Handout A: The Economics of the Financial System PDF

24ECB015/ 24ECC014 The Economics of the Financial System Reference materials A. Financial market pricing Contents This first handout contains a preliminary section A0 and the material A1‐A3 to be covered in the first three lectures in Weeks 1‐3. A0....

24ECB015/ 24ECC014 The Economics of the Financial System Reference materials A. Financial market pricing Contents This first handout contains a preliminary section A0 and the material A1‐A3 to be covered in the first three lectures in Weeks 1‐3. A0. Preliminary, Pgs 2‐4. Overview of the Financial System A1. Pgs 5 – 16 Fixed income instruments. The price and yield of bonds. A2. Pgs 18 – 27 Equity markets and equity pricing. A3. Pgs 28 – 36 Demography, technology and the returns to investment. Appendices, pgs 37‐44 (note my critique of “supply and demand” in bond markets). Your key study tasks for the first four weeks of the semester.  Referring to these notes and lectures and readings, practice questions from the multiple choice question bank, (topics A0.‐A3.)  Prepare the Topic A workshops in week 4 (on topics A1.‐ A3.) Reading, general. The recommended textbook, Mishkin, 2021, The Economics of Money, Banking and Financial Markets, available as e‐book via Learn, covers A0‐A2 with some gaps (little on liquidity; very little on topic A3.) Note: Mishkin is US focused. Often in the UK and Europe we use different financial terms than in the US, especially when describing financial institutions. Chapter 2 of Mishkin is an overview of the financial system covering topic A0. Read this before Week 2. Chapters 4‐6 focus on topic A1, with additional mostly US detail beyond these notes. See Appendix 1 below for some additional discussion of the material in his text, including the relationship between nominal and real interest rates (the “Fisher equation”). 1 Chapter 7 in on equity pricing discussed under topic A2. Mishkin presents the Gordon Growth Model and draws a distinction between the efficient markets hypothesis (based on rational expectations), pricing based on economic fundamentals and “behavioural” perspectives. The lectures go beyond the Mishkin textbook at various points. Additional Semester 1 material is covered in more detail in three Appendices to these notes. The first for topic A1. relates the lecture discussion of bond yields to the material in Mishkin. The other two, for topic A3., look at the economic impact of low real interest rates and provide a simple general equilibrium analysis of the supply and demand for savings and how this determines real interest rates. A0 Overview of the Financial System 23ECB015/ 23ECC014 part lecture week 1 This material is covered briefly at the beginning of the week 1 lecture. It is not directly assessed in the exams (semester 1, 2); it is provided as a reference for understanding the remaining lecture material. Reading Mishkin Part 2, chapter 2. Indirect versus direct finance. Indirect (intermediated mostly via banks) and direct (market) finance. A basic distinction, illustrated in Mishkin Chapter 2, Figure 1 on the flow of funds through the financial system is between:  Direct finance: money invested in capital market instruments, bonds and equities, bought and sold on financial markets (Semester 1, Part A and Part B).  Indirect finance: money deposited in banks and loaned to borrowers (Semester 1, Part C). The proportion of savings held in bond markets, equity markets and banks intermediation varies considerably from one country to another. Germany for 2 example is well know for the importance of bank intermediation; the US for more saving is held in equities and bonds. Still, across the world: 1. bank lending remains the most important source of funds for corporate investment and for purchase of consumer durables and housing 2. bond markets are the major source of government capital market funding. 3. equity markets are important for maturing companies; 4. startups and immature companies use another form of equity, so called “private equity” because it is not traded on public capital markets where anyone can buy and sell. Private equity is illiquid i.e. difficult to buy and sell. It is held by only a small number of investors, such as the founders of companies and early investors including ‘venture capital funds’. If private companies are successful and grow to become large and profitable, then they then often “go public” through an “initial public offering” or IPO, selling shares on the equity market and allowing early investors to obtain a financial return on their investments. Sometimes also public firms are taken private through a buyout. We will look at IPOs in Topic B; but otherwise we will not discuss private equity in this module. Different types of intermediaries There are many types of intermediaries, as well banks. See Mishkin, Chapter 2, Table 3; but note his US terminology.  non‐bank ‘depository institutions’. The equivalents in the UK are building societies and credit unions. There are also non‐bank lenders who use bond and equity funding, instead of deposits, to finance lending.  Long term savings institutions including life insurers, general (“fire and casualty”) insurance, pension funds.  Market intermediaries, e.g. retail brokers, asset managers, mutual funds, exchange traded funds (ETFs), hedge funds, and investment banks. The rapid pace of technological innovation in finance (“fintech”) has also seen the emergence of other new technology‐based intermediaries, sometimes quite similar to these existing institutions, on other occasions, e.g. crowd funding platforms; peer to peer lenders, quite new. This module focuses on financial markets and the existing established financial intermediaries. 3 Note the growing importance of international finance and international borrowing/lending. You will study this more in Semester 2 than in semester 1. The buy side and the sell side When we move onto Topic B “Trading and operations” in financial markets, you need to understand the difference between the buy side and the sell side. The buy side are institutions such as asset managers, also pension funds, life insurers, sovereign wealth funds who hold and manage investment portfolios. They are the buyers of securities. The sell side are the advisers to companies and governments who issue securities to be purchased by the buy side. The sell side is dominated by the corporate advisory and investment banking arms of the large global investment banks: JP Morgan, Goldan Sachs, Morgan Stanley, UBS, Deutsche Bank, Citygroup, Bank of America, HSBC, Barclays, BNP Paribas, Societe Generale. There are also a number of other smaller competitors, either specialist advisors or regional national investment banks.  This difference between buy side and sell side is especially important in the primary markets when equities and bonds are first issued. The sell side are trying to get as high a price as possible for their clients (and themselves). The buy side are trying to get as low a price as possible for their clients.  There is strict regulation, including so called “Chinese walls” within firms that operate on both the buy side and the sell side, to prevent sell side employees passing on client’s private undisclosed information to sell side firms and giving them an unfair advantage Facilitating trade in secondary markets The investment banks are also important in the secondary markets, where bonds and securities and also foreign exchange and commodities are subsequently traded after primary issue, and their supporting derivative markets. Here the investment banks facilitate the trading of sell side firms (and also of non‐financial companies and of traders such as hedge funds and high frequency trading firms). Investment banks only do limited trading on their own account, their relationship with secondary market trading is somewhat like that between a casino and gamblers, they facilitate the trading rather than taking big bets 4 themselves. The analogy is informative: investment banks and casinos earn much more reliable profits than traders and gamblers! 5  A1 Fixed Income Instruments: The price and yield of bonds 23ECB015/ 23ECC014 Lecture week 1 Reading  Mishkin, Part 2, chapters 4 and 6.  Relevant recent articles from the Economist / Financial Times  Data on yields, especially from FRED. The different rates of return on fixed income instruments. Mishkin Chapter 6 “The Risk and Term Structure of Interest Rates” provides a brief introduction to fixed income instruments (the various types of bonds and also shorter term ‘money market instruments’ with a maturity of less than one year) and how supply and demand affects their prices and yield. Definition 1 A bond is a security promising the investor fixed regular repayments. These regular repayments are known as coupons. The borrower (the bond issuer) then repays the full or par value at a final date referred to as the “maturity” or “redemption” date. Bonds are the most important assets within the broad class of investment assets known as ‘fixed income’ – Investopedia has a nice summary guide to fixed income https://www.investopedia.com/terms/f/fixedincome.asp. Fixed income is one of the two most important asset classes. The other is equities. You will likely specialise in an asset class if you get a job in the markets, either on the sell side (investment banking and broker dealing) or on the buy side (asset management). Other asset classes include commodities, currencies (which together with fixed income are referred to as “FICC”) and (an area of great recent excitement but not yet established in the mainstream and may never be) crypto assets. The coupon payments are usually expressed as fixed percentage of the par value and typically paid every six months. Most bonds are nominal bonds – the coupon payments and the par value are fixed monetary amounts ($, €, £ etc.). A few government bonds are inflation 6 adjusted, the par value and coupon payments