Week 2 of Financial Systems
Week 2 of Financial Systems FIN 3113
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This 14 page Class Notes was uploaded by Whitney Smith on Tuesday February 9, 2016. The Class Notes belongs to FIN 3113 at Mississippi State University taught by Wei He in Summer 2015. Since its upload, it has received 34 views. For similar materials see Financial Systems in Finance at Mississippi State University.
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Date Created: 02/09/16
Chapter 02 – Determination of Interest Rates Chapter Two Determination of Interest Rates I. Chapter Outline 1. Interest Rate Fundamentals: Chapter Overview 2. Time Value of Money and Interest Rates a. Time Value of Money b. Lump Sum Valuation c. Annuity Valuation d. Effective Annual Return 3. Loanable Funds Theory a. Supply of Loanable Funds b. Demand for Loanable Funds c. Equilibrium Interest Rate d. Factors that Cause the Supply and Demand Curves for Loanable Funds to Shift 4. Movement of Interest Rates Over Time 5. Determinants of Interest Rates For Individual Securities a. Inflation b. Real Interest Rates c. Default or Credit Risk d. Liquidity Risk e. Special Provisions of Covenants f. Term to Maturity g. Summary 6. Term Structure of Interest Rates a. Unbiased Expectations Theory b. Liquidity Premium Theory c. Market Segmentation Theory 7. Forecasting Interest Rates II. Key Concepts and Definitions Real vs nominal interest rates Inflation Compound and simple interest Default risk premiums Annuity Liquidity risk premiums Effective annual return Term structure Unbiased expectations Maturity premiums Liquidity premiums Future value and present value 21 Chapter 02 – Determination of Interest Rates Market segmentation III. Teaching Notes 1. Interest Rate Fundamentals: Chapter Overview The interest rates that you actually see quoted are nominal interest rates; as a result, nominal rates are sometimes called ‘quoted rates.’ The purpose of the chapter is to examine the components of the nominal interest rate. They are a) the real riskless rate of interest that is compensation for the pure time value of money, b) an expected inflation premium that is time dependent and c) a risk premium for liquidity, default and interest rate risk. 2. Time Value of Money and Interest Rates a. Time Value of Money b. Lump Sum Valuation c. Annuity Valuation The real rate of interest is the additional compensation required to forego current consumption. This is the essence of the time value of money. That is, the value we place on money depends upon when the money is received (paid) and the time preference for consumption. Simple interest is earned if the investor spends the interest earnings each period; compound interest assumes the interest earned per period is reinvested. Present and future values of lump sums and annuities are covered but the closed form formulas for the annuities are not presented. PV = PMT (1 – (1+i/M) –N×M) / i N×M FV = PMT ((1 + (i/M)) – 1) / i i = nominal rate PMT = annuity payment N = number of years M = number of compounding periods per year Comparative statics for lump sum and annuity calculations are discussed in the text. d. Effective Annual Rate For investments with maturities other than annual one may need to calculate an equivalent annual return (EAR) in order to compare rates among investments with different maturities (compounding frequencies). The EAR is the equivalent annual rate that would give the same future value if the investment had only annual compounding. 3. Loanable Funds Theory 22 Chapter 02 – Determination of Interest Rates The interaction of supply and demand of funds sets the basic opportunity cost rate (real interest rate) in the economy. The Federal Reserve estimates supply and demand of funds from households, business, government and foreign sources through its flow of funds accounts. Flows of funds tables are available at the Federal Reserve website at www.federalreserve.gov. a. Supply of Loanable Funds Source Text Table 22 Funds August 07 data Supplied Demanded Supply Demand Trill $ Trill $ Net $ Net %* % % Households $42.52 $13.43 $ 29.09 25.4% 37.1% 11.7% Business Nonfinancial 14.62 33.44 (18.82) 16.4% 12.8% 29.2% Financial Intermediary 40.71 54.76 (14.05) 12.3% 35.5% 47.8% 3.2% Government 3.80 7.51 ( 3.71) 3.3% 6.6% Foreign 12.93 5.44 7.49 6.5% 11.3% 4.7% Totals $114.58 $114.58 $ 0.00 0.0% 100.0% 100.0% *Net percentages are the net supplied (demanded) by that sector as a percent of total funds supplied (demanded) by all sectors. 