation (15.3) gives the two-year bond price, which is identical to the price derived in equation (15.2).

    The expression for the price of a two-year bond involves two interest rates: the current one-year rate and the expected future one-year rate. Likewise, the expression for the price of a bond that matures in n years

    would involve n interest rates. A summary measure of the return on n-year bonds is the yield to maturity,

    defined as the constant interest rate that equates the bond price with the present value of the future payments on the bond. The yield on an n-year bond is approximately equal to the average of the current

    one-rate interest rate and the expected one-year rates over the next n-1 years.

For example, the two-year bond yield (denoted by i) is defined by 2t

     e $100/(1+i)= $P=$100/[(1+i)(1+i)], (15.5) 2t2t1t1t+1


which implies

     e (1+i)=(1+i)(1+i) (15.6) 2t1t1t+1


     e i?(i+i)/2. (15.7) 2 t1t1t+1

    The yield curve plots yields against bond maturities. The yield curve will slope up (yields will be higher on longer maturities) when financial market participants expect short-term interest rates to increase in the future. The yield curve will slope down when market participants expect short-term interest rates to decline.

2. The Stock Market and Movements in Stock Prices

    Firms raise needed funds through debt (issuing corporate bonds or taking bank loans) and equity (selling ownership sharesstockin the firm). Corporate bonds promise interest and principal repayments and are priced according to the methods described above. Stocks, by contrast, have no predetermined payments. Periodically, the firm pays some of its profits as dividends to stockholders, but the amounts of these payments are under the firm's discretion.

Ignoring speculative bubbles, described in Section 15.3, the price of a stock (denoted $Q) is the expected t

    present discounted value of future dividends. Thus, the ex-dividend pricethe price after the current

    year's dividend has been paidis given by

     eee $Q=$D/(1+i) + $D/[(1+i)(1+i)] + . . . (15.8) tt+1tt+2tt+1

     ewhere $D is the expected dividend next year. Note that the stock price must take into account dividends t+1

    over the entire life of the firm. Equation (15.8) can be recast as an expression for the real stock price by replacing nominal dividends with real dividends and by discounting by real (instead of nominal) interest rates.

    As described in an appendix to the chapter, the expression for the stock price can be derived from arbitrage between stocks and one-year bonds. Intuitively, arbitrage implies expected returns from stocks and bonds will be equalized. Thus, dividends will be discounted by bond interest rates (and expected interest rates). Moreover, the one-year return on a stock depends upon the dividend and the sales price of the stock after one year. The future sales price, however, will itself depend upon future dividends, so (again ignoring bubbles) the stock price can be written as an infinite series of discounted dividends.

    Since stock prices depend upon expectations about the future, they change only when new information (“news”) changes these expectations. As a result, apart from those cases where a few investors have better

    information than the rest of the market, changes in stock prices cannot be predicted. News that leads to increased expectations of output tends to increase stock prices, because higher output means higher profits and higher dividends. News that leads to increased expectations of interest rates tends to reduce stock prices, because higher interest rates make investment in bonds more attractive relative to stocks. In practice, a large part of the effect of news on the stock market is the market's evaluation of how the Federal Reserve will change policy in response.

    For example, consider the response of the stock market to an unexpected increase in consumer spending. If the Fed is expected to do nothing, the response is ambiguous, because output increases (which tends to increase stock prices), but interest rates also increase (which tends to reduce stock prices). However, if the Fed is expected to increase the money supply to prevent interest rates from rising, stock prices will increase;


    if it is expected to reduce the money supply to prevent output from increasing (and thus reduce inflationary pressure), stock prices will fall.

    In general, a monetary expansion will have very little effect on stock prices if it is anticipated, since expected dividends and interest rates do not change. In this case, the monetary expansion itself is not news. The information that led to the expectation of the monetary expansion was news, and stock prices incorporated the effects of the monetary expansion then. To the extent that it is unanticipated, a monetary expansion will lead to an increase in stock prices, since it implies higher output (and thus higher dividends) and lower interest rates.

3. Bubbles, Fads, and Stock Prices

    The present value of dividends is called the fundamental value of a stock. At times, stock prices deviate from their fundamental values. Sometimes this occurs for no good reason. Some financial investors may not be rational and may pay a high price for stocks simply because they have done well in the past. In contrast to these fads, sometimes stock prices exceed their fundamental values because investors expect stock prices to rise in the future. These episodes are called rational speculative bubbles. Even though a crash is possible when stock prices exceed their fundamental values, it may make sense for investors to pay a high price for stocks if there is a chance that prices will increase in the future.

    Bubbles and fads are important because overpriced stocks are vulnerable to crashes, which can affect real activity.


1. Points of Clarification

    Bubbles cannot exist on bonds with fixed maturity. The possibility of an asset bubble depends upon the price exploding (growing forever at too high a rate). Since bonds have a fixed terminal payment, there is no possibility that bond prices will rise forever.

2. Alternative Sequencing

    This chapter is optional, even within the module on expectations. It is not required for most of Chapters 16 and 17. Moreover, instructors pressed for time could limit attention to bond pricing and the yield curve and omit discussion of the stock market.

3. Enlivening the Lecture

    This chapter provides a wealth of possibilities to stimulate discussion in lecture. A useful tool is the yield curve, which is readily available in the newspaper and provides a good point of departure for a discussion of financial markets in the context of current economic events. Students might also appreciate a primer on reading the financial pages of the newspaper.


    The main text assumes that investors are risk neutral. An appendix explores the implications of allowing for risk. Essentially, riskier assets are charged a risk premium (denoted by ;), which requires them to pay

    a higher expected return. As such, the risk premium acts as an increase in the discount rate, so that increases in the risk premium reduce stock prices. The text notes that the average risk premium on stocks over bonds has been about 5% in the United States over the past century and that the risk premium varies over time, contributing to variations in stock prices.



    Long-term interest rates tend to move in the same direction, but by a smaller amount, than short-term interest rates. Presumably, this fact reflects market expectations that part of the movements in short-term interest rates will be temporary.


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