are adjusted upwards to compensate for the erosion of monetary values resulting from inflation. Example 1 HM Treasury, via the UK Debt Management Office, issues bonds several times a month. The current financial year bond issues are recorded in their debt market report, updated after each issue, available here: https://www.dmo.gov.uk/data/pdfdatareport?reportCode=D5D On the day of our first lecture Tuesday 3rd October 2023 they plan to issue a 30 year bond, the 1½% Green Gilt 2053. The amount is not yet decided as I update these notes, but the previous issue on the 4th July, 2023 was for £2bn Suppose you purchase £100mn (par value) of the 1½% Treasury Gilt 2053. As holder, you will get a coupon payment of ½ 1½% £100mn £750,000 every six months, on the 3rd April and 3rd of October each year. Then on 3rd October 2053 you will get the last payment of £100,750,000 i.e. the par value plus the final coupon payment. One final point. The price you pay for the 1½% Treasury Gilt 2053 on Tuesday 3rd October may not equal the par value, you will have to pay the market price which may be higher or lower than par (in practice this is likely to be lower than par value because yields are much higher than the 1½% coupon). This is discussed further below when we look at bond yields. The box gives an example of a UK government bond (known as ‘gilts’ short for ‘gilt edged security) from the UK Debt Management Office annual debt report. The very largest issues of UK gilts are sold to an investment bank syndicate. Most issues are auctioned. A few are “index linked”. Types of bonds (more detailed material, on first reading you can skip to pg 8, prices and yields) I won’t go through this material in the lectures. This should be read alongside the textbook. Let’s look a bit more closely at the many different kinds of bonds. Governments account for the largest share of bond issues; but local government, financial institutions and non‐financial companies also issue many bonds. Bonds are most often issued in local domestic markets. But some bonds (“euro bonds”, “international bonds”) are sold in overseas markets. Here are some of the most important in today’s financial markets: 7   Domestic government bonds. The governments of all developed industrial countries – most importantly the US, UK, Japan, Germany, Italy and France – issue large amounts of bonds into their domestic markets and usually in their own currency. So US government mostly issue bonds in US dollars; the Japanese government in Japanese Yen, etc. These can be very long‐dated, 30 years plus has been common for US/ UK, but other countries, especially where there are concerns about possible rise of inflation, find it easier to issue 5 – 10 year maturities.  Sovereign bonds are another term for bonds issued by governments. This term is most usually applied when governments from emerging markets issue bonds overseas in foreign currency. Because these are issued in other countries these are classified as “Eurobonds” (see below) Sovereign bonds issued by emerging markets overseas in foreign currency are riskier than the bonds issued by developed country governments in their own currencies and sold to domestic investors. When issuing in their own currencies, governments can always refinance by “monetary financing” i.e. borrowing from their own central bank. Emerging market governments borrowing in foreign currency must raise taxes to repay their borrowing, and these must be worth enough in foreign currency, to repay their bond obligations. Greece, Portugal and other Euro periphery countries have had similar difficulties repaying government debt because they have borrowed, effectively, in a foreign currency the Euro. They cannot use monetary financing (borrowing from the European Central Bank) to repay bond obligations.  Corporate bonds. The second main type of bond are corporate bonds. Corporate bonds are issued by companies and backed by their own current and future earnings. If a company is profitable the bond will be repaid. If the company is not profitable then it may “default” on the bond i.e. not make full repayment. Because of this default risk, investors treat corporate bonds differently from government bonds. They demand higher returns and also oten special protections, known as “covenants”, to protect investors from actions taken by borrowers e.g. there might be restrictions on further bond issues. The term “note” is a close synonym for a corporate bond (a medium‐term note would usually have a maturity of 1‐5 years). Often the term bond is used to refer to a single one time issue, while the term note is used to refer to a bond that is issued on repeated occasions over a period of years at times chosen by 8 the borrower (under a so‐called note programme). Notes issued under a note programme typically pay a slightly higher interest rate than a one‐time bond issue, but offer the issuer greater flexibility for managing cash flows. Terminology does vary. In the US the term “Treasury note” is used to refer to a US government bond with maturity of between 1 year and 9 years, while the term “Treasury bond” refers specifically to US government bonds with maturities of 10 or more years.  Eurobonds and international bonds. In the 1960s, for the first time since the gold standard era, a large market grew up for sale of bonds in foreign countries. The most important of these markets are the so called “Eurobond” market in London, Luxembourg, Belgium and other European countries. The biggest impetus behind establishing this market was in order to avoid tax and interest rate controls applied in the US. The distinguishing feature of the Eurobond markets are that they are open for “offshore” investment activity, meaning that both bond issuer and bond investor could come from anywhere in the world. In fact the term “Eurobond” does not necessarily mean a market in the Euro area or even in Europe! Most Eurobond buying and selling takes place in London and there are smaller Eurobond (i.e. offshore) markets (open to issuers and investors from any country) in New York, Hong Kong, Singapore and elsewhere. There are two main types of issuers in the Eurobond markets. Sovereign governments and large companies (often from emerging markets). They issue in international currencies, most often in $US but also in Euros or sometimes Yen or Pounds. Coupons are often floating rate based on London LIBOR rates. As well as Eurobonds there are also “international bonds” issued in large domestic markets such as the US or Japan by overseas issuers. One example are so called “Yankee bonds” issued by US companies in Japan, and usually denominated in Yen. International bonds are not the same as Eurobonds because they are traded in local currency in domestic markets, not in international currency in an offshore Eurobond market. Thus, while the issuer is international, the investors are domestic.  Public corporation bonds Bonds issued by publicly owned companies, for example by government owned post offices, airlines or other companies. There are often guaranteed, explicitly or implicitly, by their governments. 9  Municipal or local government bonds. Bonds issued by sub‐national units of government e.g. US states and municipalities (cities) in the US, provinces in Canada, states in Australia, UK local authorities, German Lander etc. Municipal bonds are not usually guaranteed by central government, but when there are financial problems central government may provide support. In the US municipal bonds have special tax status, personal investors do not have to pay federal income tax on the coupons paid from US municipal bonds. Local or national governments may also often guarantee bonds issued by local infrastructure companies, providing services such as electricity, buses or trams  Mortgage backed securities or MBS and other loan backed or asset backed securites (ABS). These are bonds backed by a pool of mortgages (or by other loans or even by corporate bonds). The coupons and final principal repayment come from the payment of interest and principal from the mortgages. There are other similar securities backed by other forms of loans, including credit card receivables, student loans, small business loans. An evaporation of liquidity in the secondary market for loan backed securities was central to the global financial crisis of 2007‐08. Box: further detail on mortgage (MBS) and loan backed securites (ABS). not needed for module assessment. May be useful for interview in fixed income. There are different types of mortgage backed securities. The two most important are: (i) Agency MBS, issued by Fannie Mae, Freddie Mac or other government agencies in the US. These are backed by (an implicit) government guarantee. (ii) Private MBS (sometimes called “private label”) where the only support is from the issuing bank. Outside of the US, mortage backed securities are always private label not publicly backed. Private label MBS are not just issued to finance residential property (housing and apartments); they are also issued to finance commercial property (such as shopping centres or office blocks). Thus, in the markets there is a distinction between RMBS (residential mortgage backed securities) and CMBS (commercial mortgage backed securities). There are also similar private label securities secured on other retail loans – such as credit card receivables, small business loans, student loans. 10  The first MBS issued in the 1980s, known as “pass through” MBS, did not pay a coupon, instead the money paid out to investors was simply proportional to the payments received, whether interest and principal repayment, from the underlying mortgage loans. Later market practice changed, with almost all mortgages “tranched” into several slices or tranches, and ranked in the seniority of their claims on the underlying mortgage payments. Payments had a “waterfall” structure, with the most senior tranches paid first (according to a coupon rate formula), the mezzanine or middle ranked trances paid next, and the junior tranches paid only after the other tranches. Finally an equity trance receives any residual payments. A further risk common in MBA and ABS is prepayment risk, which arises when interest rates fall and loans are repaid earlier than contractually due. MBS very often offer floating rather than fixed coupon rates, especially if the underlying mortgages were also floating rate.  