23 Chapter 02 – Determination of Interest Rates The predominant suppliers of loanable funds are households at about 37% (although only at about 25% net of borrowing demand). The second largest net supplier of funds is the foreign sector. The U.S. has become increasingly reliant on foreign sources of funds to fuel our funds’ demands. This reliance becomes increasingly problematic with the recent fall in the value of the dollar. Household savings increase with higher interest rates and the supply curve is upward sloping with respect to interest rates. However, the main determinants of household savings are 1) income and wealth, the greater the wealth or income, the greater the amount saved, 2) attitudes about saving versus borrowing, 3) credit availability, the greater the amount of easily obtainable consumer credit the lower the need to save, 4) belief about safety of the Social Security system and 5) tax policy. In the U.S. tax policy favors borrowing but taxes virtually all savings (except retirement savings). As a result, the supply curve is steeper than one might expect. At higher interest rates, savers do not have to save as much to hit specified future values, so savings are not that sensitive to interest rates. Where consumers put their savings is sensitive to interest rates, they move out of liquid accounts as interest rates rise (as the price of foregoing higher rates of return to maintain liquidity rises). Households apparently try to smooth consumption patterns over different levels of income. As income falls they save less to maintain consumption, as income rises households save more. Other factors include the perceived riskiness of investments, near term spending needs, Federal Reserve policy and general economic conditions. Favorable economic conditions also increase savings by increasing income and wealth. Note that on net the foreign sector is the second largest supplier of funds at about 6.5% of total funds supplied net of borrowing. Foreign funds suppliers examine the same factors as U.S. funds suppliers except that they must also factor in expected changes in currency values, global interest rates and different tax rates and sovereign risk. There is typically some built in demand for U.S. investments however because the U.S. is considered a safe haven, i.e., a country with relatively low political and economic risk and a stable currency. As the dollar continues to decline however, the ‘safe haven’ status of the U.S. dollar is likely to erode, probably resulting in increasing shifts in funds to the euro. Ultimately the so called ‘global reserve currency status’ of the dollar is increasingly at risk. The dollar is used to price many commodities, including oil and gold; the dollar is the primary foreign currency reserve asset for many central banks and many exports are dollar denominated even if the ultimate destination is not the U.S. In reality it will take many years to unwind the dollar’s dominance in the global financial markets, if that unwinding is to occur at all. I would argue that the dollar will lose its reserve status eventually if China continues to grow and dominate Asia and if Europe increases its commitment to growth policies and continues deconstructing some of their increasingly expensive social welfare programs. The time frame required for a major shift away from the dollar will probably be forty to fifty years however because China will remain far too risky for quite a while and Europe must demonstrate a commitment to growth. 24 Chapter 02 – Determination of Interest Rates b. Demand for Loanable Funds As of 2007, business demand (financial and nonfinancial) comprised about 77% of funds demanded. The quantity of loanable funds demanded is greater at lower interest rates. Businesses prefer to finance internally when interest rates are high. The demand for loanable funds by households for big ticket items is quite sensitive to interest rates as these items comprise a large percentage of their budget (homes, autos, boats, etc). The Federal government’s demand for funds is relatively insensitive to interest rates, but not wholly so because much of the interest owed on the Federal debt is financed by borrowing. As interest rates rise, the Federal government has to borrow more to pay off the interest on the existing debt. State and local government financing is also quite sensitive to interest rates. New municipal offerings drop when interest rates rise. Not surprisingly, government entities that cannot print money (or raise taxes) are more sensitive to financing costs! c. Equilibrium Interest Rate It is the job of the 12 Federal Reserve banks to estimate aggregate supply and demand of funds from the various sectors at different interest rates and then build the aggregate supply and demand curves. In free capital markets the interest rate observed will tend toward equilibrium at the rate that intersects the supply and demand curves for each traded instrument. d. Factors that Cause the Supply and Demand Curves for Loanable Funds to Shift Increase Affect on Su Affect on Demand Wealth & income Increase N/A As wealth