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Lecture 6 • Key issues: • Understanding bond prices and bond yields • Being able to interpret the market expectations expressed in the yield curve • The effect of stock market movements Structure of lecture 1. 2. 3. 4. 5. 6. The vocabulary of the bond market Bond Prices and Bond Yields Yield Curve and economic activity Stock Market movements The Stock market and economic activity Bubbles, Fads and Stock Prices 1. Vocabulary of bond markets Government bonds are bonds issued by government agencies to raise finance/borrow. • Corporate bonds are bonds issued by firms to raise finance/borrow (e.g. Eskom). Bond ratings are issued by Standard and Poor’s Corporation and Moody’s Investors Service. (Highly criticised for giving AAA ratings to what turned out to be toxic sub-prime assets) • The risk premium is the difference between the interest rate paid on a given bond and the interest rate paid on the bond with the highest rating (ie. with high spreads from the bonds with the lowest interest rates). • Bonds with high default risk are often called junk bonds. (High yielding bonds as high risk is associated with high reward) Vocabulary of bond markets Bonds that promise a single payment at maturity are called discount bonds. The single payment is called the face value of the bond. Bonds that promise multiple payments before maturity and one payment at maturity are called coupon bonds. The payments before maturity are called coupon payments. The ratio of the coupon payments to the face value of the bond is called the coupon rate. The current yield is the ratio of the coupon payment to the price of the bond. The life of a bond is the amount of time left until the bond matures. U.S. government bonds classified by maturity: • Treasury bills, or T-bills: Up to one year. (SA – 91-day Treasury Bill) • Treasury notes: One to ten years. (e.g. SA - R189 and R153 bonds (maturing 2013)) • Treasury bonds: Ten years or more. (e.g. SA - R197 and R186 bonds (maturing 2023)). Bonds typically promise to pay a sequence of fixed nominal payments (R100). However, other types of bonds, called indexed bonds, promise payments adjusted for inflation (R100x(1+π) rather than fixed nominal payments. (SA – inflation-linked bonds) 2.Bond Prices and Bond Yields • Bonds differ in two basic dimensions: – Default risk, the risk that the issuer of the bond (e.g. government or company) will not pay back the full amount promised by the bond. – Maturity, the length of time over which the bond promises to make payments to the holder of the bond. • Bonds of different maturities each have a price and an associated interest rate called the yield to maturity, or simply the yield. • • Yields on bonds with a maturity of a year or less are called short-term interest rates Yields on bonds with a longer maturity are called long-term interest rates Yield Curve • The relation between maturity and yield is called the yield curve, or the term structure of interest rates. • On any given date the yields on bonds of different maturities are traced or plotted along the yield curve. See Fig 15.1 for US Nov 2000 vs June 2001 • A normal yield curve is upward sloping as longterm interest rates > short-term interest rates • An inverted yield curve is downward sloping as long-term interest rates < short-term interest rates The yield curve, which was slightly downward sloping in November 2000, was sharply upward sloping seven months later Bond Prices as Present Values • Consider two types of bonds: – A one-year bond—a bond that promises one payment of $100 in one year. Price of the one-year bond (where i1t indicates the one year interest rate): $100 $ P1t 1 i1t – The price of the one-year bond varies inversely with the current one year nominal interest rate – A two-year bond—a bond that promises one payment of $100 in two years. Price of the two-year bond: $100 $ P2 t (1 i1t )(1 i e 1t 1 ) – The price of the two-year bond varies inversely both with the current one year nominal interest rate and with the one-year nominal rate expected for next year Arbitrage and Bond Prices • Arbitrage is defined as the proposition that expected returns on two assets must be equal (this equal expected return is due to market participants bidding up and down asset prices as they aim to make riskless profit out of price/valuation differences) • Question regarding bonds: If you have a choice between one-year bonds or two year bonds and what you care about is how much you will have one year from today, which bonds should you hold? One-year bonds vs two-year bonds (for one year) • One-year bonds ($1): – For every dollar you put in one-year bonds, you will get (1+ i1t) dollars next year = ($1 x (1+ i1t)) (See Fig 15.2) • Two-year bonds: – The price of two-year bonds is $p2t, Therefore each $ you put into twoyear bonds buys you $1/$P2t bonds today – When next year comes the bond bond will have one more year until maturity and will in effect be a one-year bond, with an expected price of a one-year bond at that time i.e. $Pe1t+1 – Therefore, when next year comes the 1$ that you have put into twoyear bonds is equal to the quantity of two-year bonds that you bought ($1/$P2t) times the price at which you can sell one-year bonds ($Pe1t+1 ) – You can expect to receive $1/$P2t times $Pe1t+1 dollars next year, which equals $Pe1t+1 /$P2t = ($1 x $Pe1t+1 /$P2t ) (See Fig 15.2) Figure 15.2 Returns from Holding One-Year and Two-Year Bonds for One Year Arbitrage and Bond Prices • Based on arbitrage forces it can be assumed that the expected returns are equal for holding a one year bond or for holding a two-year bond for one year i.e. $ P e 1t 1 1 i1t $ P2 t • If this were not the case and for e.g. the expected returns were higher for holding a two-year bond for one year, then there would be no demand for holding one-year bonds • This is also based on the expectations hypothesis – that investors are only about expected returns (abstracting away from questions for the relative riskiness of the two bonds – of which the two-year bond would be more risky as the price at which it will be sold after one year is uncertain) Arbitrage and Bond Prices • If two bonds offer the same expected one-year return, then: 1 i1t which is equal to: $ P e 1t 1 $ P2 t $ P e 1t 1 $ P2 t 1 i1t • i.e. arbitrage implies that the price of a two-year bond today is the present value of the expected price of the bond next year. • Question: What does the expected price of a one-year bond next year depend on i.e. what does $Pe1t+1 depend on? • The price of a one-year bond paying $100 next year will depend on the one-year $100 interest rate next year i.e. e $P • This gives: 1t 1 (1 i e 1t 1 ) $100 $ P2 t (1 i1t )(1 i e 1t 1 ) • Which tells us that the arbitrage between one- and two-year bonds implies that the price of two year bonds is the present value of the payment in two years (namely $100) discounted using the current and next year’s expected one year interest rates From Bond Prices to Bond Yields Bond yields contain the same information about future expected interest rates as bond prices – but they do so in a clearer way. Definition: The yield to maturity on an n-year bond, or the n-year interest rate, is the constant annual interest rate that makes the bond price today equal to the present value of future payments of the bond. For example: the yield two maturity, or two-year interest rate, based on the previous example, would make the present value of $100 in two years equal to the price of the bond today i.e.: $100 $ P2 t (1 i2 t ) 2 If the bond sells for $90 today (i.e. $P2t = $90) then the two-year interest rate (i2t) , (yield to maturity) equals: $90 = $100/(1+i2t)2 (1+i2t)2 = $100/$90 (1+i2t) = ($100/$90)1/2 i2t = 5,4% From Bond Prices to Bond Yields • Question: what is the relation of the two-year interest rate (yield to maturity) to the current one-year interest rate and the expected one-year interest rate? $100 $100 2 • Eliminating $P2t gives: (1 i ) (1 i )(1 i e 1t 1 ) 2t 1t 1 i2t 2 1 i1t 1 i1et 1 • Which is equal to: • This relates the two year interest rate (yield to maturity) (i2t), the current one-year interest rate (i1t) and next year’s expected oneyear interest rate (ie1t+1), which can be approximated as: i2 t 1 (i1t i1et 1 ) 2 • i.e. the two year interest rate is (approx.) the average of the current one-year interest rate and next year’s expected one-year interest rate • More generally, the yield on a 10 year bond is (approx.) equal to the average of the current one-year interest rate and the one-year interest rates expected for the next nine years 3. Yield Curve and economic activity •Interpreting the Yield Curve • By looking at yields for bonds of different maturities we can infer what financial markets expect short-term interest rates will be in the future – An upward sloping yield curve means that long-term interest rates are higher than shortterm interest rates. Financial markets expect short-term rates to be higher in the future. – A downward sloping yield curve means that long-term interest rates are lower than shortterm interest rates. Financial markets expect short-term rates to be lower in the future. • Using the following equation, you can find out what financial markets expect the 1-year interest rate to be 1 year from now: e i1t 1 2i2t i1t • the one-year interest rate expected for next year is equal to twice the yield on a two-year bond minus the current