Structured credit securities Another type of bond, similar to a mortgage backed security because it is backed by a pool of assets, is the “structured credit security” (examples include the CDO or collateralised debt obligation, CLO or collateralised loan obligation, and other more complicated products). Structured credit securities, like MBS, are tranched into different “slices” and usually repayments are based on a floating coupon rate. Problems with MBS, ABS and with structured credit securities were a major source of financial difficulties in the global financial crisis of 2007‐2011. We will not discuss structured credit products in detail, but some forms of structured credit instruments for example “collaterised loan obligations” or CLOs are still widely sold and traded.  Covered bonds. This type of bond, issued in large quantities in Germany and in Austria (where they are known as pfandbriefe) are similar to MBS, they are also backed by a pool of loans. But they differ from MBS for two reasons: first they are issued subject to strict legal guidelines, which ensure they are of low risk; secondly the loans remain “on balance sheet” i.e. they have the explicit backing of the issuing bank. 11  Islamic bonds, known as “Sukuk”. Islamic law, like Christian usury laws that were in force for many centuries in Europe, discourages the charging of interest. To get around this prohibition there is now a fairly large and rapidly growing market for so called Islamic bonds, known as Sukuk. However the term “bond” is a bit misleading, because the income on these bonds is not based on coupon rates but rather on a principal of sharing of returns. They are thus, in many ways, more like equity than like a bond. The largest markets for the issue of Islamic bonds are Dubai, London and Kuala Lumpur in Malaysia. Market prices and yields on bonds We now come to the most important material of Topic A1. There will be MCQ questions on this in the January exam. The market price of a bond – the price at which it is bought and sold in the market – can be higher or lower than the par value. If it equals the par‐value, then this is a rare co‐incidence. The bond yield is a more useful summary of a bond than the market price (even when we express price relative to par value). Coupon rates differ a lot from one bond. So does the maturity – the number of years until the par value is repaid. Coupon and maturity both affect price, so it is not possibly to make meaningful comparisons of the prices of different bonds. We instead use yields – a standard measure of return on a bond investment – for comparing the market price of different bonds or over time// Definition 2 The yield (or ‘yield to maturity’) of a bond is the discount rate (or internal rate of return’) at which the present value of promised future repayments of coupon and principal equal the current market price. The figure below, from the Financial Times, illustrates the “yield curve” or the term structure of interest rates in the UK. It shows how yields on UK government bonds vary with maturity, as of 19th Sept, 2023. We see that in just a month medium and longer term yields, 6m or more, have fallen around 0.5% but 1m and 3m are little changed. Also, currently, the yield curve is “inverted” meaning that short term yields, 1 month to 6 months, are higher than longer term yields 2 years and longer. 12 Calculating yields. We can focus on a very simple example, the yield 𝑖 on a one‐year bond, paying a single coupon of 5% along with the repayment of the par value. Using the standard convention that par value is 100, the market price is the present value of the repayment discounted at the yield 𝑖. 100 5 𝑃 1 𝑖 So, the yield is given by: 𝑖 105/𝑃 1 The following table shows calculations of this yield for different market prices Table 1: some calculations of yield for a single payment one year bond. Par Coupon Market value Repayment in Discount rate value rate 𝑃 year 1. 𝑖 105/𝑃 1 100 5% 98 105 7.14% 100 5% 99 105 6.06% 100 5% 100 105 5.00% 100 5% 101 105 3.96% 100 5% 102 105 2.94% 13 Note that: (i) As the market price rises, the yield falls; (ii) When the market price equals the par value then the yield equals the coupon rate. (iii) When the market price is higher than par the yield is below the coupon rate (and vice versa, when market price is lower than par the yield is below the coupon rate). In practice yield calculations are a little more complicated than in this table. Bonds return payments to investors periodically over several years, not just at single point in time. This means there is no simple direct formula for the calculating the yield from the coupon and market price. The yield must be calculated as an ‘internal rate of return’ 𝑖, solving for 𝑖 in an equation similar to the following. 𝑐 100 𝑐 100 𝑐 100 𝑐 100 1 𝑐 100 𝑃 ⋯ 1 𝑖 1 𝑖 1 𝑖 1 𝑖 1 𝑖 In the case of a three‐year 0.25% government gilt at time of issue, this equation becomes 0.125% 100 0.125% 100 0.125% 100 0.125% 100 𝑃 1 𝑖. 1 𝑖 1 𝑖. 1 𝑖 0.125% 100 0.125% 100 100 1 𝑖. 1 𝑖 1 𝑖 (Questions to check understanding. Why are the numbers 100 included in this equation? Where does 0.125% come from? Why do we have periods 0.5, 1.5, 2.5? This example formula is for the yield calculation at time of initial issue, exactly six months before the first coupon and three years before the final coupon and repayment of principal. How would the formula be adjusted on 5th January, when it is only three months before the first coupon and two years and nine months before the final coupon?) There is no simple ‘closed form formula’ to solve for 𝑖 in this and similar equations. But these and similar equations can be quickly and easily solved numerically, using Excel or other computer programs. Also, even though the equations are more complicated, all the findings (i), (ii) and (iii) above for the single payment bond still hold true. So, if 𝑃 100 then 𝑖 0.25%. If 𝑃 100 then 𝑖 0.25%. If 𝑃 100 then 𝑖 0.25%. 14 We will not look further at how these calculations are made (this is a whole special subject in finance known as ‘bond mathematics’ which is also used in modelling market risk). You should though be aware of some key points.  Bond yields are the promised annual average return on a bond, assuming all coupons and principal are returned as promised.  Bond prices and bond yields are inversely related. If demand for bonds falls (for example because perceived risks of inflation or default have risen), then the price falls and the promised return (the yield) rises.  Bond yields are nominal not real (they are nominal interest rates). In periods of higher expected inflation, bond prices fall to compensate for the anticipated erosion in the real value of future payments, & yields rise.  Risky bonds are often given a ‘credit rating’ by a rating agency, such as S&P,. Moody’s or Fitch‐IBCA. These letter ratings (for example the AAA, AA, A, BBB, BB, B, CCC, CC,. C and D ratings given by S&P and Fitch) represent a comparative assessment or opinion on the quality of the bond (with AAA being the very best quality most likely to make all promised payments and C the worst, conventionally BBB and better are referred to as ‘investment grade bonds’, others as ‘speculative grade’).  Bond yields are also affected by ‘liquidity’, the ability to buy or sell with limited impact on market price, investors prefer holding liquid bonds so these have higher prices and lower yields lower than other similar bonds; and by tax treatment, bonds with favourable tax treatment such as US ‘municipal bonds’ have higher prices and lower yields. Government bonds, issued by the large industrial nations such as the US, France, Japan, the UK and Germany, are liquid and, at least in terms of nominal money, low risk. Credit and liquidity risk can be ignored. Other bonds – corporate bonds or bonds issued by governments of smaller and emerging market nations, structured credit securities ‐‐ issued by other issuers, even when denominated in the same currency are of higher risk and so offer higher yields. The difference between the yield on a bond and the yield on a corresponding government bond in the same currency is known as the credit spread. 15  Example 3: a credit spread Easyjet, the airline, in 2021 issued €500mn par value of bonds maturing on 6th Nov 2025, i.e. four years from issue. The current yield, when preparing this example in 2021, was 0.49% This compared with the yield on four year German government bond, the bund, which was then approximately ‐0.65% (yes a negative yield) Thus the four year credit spread on the Easy jet bond is 0.49+0.65=1.04%. This credit spread compensates investors for the higher credit and liquidity risks of Easy Jet bonds compared to German government bonds. Credit spreads reflect risk of default, but they also reflect liquidity risks (bonds of small issuers that are difficult to sell have lower market prices and higher credit spreads) and also tax treatment (US municipal bonds have favourable tax treatment and so have higher prices and low sometimes negative credit spreads). The first week 4 class question asks you to investigate what determines the yield (rate of return) on different fixed income instruments. I am expecting you to support your findings with statistics on yields and examples. Bond risks, bond pricing and bond yields. There is one simple rule to keep in mind, when looking at these statistics bond prices and yields. Higher risk means a lower market price and a higher yield to compensate for greater risk. Some points that follow from this:  Longer maturity means greater risk and higher credit spreads. Repayments on short maturity bonds, with only one or two years until repayment of principal are usually quite predictable. As long as the issuer is financially strong, the likelihood is the bond will be repaid in full. Longer maturity bonds, especially those of ten years or upwards, there is a greater likelihood of something going wrong, e.g. unexpectedly high inflation, or the borrower defaulting on the repayments of coupons and principal, so yield must be higher.  