and income increase, funds suppliers are more willing to supply funds to markets. Result: lower interest rates Risk Decrease Decrease As the risk of an investment decreases, funds suppliers are less willing to purchase the claim. All else equal, demanders of funds would be less willing to borrow as well. Result: higher interest rates Near term spending needs Decrease N/A As current spending needs increase, funds suppliers are less willing to invest. Result: higher interest rates Monetary expansion Increase N/A As the central bank increases the supply of money in the economy, this directly increases the supply of funds available for lending. Result: lower interest rates Economic growth Increase Increase With stronger economic growth, wealth and incomes rise, increasing the supply of funds available. As U.S. economic strength improves relative to the rest of the world, foreign supply of funds is also increased. Business demand for funds increases as more projects are profitable. Result: indeterminate effect on interest rates, but at more rapid growth rates interest rates tend to rise. Utility derived from assets Decrease Increase 25 Chapter 02 – Determination of Interest Rates As utility from owning assets increases, funds suppliers are less willing to invest and postpone consumption whereas funds demanders are more willing to borrow. Result: higher interest rates Restrictive covenants Decrease As loan or bond covenants become more restrictive, borrowers reduce their demand for funds. Result: lower interest rates Taxes Taxes on interest and capital gains reduce the returns to savers and the incentive to save. The tax deductibility of interest paid on debt increases borrowing demand. Result: Higher interest rates Currency Increase Foreign suppliers of funds would earn a higher rate of return if the currency appreciates and a lower rate of return measured in their own currency if the dollar depreciates. Foreign central banks often buy U.S. Treasury securities as part of their attempts to prevent their currency from appreciating against the dollar. Result: Lower interest rates 26 Chapter 02 – Determination of Interest Rates Increase i Affect on Sup Affect on Demand Expected inflation Decrease Increase An increase in expected inflation implies that suppliers will be repaid with dollars that will have less purchasing power than originally anticipated. Suppliers lose purchasing power and borrowers gain more than originally anticipated. This implies that supply will be reduced and demand increased. Result: Higher interest rates The marginal propensity to consume (MPC) and the marginal propensity to save (MPS) affect household choices of how much of their income they wish to spend and save respectively. The MPC would appear to have increased (and the MPS decreased) inter generationally in the U.S. This is probably because of reduced stigma associated with debt and increased availability of credit. 4. Movement of Interest Rates Over Time Interest rates fluctuate in a nearly continuous manner due to the actions of traders. In a free market (capitalist) society, governments do not set prices. Interest rates are the price of borrowing money associated with a specific instrument or claim. Actions to buy, sell and issue securities affect interest rates. In turn, demand and supply of funds fluctuate daily as current and expected macro and instrument specific conditions evolve. 5. Determinants of Interest Rates For Individual Securities a. Inflation b. Real Interest Rates & Fisher Effect Inflation is the rate of change in the overall price level. The Consumer Price Index (CPI) is the most commonly quoted measure of inflation. The CPI purports to measure the price level of a market basket of goods and services purchased by the typical urban consumer. The Fisher effect states that nominal rates equal real rates plus a premium for expected inflation. This relationship is the basis for the term structure. Differences in annual expected inflation rates cause differences in bond rates with different maturities. The nominal interest rate is the additional dollars earned from an investment. The real interest rate is the additional purchasing power earned from an investment. The real interest rate refers to the marginal gain in units purchased rather than in dollars. Teaching Tip: Sometimes we think that exante real rates cannot be negative, but they can because of the convenience yield of liquidity. They have been negative in recent years in both the U.S. and Japan. 