one-year interest rate •e.g. Fig 15.1 on June 1 2001 the one-year interest rate it+1 was 3,4% and the two-year interest rate i2t was 4,1%, therefore the financial markets expected the one-year interest rate one year later (on June 1 2002) to equal: 2x4.1% 3.4% = 4.8% i.e. 1.4% higher than the one-year interest rate on June 1 2001 (i.e. yield curve is upward sloping) The Yield Curve and Economic Activity • Question how did the US Yield Curve in Fig 15.1 go from being downward sloping in November 2000 to being upward sloping in June 2001 • Answer: Because the slowdown in the first half of 2001 led to a sharp decline in shortterm interest rates combined with an expectation in financial markets that output would recover and that expected short-term interest rates returning to higher levels in future IS-LM analysis • In November 2000 (Fig. 15.3) economic growth was being forecast to slow down i.e. a soft landing back to the natural rate of unemployment, with a small decrease in the interest rate (as per the slightly downward sloping Yield Curve in Fig. 15.1) • From November 2000 to June 2001 (Fig.15.4) the economy deteriorated more sharply than predicted (IS curve) so the Fed initiated a monetary policy expansion (LM curve). As result in June 2001 output was higher and interest rates lower at A’ that economy would have been at B with no monetary expansion • In June 2001 (Fig15.5) markets expected investment spending to pick up (IS curve) and markets expected tighter monetary policy in future (LM Curve), move from A to A’, therefore upward sloping Yield Curve in June 2001 as in Fig. 15.1 – The anticipation of higher short-term interest rates in future was the reason long-term interest rates remained high – The flat portion of the yield curve in June 2001 for maturities of up to one year indicated that markets did not expect interest rates to start rising until June 2002. In fact interest rates did not rise until June 2004 (two years later) The Yield Curve and Economic Activity Figure 15 - 3 The U.S. Economy as of November 2000 In November 2000, the U.S. economy was operating above the natural level of output. Forecasts were for a “soft landing,” a return of output to the natural level of output, and a small decrease in interest rates. The Yield Curve and Economic Activity Figure 15 - 4 The U.S. Economy from November 2000 to June 2001 From November 2000 to June 2001, an adverse shift in spending, together with a monetary expansion, combined to lead to a decrease in the short-term interest rate. The Yield Curve and Economic Activity From this figure, you can see the two major developments: – The adverse shift in spending was stronger than had been expected. Instead of shifting from IS to IS’ as forecast, the IS curve shifted by much more, to IS’’. – Realizing that the slowdown was stronger than it had anticipated, the Fed shifted in early 2001 to a policy of monetary expansion, leading to a downward shift in the LM curve. The Yield Curve and Economic Activity Figure 15 - 5 The Expected Path of the U.S. Economy as of June 2001 In June 2001, financial markets expected stronger spending and tighter monetary policy to lead to higher short-term interest rates in the future. The Yield Curve and Economic Activity •Financial markets expected two main developments: – They expected a pickup in spending-a shift of the IS curve to the right, from IS to IS’. – They also expected that, once the IS curve started shifting to the right and output started to recover, the Fed would start shifting back to a tighter monetary policy. 4. Stock Market movements • Firms raise funds in two ways: – Through debt finance —bonds and loans; and – Through equity finance, through issues of stocks or shares. Instead of paying predetermined amounts as bonds do, stocks pay dividends in an amount decided by the firm (typically dividends move in the same direction as profits, but some profit is retained to finance future investment). Stock prices are volatile (See Fig.15.6) The Stock Market and Movements in Stock Prices Figure 15 - 6 Standard & Poor’s Composite Index, in Real Terms, since 1980 Note the sharp increase in stock prices in the 1990s, followed by the sharp decrease in the early 2000s. Stock Prices as Present Values • What determines the price of a stock? The price of a stock must equal the present value of future expected dividends. Where $Qt = the price of a stock (after the dividend has been paid this year i.e. ex dividend) $Dt = the expected dividend this year $Det+1 = the expected dividend next year $Det+2 = the expected dividend two years from now, etc. $ Dte1 $ Dte 2 $Qt ... e 1 i1t 1 i1t 1 i1t 1 The (nominal) price of a stock is equal to the present value of the dividend next