Bonds issued by the major governments are at no risk of default. They are still subject to risks of higher inflation and higher market rates of 16  interest, so yields rise with maturity. Corporate bonds of similar maturity are also subject to default risk, and are harder to buy and sell than government bonds so have greater liquidity risk. For these reasons the corporate bonds have higher yields than the corresponding government bonds. This difference in yield is called the credit spread. Mishkin Chapter 6 has more on the “term structure of interest rates” i.e. the yield curve, the relationship between government bond yields and maturity. These yields are affected additionally by expectations of future interest rates (“expectations theory”) and by demand for specific maturities (“segmented markets theory”/ “ preferred habitat theory”). You do not need this detail for assessment. Typically, the yields on longer maturity government bonds are higher than on short maturity government bonds (because the risks of inflation and higher market rates of interest are greater for longer maturity bonds). This is a “risk premium” or “liquidity risk premium”. But sometimes, when inflation and interest rates are high but expected to fall over time, then the yield on longer maturity government bonds are then lower than on short maturity. This unusual situation, which arises at times of inflationary pressures, such as 2021‐2023, is known as “an inverted yield curve”. 17  A2. Equity market pricing 23ECB015/ 23ECC014 Lecture week 2 Reading  Mishkin, Part 2, chapter 7. Relevant articles in both the Financial Times and in The Economist. As we shall see equity prices have increases substantially over the past three decades, much faster than incomes and earnings. However increasing global real interest rates, increased risk aversion in economically difficult times and rising share of labour income in GDP could limit or even reverse much of the rise of stock prices since the 1990s over the next twenty years. Is this good news or bad news? This could be good news for younger generation – investors such as yourselves – because it means you will have to invest less to achieve a decent retirement income. Some background on equities An equity is a share in the ownership of a company, entitling the owner to payment of dividends and also to the right to vote at annual general meetings. Companies can have very few shareholders, perhaps only one single shareholder, or many thousands sometimes even millions of shareholders. As discussed under A0, You should be aware of difference between public equity and private equity.  Public equity (or publicly traded equity) is equity that is listed on a stock exchange and ‘admitted’ for trading, on the exchange systems and through other approved trading mechanisms.  Private equity is equity not listed on a stock exchange. Usually there are only a small number of owners, perhaps just a single owner. This topic is about the pricing of public equity listed and traded on stock exchanges. Sometimes only part of the equity of a company is listed while the rest remains unlisted and is held by a major shareholder (or shareholders). These unlisted 18 shares might be held by the original founders or their family, in order to maintain control and protect the company from an unwanted takeover. Publicly traded equity can be held directly by individuals; this is relatively common in some countries, for example in the US and China, but less common in the UK or other countries in Europe. Public equity is also be held by ‘institutional investors’ (insurance companies, pension schemes), by other companies and governments. Anyone can buy public equity, provided shares are actively traded on the market and they can pay the required price. Summary information on publicly traded equities are easily available, e.g. using the so called “Tear Sheets” published by the Financial Times, in Yahoo Finance or elsewhere. An example: here is a link you might follow for the energy company Centrica or find your own preferred company. The London stock exchange “ticker” for Centrica is CNA, hence CAN:LSE https://markets.ft.com/data/equities/tearsheet/summary?s=CNA:LSE 19 Some basic theory Express share prices as the present discounted value of future dividends 𝐷 𝐷 𝐷 𝐷 𝑃 ⋯ ⋯ 1 𝑘 1 𝑘 1 𝑘 1 𝑘 𝐷 1 𝑘 If expected dividends grow at a constant rate of 𝑔 per annum, then we have the “Gordon growth model” of stock prices: 𝐷 𝑃 𝑘 𝑔 It follows that the principal drivers of stock prices are: (a) the level of dividends 𝐷 (in the next period); (b) the expected future growth of dividends 𝑔; and (c) shareholder required expected return 𝑘 Here 𝑔 and 𝑘 are usually expressed in money terms, reflecting the growth rates and required returns in the currency in which the equity is traded, without any correction for inflation. This is not a major problem because higher inflation will increase both 𝑔 and 𝑘. Note that in practice it is difficult to have precise figures for 𝑘 and 𝑔. Typically we use this equation to compare similar shares, for example two companies in the same industry, and we can assume 𝑘 is the same for both. Then we can focus simply on analysing the expected growth of the two companies. See example on the next page. Mishkin Chapter 7 discusses this model in greater detail. Models along the lines of the Gordon model are routinely used by equity analysts in their buy and sell recommendations (though typically they will only assume a constant growth rate from 3 years ahead and beyond). We will use this model to understand the principal factors driving stock prices. 20 A practical example, comparing share prices,‐ P/E ratio & Gordon model Take two firms in the same sector e.g. supermarkets. 1. We first look at the P/E ratio, which provides a simple valuation metric. The basic idea is simple, if the price of shares is low, compared to earnings, then the share looks cheap (low P/E ratio, buy); if the price of shares is high, compared to earnings then the share looks expensive (high P/E ratio, sell). Using “earnings per share” EPS and a recent share price to calculate the P/E ratio for these two supermarkets, suggests that the two companies are priced about right, compared to each other. No obvious trading opportunity here ! Sainsbury’s https://markets.ft.com/data/equities/tearsheet/summary?s=SBRY:LSE EPS 0.1785 Share price 253.90. P/E ratio 253.90/(100 x 0.1785)=14.22 Tesco’s https://markets.ft.com/data/equities/tearsheet/summary?s=TSCO:LSE EPS 0.1951 Share price 278.40. P/E ratio 278.40/(100 x 0.1951)= 14.27 2. Now let’s apply the Gordon model In this case we also need a “dividend payout ratio”, representing next periods dividends as a percentage of current earnings, to obtain 𝐷. For simplicity we will assume the dividend payout ratio is 90% (in practice it will vary a lot as income fluctuates more than dividends). Sainsbury’s 𝐷 0.1785 90% 0.16065 Tesco’s 𝐷 0.1951 90% 0.17559 In the case of supermarkets we can have a good guess at 𝑔: it will be around 4‐ 5% because long term we can expect real consumer incomes growth of around 2% per annum and inflation of 2‐3%. Lets assume 𝑔 4%. We then obtain 𝑘 by reverse engineering from the price Gordon model, using 𝑘 𝑔 𝐷 /𝑃 for one of the firms. Let’s use Sainsbury’s, so we have 𝑘 𝑔 𝐷 /𝑃 4% 100 0.16065 /253.9 4% 100 0.16065 /253.9 4% 6.327% 10.327%. Finally we price Tesco’s: predicted price, about one third lower than actual price (so consistent with the P/E analysis) 𝐷 100 0.17559 𝑃 277.52 𝑘 𝑔 10.237% 4% 21 Now some data A look again, at chart from lecture 2 (now updated to 2024Q3) US: Inflation, 10 year bond yield and share prices 220.00 Willshire 5000 nominal GDP ratio peak 2021Q3 195% of GDP 18 peak 2024Q3 197% of GDP 170.00 13 Dot Com 120.00 bubble ‐30% 8 70.00 GFC ‐30% 3 20.00 ‐2 ‐30.00 CPI Inflation (lhs) 10 year benchmark yield (lhs) Willshire 5000 to nominal GDP (% rhs) Source: FRED database, Federal Reserve of St Louis, Yahoo Finance, data Oct, 2023; Oct 2024 Interpretation  The blue line, measured on the right‐hand scale, is the ratio of US stock prices (the broad index the Willshire 5,000) to US GDP (national income). Since the early 1980s until early 2000s US share prices have increased over eight times as much as national income.  The grey line, measured on the left‐hand scale, is the yield on 10‐year US bonds from 1971 to 2021. This nominal interest rate rose during the high inflation years of the 1970, peaked at 15% in 1981Q3 and has fallen steadily until recently, reaching a low of around 0.5% at the beginning of the Covid‐19 pandemic, but has since risen to around 3%  The orange line, measured on the left‐hand scale is US consumer price inflation from 1971 onwards (excluding volatile food and energy). The two early peaks are the OPEC oil price shocks of 1973 and 1979. The shift at the US Federal Reserve (under chairman Paul Volcker) firm anti‐ inflationary monetary policy, led to rapid and permanent decline inflation which has fluctuated around 3% per annum during the 1980s and 1990s, and around 2% per annum from 2000 to 2021. It then rose substantially following the global pandemic and because of the Ukraine war, and has only this year begun to fall. 22   The gap between the grey line and the orange line (nominal 10 year yield minus inflation) is one measure of the real interest rate. This measure of the real interest rate has fallen from around 6% in the 1980s to become negative during the post‐Covid inflation; but has recently risen to around 1%. Could equity prices collapse? Notice that in the 1970s, and again in the years 2000‐2009, US share prices fell dramatically, relative to GDP (national income). Could this happen again? The rest of this lecture uses the ‘Gordon growth model’ to examine this possibility. Lower required returns can explain much of the rise in share prices relative to incomes. Note on how to read the following table. Headings Assumed parameter values Intermediate calculations Final intermediate calculation Application to share prices High real Low real interest interest rates/ risk rates/ risk premium premium Year 1985 2024Q3 𝑟 the real interest rate 6% 0% 𝜋 expected inflation 5% 3% 𝑖 the nominal interest rate 𝑖 𝑟 𝜋 11% 3% 𝜌 the equity risk premium 7% 4% 𝑘 the required equity return 𝑘 𝑖 𝜌 18% 7% 𝜑 real dividend growth 3% 2% 𝑔 nominal dividend growth 𝑔 𝜑 𝜋 8% 5% 𝐷 (assumed fixed % of GDP) 100 100 𝑘 𝑔 𝑘 𝑔 10% 2% 𝑃 (from Gordon model) 𝐷/ 𝑘 𝑔 1,000 5,000 23  … higher share of profits in GDP also important Share of corporate profits in US GDP rose from 1950‐1970 average of 5% to around 7% recently. This increases the predicted Willshire 5,000 index further, from 5,000 to 7,000: [An aside. The rate of inflation 𝜋 does not directly impact these calculations, because it is included in both 𝑘 and 𝑔. As a result the 𝑘 𝑔 remains unchanged when 𝜋 rises. Higher inflation may though make investors and companies more risk averse, and so increasing 𝜌, lowering 𝑔 and reducing equity prices] So we can ‘explain’ the substantial rise in equity prices using ‘fundamentals’ i.e. the Gordon growth model. But this is not really explanation – we are coming close to ‘retrofitting’, altering the equity risk premium (which cannot be easily measured) to get the model to fit the data. Still, this suggests that the rise in equity prices of the past 30 years is not necessarily irrational, it can be explained by fundamentals. It is not obviously a bubble that will burst. I would not say the same thing about the prices of cryptocurrencies such as Bitcoin. I cannot explain these using a model of rational investing. These may be a bubble. So be very careful about investing in cryptocurrencies. We will not study cryptocurrencies in this module, so you do not need them for the January or summer exams. But stock prices could still fall from current levels, possibly a long way.  𝑔 might fall (recession/ slow growth)  𝑘 can rise, either because 𝑟 the real interest rate rises or because ‘equity risk premium’ 𝜌 rises (both have fallen substantially , but there is no guarantee that they will stay low).  Labour shortage could reduce the share of profits in GDP. This modelling is not a prediction Be aware of the limitations of these calculations. The Gordon growth model (and other similar models) are mainly used for comparing the price of different 24 equities, based on expected dividend growth and risk premium for individual firms (𝑔 , 𝜌 ) not for pricing the entire market. Consider two similar firms in the same industry, where the risks of future earnings/ dividends are similar. Then we can assume the same 𝜌 and focus on whether the difference in share prices is justified by the prospective difference in dividend or earnings growth rates. Typically, this is modelled over two to five years, with growth assumed to be the same for both firms thereafter. It can also be applied to compare share prices of firms against the market as a whole. We can then use past equity price data and asset pricing models such as the CAPM to estimate 𝜌 for each firm. But for the market itself we have no basis for determining 𝜌 today. What I have done is to ‘retrofit’ the model to the data, showing with a large enough decline in 𝜌 , consistent with the empirical evidence from past returns on the magnitude of 𝜌 , fundamentals can explain the dramatic rise in share prices over forty years. We know that 𝜌 can change substantially over time. It has fallen a lot in past decades but could easily rise in the future. So, while the model says current equity prices are consistent with fundamentals it says less about the future. Why university lecturers, younger than me, are considering strike action. A final reflection. What we can say is that future returns from buying and holding stocks (and bonds) are much lower than twenty or thirty years ago. Lower returns means that we must pay much more into our pensions now than in the past to guarantee our future retirement benefits. I was lucky, much of my pension contributions purchased shares at relatively low prices. My younger colleagues pension contributions do not go so far. To ensure the USS pension scheme does not go bust, all university staff in the pension scheme, along with their employers the universities, are being forced to accept lower pension benefits (and universities are putting more money into the scheme). There is no easy answer. Staff would prefer not to have reduced pension benefits, but either government or students have to pay for that. 25 Can a fall in share prices be good news ? It is possible that a crash in share prices, falling say 50% below current levels, could be good news. This would be true for you as young savers if it was because of 𝑟 ↑, 𝜌 ↑ and hence higher required returns (not because of 𝑔 ↓) In this case, with lower share prices but unchanged future dividends, the future returns to investment in equities will be higher. This means that you, as young savers, would then find it easier to save for the future. And my youngest colleagues in the USS pension scheme will not have to pay so much to ensure an adequate standard of living in retirement. What about others. For example someone like me, an older saver not far off retirement? Or someone, such as younger colleagues of mine, maybe two thirds through their career who has been making pension contributions when share prices have been quite high? 26  A3 Demography, technology and real bond yields 23ECB015/ 23ECC014 Lecture week 3 This topic is more technical than A1 or A2 – with more economics content. There will be MCQ questions related to this topic in the January exam, but they will be quite basic questions and there will be no compulsory questions on this topic in the semester 2 exam. So, you do not have to master all the technical details here. This is though a chance to apply your knowledge of economics to understanding the intergenerational challenges that are affecting all our lives. Reading  The Economist. In 2016 the Economist had several insightful articles on global real interest rates. I give weblinks, but you will need to use the Proquest Library account if you do not have your own subscription. Look in particular at a leader in Sept The Economist (2016) Low Rate World discussed the policy implications of low rates. https://www.economist.com/leaders/2016/09/24/the‐low‐rate‐world This is accompanied by The Economist (2016) Fall of Interest Rates: Low Pressure. https://www.economist.com/briefing/2016/09/24/low‐ pressure This article discusses the role of central banks and of deeper economic forces in reducing global interest rates. (less relevant to our class topic, the cause of low interest rates, but also worth looking at for discussion of the economic are: The Economist (2016) https://www.economist.com/briefing/2016/09/24/fade‐to‐grey examines the impact on pensions; The Economist (2016) Fall of Interest Rates (1) Nope to Nirp https://www.economist.com/fin tance‐and‐ economics/2016/02/18/nope‐to‐nirp looks at the impact on monetary policy; and The Economist (2016) Fall of Interest Rates (2) The Lowdown https://www.economist.com/finance‐and‐economics/2016/02/18/the‐ lowdown impact on the life insurance industry. ) 27   Goodhart and Pradhan, “The Great Reversal” Chapter 6. More advanced than required for the exams, for those who want to go beyond the assessmed. Available as e‐resource via Learn. This book addresses what is – alongside climate change – the biggest economic challenge of our times, the reversal of demographic forces (globalisation, rapid growth of labour force) that underpinned global economic trends in recent decades. I have also put Chapter 1 Introduction as an e‐book reading,  Here are two further papers that I will summarise: Rachel, L. and Smith, T. (2015) Secular drivers of the global real interest rate. 571. Available at: https://www.bankofengland.co.uk/working‐paper/2015/secular‐drivers‐of‐the‐global‐ real‐interest‐rate Hall, R. E. (2017) ‘Low interest rates: Causes and consequences’, International Journal ofCentral Banking, 13(3), pp. 103–118. Available at: https://www.ijcb.org/journal/ijcb17q3a3.pdf You do not need everything in these papers. Skip read and focus on what is relevant. I provide a guide below. If you don’t find very much you think is relevant, then you do not have to read very much.  Another good general discussion is provided by Bean, C. R. et al. (2015) Low for long?: Causes and consequences of persistently low interest rates. ICMB, International Center for Monetary and Banking Studies. Available at: https://voxeu.org/content/low‐long‐causes‐and‐consequences‐persistently‐low‐interest‐rates  Other relevant papers (warning, some of these are a bit technical, but the discussions are illuminating) including from the same issue of the International Journal of Central Banking as the R.E.Hall paper. Rachel, Ł. and Summers, L. H. (2019) ‘On Secular Stagnation in the Industrialized World’, Brookings Papers on Economic Activity, (Spring), pp. 1–76. Available at: https://www.brookings.edu/wp‐ content/uploads/2019/03/RachelSummers_web.pdf. Rachel, L. and Smith, T. D. (2018) ‘Are low real interest rates here to stay?’, The International Journal of Central Banking, 13(3), pp. 1–42. Available at: https://www.ijcb.org/journal/ijcb17q3a1.pdf This is a shortened version of their Bank of England discussion paper. Gourinchas, P.