year, discounted using the current one-year interest rate plus the present value of the dividend two years from now, discounted using both this year’s one-year interest rate and next year’s expected one-year interest rate, etc. Stock Prices as Present Values (Real) • The real stock price is given as the present value of real dividends, discounted by a sequence of one-year real interest rates i.e. Dte1 Dte2 Qt ... e 1 r1t 1 r1t 1 r1t 1e • Implications: – Higher expected future real dividends lead to higher real stock prices – Higher current and expected future one-year real interest rates lead to lower real stock prices 5. The Stock Market and Economic Activity • Stock prices follow a random walk if each step they take is as likely to be up as it is to be down. (Qt = Qt-1 + μ where μ is a random error term) Stock movements are therefore unpredictable. • Note: if there is wide belief that stocks will be priced 20% higher in a year’s time (a much better return than the alternative bonds) then stock prices will be bid up today to equalise returns between stocks and bonds. • Even though major movements in stock prices cannot be predicted, we can still do two things: – We can look back and identify the news to which the market reacted. – We can ask “what if” questions e.g. (1) what if the monetary authorities embark on expansionary policies (e.g. R cut) or (2) what if there is a boom in consumer spending A Monetary Expansion and the Stock Market • If the monetary authority adopts on expansionary policy then the LM shifts and interest rates decrease and output increases (Fig.15.7) in the short-run (prices sticky) • But, what happens to the stock market? • Answer: It depends on what participants in the stock market expect of monetary policy before the expansion takes place. – If fully anticipated then the stock prices will not reacted ( expected future dividends and future interest rates are “already factored in” and the is no change to $Qt) – if the move is (partly) unexpected then stock prices will rise because: • (1) there will be lower interest rates for some time and this increases the present value of $Qt • (2)the monetary expansion implies higher output and higher dividends A Monetary Expansion and the Stock Market Figure 15 - 7 An Expansionary Monetary Policy and the Stock Market A monetary expansion decreases the interest rate and increases output. What it does to the stock market depends on whether financial markets anticipated the monetary expansion. Unexpected increase in consumer spending (IS curve) • Due to an unexpected increase in consumer spending the IS curve shifts up leading to increased output and increased interest rates (Fig 15.8a) • For stock prices this unleashes two contradictory effects – Firstly, higher output is associated with higher dividends and increased stock prices – Secondly, a higher interest rate results in lower stock prices (reduced present value) • Which of the two effects dominates? – This depends on the slope of the LM curve (See Fig.15.8(b) ) – a flat LM curve leads to a small increase in r and a large increase in y stock prices rise – A steep LM curve leads to a large increase in r and a small increase in y stock prices fall – A steep LM curve indicates a high degree of output inelasticity to changes in interest rates An increase in consumption spending and the Stock Market Figure 15 – 8a An Increase in Consumption Spending and the Stock Market The increase in consumption spending leads to a higher interest rate and a higher level of output. What happens to the stock market depends on the slope of the LM curve and on the Fed’s behavior. An increase in consumption spending and the Stock Market Figure 15 – 8b An Increase in Consumption Spending and the Stock Market If the LM curve is steep, the interest rate increases a lot, and output increases little. Stock prices go down. If the LM curve is flat, the interest rate increases little, and output increases a lot. Stock prices go up. An increase in consumption spending and the Stock Market • A key question is how will the monetary authorities react to an increase in consumption spending? • See Fig.15.8c Accommodation versus tightening • Accommodation (increase money supply in line with increased money demand) leads to a downward shift in the LM curve – stock prices will rise as output is up and interest rates do not rise • Tightening – as the monetary authority fears inflation due to increased consumption they contract money supply (shifting up LM curve) – stock prices will fall as there is no change in output (expected profits and dividends) and the interest rate is likely to be higher for some time • No change to monetary stance – effect on stock prices is ambiguous An