‐O. (2017) ‘Discussion of ‘Are Low Real Interest Rates Here to Stay?’’, International Journal of Central Banking, 13(3), pp. 43–53. Available at: https://www.ijcb.org/journal/ijcb17q3a1_disc.pdf Juselius, M. et al. (2017) ‘Monetary Policy, the Financial Cycle, and Ultra‐Low Interest Rates’, International Journal of Central Banking, 13(3), pp. 55–89. Available at: https://www.ijcb.org/journal/ijcb17q3a2.pdf 28 Giannoni, M. (2017) ‘Discussion of “Monetary Policy, the Financial Cycle, and Ultra‐Low Interest Rates.”’, International Journal of Central Banking, 13(3), pp. 91–102. Available at: https://www.ijcb.org/journal/ijcb17q3a2_disc.pdf The decline in global real interest rates observed over the past forty years is a major policy issue. In these notes and the lecture I will summarise some of the debate on the extent to which this happened, why this has happened and what the economic implications are. You do not need to follow all the technical details. The exams will though have questions that require a broad understanding of this topic. Some key points to help you.  There are many different interest rates available for saving and borrowing, from both financial institutions and in financial markets. Mishkin Chapter 4 discusses many of these. His chapter is useful background but not the central concern here, since the puzzle of falling real interest rates is a general concern that applies to all interest rates.  As in Mishkin Figure 5, we need to distinguish nominal interest rates (the rates of return promised on loans and deposits and on ‘fixed income securities’) from real interest rates (which are of greater interest to economists). There is though a difficulty. It is straightforward to measure nominal interest rates on different instruments (their yields). Real interest rates are usually estimated from a model. Depending on the model used the estimate of real interest rates and how they have changed over time differs. Still, there is broad agreement that global real interest rates have fallen substantially, perhaps as much as 4.5% or even more, over the past forty years. These notes now look closely at the Rachel and Smith (2015) Bank of England working paper. Read their Executive Summary. Then have a look at their Chart A1 (pg 6). This correspond to the Fisher chart Figure 5 in Mishkin – but notice that their estimate of inflation expectations (one year ahead inflation) in the advanced countries fell from around 5% to 2% from 1990 to 1999 and since then has remained at around 2% (Mishkin has inflation expectations falling to zero, I am sceptical about this. Inflation itself remains close to 2% in most countries, why should expected inflation have fallen to 0%, I trust the Rachel and Smith estimates more). Over the same period 10‐year bond yields have fallen from 9.5% to less than 2%. 29 Thus, on this measure reported by Rachel and Smith the real interest rate has fallen from 4.5% (9.5% ‐ 5%) to 0% (2% ‐ 2%). The rest of Section A of Rachel and Smith provides more detail, looking also at emerging markets (where real rates of interest have fallen by much less); examining an alternative measure of real interest rates based on so called “inflation indexed bonds” which reveal a similar decline in real interest rates as those based on inflation expectations, and in their box A1 examining the longer historical record. The next two sections of Rachel and Smith Section C and D discuss several standard economic explanations of lower real interest rates. You do not need all the detail, but you should understand their overall analysis and its emphasis on three basic determinants of real interest rates: (i) lower trend growth 𝑔 (a change in technology); (ii) lower desired investment, because of a reduced ratio of capital to output 𝐾/𝐿 (which can also be a consequence of changes in technology) and (iii) higher desired savings (a change in preferences). The long‐term growth rate depends on the growth of capital and labour and the rate of technical change. Rachel and Smith frame their discussion using the well‐known “Ramsey” model (a multiple period generalisation of the two period analysis in Appendix 3, figures A1 and A2, below and a staple of MSc level Economics teaching.) This yields a ‘neoclassical’ formula for real interest rates (Figure C1) (with 𝑞 representing technology; 𝜎 and 𝜃 preferences). 𝑞 𝑟 𝜎 𝜃 𝛼∙𝑛 𝑞 is the rate of technological progress (steepness of production possibility frontier in Figure A2, i.e. technology), 𝜎 household inter‐temporal elasticity of substitution (determines “convexity” or curvature of the indifference curves in A2); 𝜃 is the rate of time preference (the steepness of the indifference curves i.e. preferences again); and 𝑛 labour force growth. In this model the long‐term rate of growth is 𝑔 𝑞 𝑛. Anything that increases the long‐term rate of growth requires a higher real rate of interest to restore general equilibrium, how much higher depending on the willingness of households to save to enjoy more consumption in the future. Rachel and Smith (2015) then discuss the factors reducing real interest rates: 30  Section C examines the factors determining trend global growth and whether this growth has declined in recent years. This part of their paper is quite complicated covering a range of different views. They conclude (see their Chart C24 Global Growth accounting) that actual output growth at global has not fallen much, even following the crisis of 2007‐08; but there are good reasons to think that prospective future economic growth has fallen globally by around 1 % per year resulting in a corresponding fall of real interest rates. What determines trend growth? (background material that you do not need for the exams). There is a lot written on trends in productivity growth – both at the technological frontier and through ‘catch up’ and how these is affected by various factors, including population growth, education, inequality and the emergence of new products and production technologies. Rachel and Smith Section C review this complicated literature. There are different theories about the determinants of productivity growth and the empirical evidence distinguishing between these theories and quantifying the importance of different determinants is unclear. There is for example different views on how successful and important investment in new ideas e.g. patents are in boosting output; or on whether the opportunities for future growth can continue for ever through successive technical breakthroughs e.g. the internet or are declining over time (or as some researchers argue occur as a series of unpredictable ‘innovation waves’, implying that future productivity growth is possible but not certain). Inequality (which also increases desired saving) may reduce growth through pressure for social expenditures and redistribution that blunts incentives for creating new products and technologies. Related to this is the increasing size of fiscal deficits in many countries, effectively and increase in the demand for borrowing (and supply of government bonds) that has two offsetting impacts. First, a direct impact on the bond/ savings market increasing demand for funds. Second an offsetting effect introducing expectations of high future levels of taxation and hence reducing private investment and lower future growth.  Section D discusses desired savings, highlighting three reasons why this has increased in recent decades (i) demography i.e. the increased share of the population of working age (an increase that is due to reverse as the 31  population of many advanced countries age and “baby boomers” such as myself retire); which according to ‘life cycle’ theory of saving and investment in which most saving is for retirement by people of working age, so the baby boom has have increased desired savings (ii) rising inequality, wealthier individuals tend to save more of their income so increased inequality increases desired savings (iii) and, finally, the so called ‘global savings glut’ the major increase in savings since the Asian financial crisis of 1997 by governments in emerging markets, building up large reserves of foreign exchange to protect themselves against another future crisis.  Section D also discusses desired investment, i.e. further factors that may have reduced investment, other than the underlying rate of productivity growth 𝑔. These other factors are a reduction in the relative price of capital and reduced public investment. The final Section E of Rachel and Smith brings these various explanations together, assessing their relative importance (Charts E1 and E2). Shifts in preferences (ie. desired saving) explain about 300 basis points (3%) of the fall in real interest rates, with the largest impacts from demography and smallest from the global savings glut. A recent post‐2008 decline in anticipated future growth explains a further 100 basis points (1%) decline in real interest rates. Can real interest rates differ between countries? As factual question the answer is clearly yes. An example is Japan in the 1990s when the growth rate fell sharply and real interest rates also declined substantially, relative to rates in other advanced countries. Differences in growth rates thus can help explain differences in real interest rates between countries. This is also an obvious explanation of why emerging markets have higher real interest rates than advanced countries, they are able to grow faster because of “catch up” growth (while at the same time catch up growth also contributes to overall global growth and hence influences the average global real interest rate). An underlying issue here though is the extent of integration of national capital markets. If savings and investment move easily from one country to another then movements in real interest rates should be dominated by changes in the overall global real interest rate, with little variation between individual countries. Over time as part of the overall trend of globalisation international capital markets have become more closely integrated. This can be expected to reduce differences in real interest rates between countries. 