Increase in Consumption Spending and the Stock Market Figure 15 – 8c An Increase in Consumption Spending and the Stock Market If the Fed accommodates, the interest rate does not increase, but output does. Stock prices go up. If the Fed decides instead to keep output constant, the interest rate increases, but output does not. Stock prices go down. Summary on stock prices • How stock prices respond to a change in output depends on a range of factors (See US example from recent history): 1. What the market expected in the first place – (e.g. is it factored in) 2. The source of the shocks behind the change in output (e.g. monetary expansion vs consumption boom) 3. How the markets expect the monetary authorities to react to the output change (accommodation vs tightening) Making (Some) Sense of (Apparent) Nonsense: Why the Stock Market Moved Yesterday and Other Stories Here are some quotes from the Wall Street Journal from April 1997 to August 2001. Try to make sense of them, using what you’ve just learned: April 1997.Good news on the economy, leading to an increase in stock prices: “Bullish investors celebrated the release of market-friendly economic data by stampeding back into stock and bond markets, pushing the Dow Jones Industrial Average to its second-largest point gain ever and putting the blue-chip index within shooting distance of a record just weeks after it was reeling.” (Output growth – profits dividends stock prices ) December 1999.Good news on the economy, leading to a decrease in stock prices: “Good economic news was bad news for stocks and worse news for bonds. . . . The announcement of stronger-than-expected November retail-sales numbers wasn’t welcome. Economic strength creates inflation fears and sharpens the risk that the Federal Reserve will raise interest rates again.” (Fed will respond with tightening policies due to inflation fears – interest rates up and stock prices ) Making (Some) Sense of (Apparent) Nonsense: Why the Stock Market Moved Yesterday and Other Stories September 1998. Bad news on the economy, leading to an decrease in stock prices: “Nasdaq stocks plummeted as worries about the strength of the U.S. economy and the profitability of U.S. corporations prompted widespread selling.” (output contraction – profits dividends stock prices ) August 2001. Bad news on the economy, leading to an increase in stock prices: “Investors shrugged off more gloomy economic news, and focused instead on their hope that the worst is now over for both the economy and the stock market. The optimism translated into another 2% gain for the Nasdaq Composite Index.” (expectation of output growth and no risk of higher interest rates – stock prices ) 6. Bubbles, Fads, and Stock Prices • Stock prices are not always equal to their fundamental value, defined as the present value of expected dividends. • Stocks are sometimes overpriced or underpriced – overpricing ends with a crash (US 2009) or a long slide (Japan 1989-1992) • Such overpricing can occur even when investors are rational e.g. it is rational to buy a stock whose fundamental value is 0 (it will never make a profit or pay dividends) if they buyer expects the price at which the stock can be sold in future is higher than the current purchase price • i.e. rational speculative bubbles occur when stock prices increase just because investors expected them to (see Tulipmania in 17th century Holland and Russia 1994) • Deviations of stock prices from their fundamental value are called fads. Famous Bubbles: From Tulipmania in Seventeenth-Century Holland to Russia in 1994 Tulipmania in Holland In the seventeenth century, tulips became increasingly popular in western European gardens. A market developed in Holland for both rare and common forms of tulip bulbs. Bulb prices increased to the price of a house in 1637 and then a few years later fell to 10% of their peak value The MMM Pyramid in Russia In 1994 a Russian “financier,” Sergei Mavrody, created a company called MMM and proceeded to sell shares, promising shareholders a rate of return of at least 3,000% per year! The trouble was that the company was not involved in any type of production and held no assets, except for its 140 offices in Russia. The shares were intrinsically worthless. The company’s initial success was based on a standard pyramid scheme, with MMM using the funds from the sale of new shares to pay the promised returns on the old shares. The scheme collapsed and shareholders lost their money. Conclusion • Our focus this week has been on how expectations and news on economic activity effects bond and stock prices • Next week we will look at how bond and stock prices affect economic activity by influencing consumption and investment spending