32 Rachel and Smith provide a thorough overview of the determinants of real interest rates and explanations of why they have fallen over time. You should though be aware that their quantitative estimates of the importance of these different factors are only plausible estimates (“guestimates”). The modelling on which these are based is far from compelling. Other researchers might quantify the causes differently or emphasise other explanations. Further analysis from Robert E Hall: financial frictions and risk splitting Once you have grappled with the analysis provided by Rachel and Smith (2015) then I encourage you to turn to Hall (2017). He provides a succinct and insightful discussion of some of the reasons for falling real interest rates from a macroeconomic perspective. This is not as essential reading as Rachel and Smith, some of his analysis is also quite technical, but if you are comfortable with macroeconomics then he can offer you further ideas about the macroeconomic determinants of the fall of real rates of interest. Key points from his analysis. 1. Figure A2 of appendix suggests that the safe rate of interest (the slope of the indifference curve at the preferred combination of consumption and saving) should equal the marginal product of capital (the slope of the production possibility frontier). Figure 1 of Hall (2017) reports estimates of the return on capital which is substantially higher than the real interest rate, by a margin that increases from around 5% in the 1990s to 15% in the early 2000s. It appears that financial frictions (discussed below) result in a large and variable wedge between the safe rate of interest and the returns from real investment. Increased financial frictions could lower real interest rates. 2. [more technical] The standard multi‐period Ramsey model (as presented by Rachel and Smith, 2015, see above) suggests that the growth rate of consumption/ output 𝑔 𝑞 𝑛 depends on the difference between the real rate of interest 𝑟 and the household rate of time preference 𝜃. Hall’s Figure 2, comparing consumption growth and the real rate of interest, does not suggest a stable relationship. A fall in real interest rates of around 4% is associated with a decline in consumption growth of 1%. This suggests an intertemporal elasticity of substitution 𝜎 of around 𝜎 0.25 i.e. consumers do not change planned consumption very much when interest rates and other financial returns alter. The lack of stability of this Ramsey equation is again evidence for the presence of 33  substantial financial frictions with varying impact on the costs of financial intermediation. 3. Finally, Hall presents a model of international risk sharing which he summarises as follows One of the manifestations of heterogeneity in investors’ risk aversion is across countries. Investors in some countries, notably the United States, collectively take on risk from other parts of the world by maintaining positive net positions in foreign equity and negative net positions in debt—in effect, these countries borrow from the risk averse countries and use the proceeds to buy foreign equity. Thus, the United States is like a leveraged hedge fund. Countries can be divided into three groups: (i) those that absorb risk by borrowing in the global debt market and buying foreign equity [see Hall’s Figure 4], (ii) those that shed risk by lending to the risk absorbers and letting those countries take on the risk of their own equity [see Hall’s Figure 5], and (iii) those whose risk preferences are in the middle and choose not to absorb or shed risk and those whose financial markets are undeveloped and do not participate in global financial markets. Hall, 2017 pg 8. Hall’s key point here is that the growth in the income and assets of the “risk shedding” countries leads to a large increase in the demand for the debt issued by the governments of risk absorbing countries, so increasing the prices and reducing the real interest rate offered on those securities. He also argues that similar trends of “risk splitting” have taken place within the United States. In simpler terms the rapid economic growth in China and South East Asia has both contributed to the global savings glut (the excess of desired savings over desired investment, consistent with the analysis of Rachel and Smith) and increased portfolio demand for safe assets such as government bonds in the US, the UK and the Euro area (a further argument not in Rachel and Smith). Finally, students may wish to read the paper by Juselius et. al. which develops further the idea that financial factors influence the real interest rate; and the critical commentary by Giannoni (but these are a fairly technical papers). 34 More on financial explanations of the decline in real interest rates Halls is presenting a version of an argument made by several economists that lower real interest rates is the consequence of increase demand for safe assets (see also Rachel and Smith 2015 Box B1 at the end of their Section B). It is certainly arguable that there has been a long‐term shift in favour of safe liquid assets such as government bonds relative to their supply and this has pushed the prices of these bonds up and their yields down. This argument is about the share of total global savings invested in safe assets and it therefore predicts that the yields on safe government bonds fall while, at the same time, yields on other riskier assets rise. There are though some reasons to be sceptical of this explanation in its simplest form. There does seem to have been some shortage of safe assets in the period after the global financial crisis of 2008 as investors have become more risk averse and regulation has required banks to hold more government bonds. But this does not explain the longer‐term trend. Also, the returns on riskier assets have not obviously risen at the same time: rather the reverse has been true, prices of equities for example have risen substantially more than nominal GDP, implying that future returns are lower than they would otherwise have been. Gourinchas in discussing Rachel and Smith (2017) makes a related argument, that the financial cycle plays an important additional role, lowering real interest rates for a sustained period following a financial crisis. His discussion is quite technical, but Figure 3 summarises his perspective. This shows that much of the fall in interest rates can be predicted (the blue line with circles) by excess leverage and the process of deleveraging following a financial crisis. Thus, it is finance and the impact of financial crises, more than demographics and lower future growth explaining low real interest rates. My own judgement: such financial explanations of lower real interest rates are closely connected with the broader concern about desired savings being higher than desired investment. High levels of debt lead to an increase in desired savings and hence lower real interest rates. Also, many countries including the US, the UK have relied and continue to rely on increasing private and public debt to maintain desired growth and employment (instead of pursuing growth through improving international competitiveness), but this only increases the gap between desired savings and desired investment. This though does not sound like a sustainable policy. An alternative approach to monetary policy not based on ever increasing debt may be needed. 35 Appendix 1: Mishkin on the determination of interest rates Mishkin chapter 5 presents a “supply and demand” analysis of bond prices and yields especially his Figure 1, pg 140). This chapter is useful preliminary reading for Topic A1, especially if you are not taking any other finance related modules. Note that:  Mishkin is analysing a particular interest rate, the yield on government bonds (for example on a 10 year US government bond). There are many other different rates of interest for both saving and borrowing from financial institutions and in financial markets.  Mishkin focuses on supply and demand for bonds and how this determines the market price of bonds. This market price is linked directly to the bond yield (what he refers to as bond interest rate).  The yields that Mishkin analyses are nominal interest rates not real interest rates.  Short run the supply of bonds is almost fixed, price and yields depend on demand. Longer run there is more scope for the supply of bonds to vary. 36 Mishkin chapters 4 and 5 discusses many of the different interest rates available in financial markets and from financial institutions. He also examines the difference between real and nominal rates of interest, in Figure 5 of Chapter 5 pg 149, using data from the FRED data base (similar to my chart above). This figure is an illustration of the so called “Fisher effect” (named after the prominent US economist of Yale University Irving Fisher, active in first half of the 20th century). Fisher argued that the nominal rate of interest (𝑖 e.g. as in Mishkin’s Figure 1) should be equal to the real rate of interest (𝑟 as in my Figure 20.5) plus the expected rate of inflation (𝜋 ). 𝑖 𝑟 𝜋 Mishkin’s figure compares another nominal interest rate, the yield on 3‐month US Treasury bills shown in red/ brown in the figure with an estimate of the expected inflation rate shown in blue in the figure. They have indeed moved together over the past six decades. 37 Appendix 2: The impact of low real interest rates. Does the decline of real interest rates matter? This Appendix is not needed for preparing classes, coursework or exam. But you should know that the decline of real interest rates of the past three decades is a major economic event with an impact on all areas of the economy and economic policy. Lower real interest rates are part of a broader story, the economic impact of demography, globalisation and the rapid rise of China as an economic power. Much of this may reverse in coming years, as argued by Goodhart and Pradhahn in their important book “The Great Reversal”. We do not know exactly how this will all work out, but it will affect your life. The following quotation from Rachel and Summers (2019) sums up the concerns about falling real interest rates: “Our diagnosis necessitates radical revisions in the conventional wisdom about monetary policy frameworks, the role of fiscal policy in macroeconomic stabilization, and the appropriate level of budget deficits, as well as social insurance and regulatory policies. To that end, much more of creative economic research is required on the causes, consequences, and policy implications of the pervasive private sector excess saving problem.” Rachel and Summers (2019) pg 2. They share the view of Rachel and Smith (2015) that an increase in desired saving relative to desired investment can explain most of the decline of global real interest rates. They are concerned about the resulting economic impact. This impact is often referred to as ‘secular stagnation’. The term secular here simply means long‐run, not explained by cyclical fluctuation in aggregate supply or aggregate demand i.e. year 1/ year 2 macroeconomics. The phrase ‘secular stagnation’ was coined by the US economist Alvin Hansen in the late 1930s to refer to the difficulties of the US economy had in recovering from the great depression of 1930‐1935. Growth was returned in the years 1934‐1937 and per capital GDP climbed back to its 1929 level (after falling by nearly 30 percent, this large fall and resulting mass unemployment is the reason it is called the Great Depression.) But by 1937 the growth of the US economy was slowing again and GDP fell again in 1938 (see https://www.multpl.com/us‐real‐ gdp‐growth‐rate ). 38 An excess of savings over investment leads to falling returns to all asset classes. It helps explains the high current valuations of the stock market as well as low real interest rates (topic A3). This is different from an increase in the demand for government bonds driven by a ‘flight to safety’, emphasised by Hall.. Falling returns on all asset classes is bad news for anyone saving for their future pension. An illustration. Consider someone with a very cautious portfolio strategy, investing only in safe assets, who invests £6,000 per year towards their retirement. The following table shows the retirement income under the two cases of returns of 0% per year and returns of 4.5% per year. As you can see you someone of your generation might expect to have a pension less than two‐fifths of the pension enjoyed by a grandparent (of course this is offset by incomes today being higher that forty years ago, but still it will be difficult for your generation to retire as well off as current retirees, especially since housing is so much more expensive than forty years ago.) Individual Born 2000 Born 1940 (your (you) grandparent ?) Portfolio returns 0% 4.5% Annual investment over 40 years £6, 000 £6,000 Pension pot after 40 years £240,000 £642,182 Annual Pension with 3% annuity rate £7,200 £19,265 Similar problems arise for state financial planning – low future returns can mean a much bigger recourse to the state for basic needs. This is offset by the much lower burden of repayment of government borrowing. But still ‘secular stagnation’ suggests major policy problems in public spending may be ahead. Another issue is that secular stagnation, by lowering demand, can undermine the inflation targeting, with inflation falling to zero or below. This in turn interferes with the transmission of monetary policy because it is difficult to lower interest rates much below 0% (the so called effective lower bound on monetary policy interest rates). This suggests a need to rethink the conventional policy prescription, using monetary policy to respond to short term shocks and maintaining inflation close to target. Instead fiscal policy may have to play a substantial role in short term macroeconomic policy responses. One further problem arising from secular stagnation, is increased risk of financial instability, resulting from a ‘hunt for yield’ as investors, unable obtain 39 satisfactory returns from safe assets, increasingly shift their portfolio into higher yielding risk assets and employing greater leverage to magnify returns. This is fine as long as the economy is doing well but in the event of a downturn (for example from a pandemic) this could result in financial problems that greatly worsen the downturn. Appendix 3: the theory of real interest rates. A supply and demand analysis of real interest rates. This appendix provides reviews the simple theory of interest rates in general equilibrium. It will be most useful to the students on BSc Economics, BSc Business Economics and Finance and BSc Mathematics and Economics, linking the material discussed less formally above under Topic A3 The determination of real interest rates, to your study of microeconomics. It is standard intertemporal analysis (I prepared these figures for an open university book chapter some years ago but also found in many microeconomics textbooks). The key idea is general equilibrium of consumption, savings and investment. Analysis begins with the optimal consumption decision, given real interests rates, as in the following diagram. Figure A1: optimal consumption choice given real interest rate 40 This is a standard analysis of ‘intertemporal’ consumption choice, i.e. the choice made by a household between consumption today, 𝐶 , and consumption in the future, 𝐶. The example here (the red dotted lines) are for a household with relatively high current income, 𝑌 , and relatively low future income 𝑌. If the household neither saves nor borrows then their consumption in each period equals their income in that period. In this case both income and consumption are represented by the point A (the ‘endowment point’). The curves 𝑈 and 𝑈 are part of the map of ‘iso‐utility’ curves that represent household preferences. These curves have the standard convex shape of iso‐ tuility curves, and also in this case there is no strong intertemporal preference (the household prefers relatively similar levels of consumption now and in the future to very different levels of consumption) The straight line, LG, represents the returns available on financial markets. It has a slope of 1 𝑟 where 𝑟 is the real interest rate earned by households on the saving they make today. This household with relatively high current income achieves highest possible utility if they save some of their current income and move away from the endowment point A to the preferred consumption point B. General equilibrium We now move onto the next figure A2 combining the savings and investment of Figure A1 with the “production possibility frontier”. Preferences are represented by the single iso‐utility curve from Figure A1 corresponding to the maximum utility achieved by the household. Production technology is represented by a production possibility frontier, representing the choice made by firms between current output and (on the horizontal axis) and future output (on the vertical axis). For a profit maximising firms the choice between current output and future output also depends on the real rate of interest 𝑟 (represented by the same straight line with slope 1 𝑟 as in Figure A1). 41 Figure A2: optimal investment choice given real interest rate and general equilibrium of savings and investment. If the real rate of interest is low, then firms earn greater profit by selling less of their current output for consumption today and using more current output as investment to produce future output. In this case they choose to be on the upper left of the production possibility frontier. If the real rate of interest is relatively high then the opposite situation obtains: profit maximising firms sell more output for current consumption and invest less to produce output in the future and they choose to be on the lower right of the production possibility fronter. Figure A2 shows the general equilibrium, the determination of the unique real rate of interest, 𝑟, at which households are maximising intertemporal utility and, at the same time, firms are maximising profit. Time to sum up. These are standard diagrams from microeconomics. What they show is how the combination of household preferences (Figure A1) and production technology (Figure A2) determine the market rate of interest (the slope 1 𝑟 of the straight line in the two diagrams). While still relatively simple, this general equilibrium analysis suggests how real interest rates alter as a result of underlying changes in preferences and 42 technology. These diagrams help answer some simple multiple choice type questions. Here is one. MCQ. A breakthrough in technology leads to a large increase in future output achieved from investment today. What is the impact? A. Real interest rates fall, future consumption rises B. Real interest rates fall, future consumption falls C. Real interest rates rise, future consumption rises D. Real interest rates rise, future consumption falls The correct answer, using Figure A2, is C. This is a vertical “stretching” of the production possibility curve, so for any given level of current saving and consumption (a point on the horizontal ‘x’‐axis) both the slope of the production possibility curve and future output/ consumption increase. The full impact depends on both “substitution effects” (the substitution of future for current consumption, through higher real interest rate) and “income effects” (consumers having higher overall income available to split between the two periods. If the income effect dominates then consumption rises in both periods (savings fall) leading to even greater rise of real interest rates. If the substitution effect dominates then current consumption could fall (savings rise) offsetting the rise of interest rates, but not by enough to restore real interest rates to their original level (because then there would be no substitution effect). 43