27 Chapter 02 – Determination of Interest Rates The Fisher Effect relates nominal and real interest rates. The approximate Fisher effect is given as i = RIR + Expected (IP) where i = nominal interest rate, RIR = real interest rate and Expected (IP) = expected inflation. The actual Fisher Effect is given as (1+i) = (1+RIR)*(1+Expected(IP)) The following example illustrates why the actual Fisher Effect is multiplicative: Suppose “It” originally cost you $1. You have $10 so could buy 10 of “it.” If inflation is 5%, in one year “it” will cost $1 + .05 =$1.05. If you invest your $10 and earn 10% + 5% = 15% (the approximate Fisher Effect) you will get back $10 * 1.15 = $11.50. Can you buy $10% more of “it?” I.E. can you now buy 10 * 1.1 or 11 of “it?” 11 * $1.05 = $11.55; so you are short 5 cents. In order to buy 10% more of it you must earn an interest rate equal to (1.10 * 1.05) 1 = 1.155 1 = 15.5% nominal interest. Then your $10 will grow to $10 * 1.155 = $11.55 and you CAN buy 10% more of it! Since both P & Q are rising, the rate charged must reflect the increments to both P and Q. The difference matters little if inflation is low and/or the time period under consideration is not very long. In international investing environments where inflation is much higher than the U.S. is currently experiencing, the difference can be material. c. Default or Credit Risk Default risk premiums (DRPs) are increases in required yield needed to offset the possibility the borrower will not repay the promised interest and principle in full or as scheduled. According to the Wall Street Journal Online, May 5 edition, credit risk premiums on Aa rated corporate debt relative to Treasuries were 1.95% and were 2.77% on Baa rated debt. DRPs on high grade debt were about 6.60%. DRPs are cyclical, and rise in periods of weak economic conditions such as the U.S. was experiencing in 2008. d. Liquidity Risk Liquidity risk premiums are increases in required or promised yields designed to offset the risk of not being able to sell the asset in timely fashion at fair value. These are similar to, but not the same as, the liquidity premiums in the term structure discussion. Liquidity risk can be more significant for some debt instruments than for stocks as many bonds trade in thin markets. 28 Chapter 02 – Determination of Interest Rates e. Special Provisions of Covenants Municipal bond (Muni) rates are lower than similar corporate bonds because interest (but not capital gains) is exempt from federal taxation. In most states the holder of a muni bond issued in that state is also exempt from state taxes. Teaching Tip: Ask students why munis are granted special tax status. What do they think about industrial development bonds which allow private corporations to issue tax advantaged munis for certain projects? Note that usage of IDBs has been restricted in recent years due to over usage by private firms seeking to exploit the tax advantage of munis. Callable bonds have higher required yields than straight bonds because the issuer will normally call them when rates have dropped, forcing the bondholders to reinvest at lower interest rates. Although it varies with interest rate expectations the premium on a callable bond might be 30 to 50 basis points. Convertible bonds have lower yields than straight bonds because the bondholder has the right to convert them to preferred or common stock at their choice. Offering a conversion feature may save 100 to 200 basis points, ceteris paribus. In most cases however, the stock has to appreciate 15%25% over the at issue price in order to make conversion attractive. f. Term to Maturity The term structure depicts the relationship between maturity and yields for bonds identical in all respects except maturity. In practice, ‘identical’ means same rating, liquidity and hopefully the same coupon (or differential tax effects will be present). The graph of the term structure can take on any shape, but upward sloping is most common (meaning longer term bonds promise higher nominal yields). The yield curve was inverted in Nov 2000 and in parts of 2006 and 2007. Note that for Treasuries, ‘on the run’ (newly issued) securities often carry price premiums over ‘off the run’ (previously issued) securities. g. Summary ij = f(Riskless real rate, Expected inflation, Default risk premium, Liquidity risk premium, Special covenant premium, Maturity risk premium) The maturity risk premium is explained in Section 6 where it is defined as the premium for holding a price volatile asset (confusingly called a liquidity premium). 29 Chapter 02 – Determination of Interest Rates 6. Term Structure of Interest Rates a. Unbiased Expectations Theory (UET) The UET states that the long term interest rate is the geometric average of the current and expected future short term rates. A simple arbitrage proof can be used to show this when interest rates are known with certainty under perfect markets: If the expected one year rates are 6%, 7% and 8% for the next three years respectively, and the three year rate is 5%, how could one make money on this relationship? Using the text’s terminology: 0R1 = 6%, 1R1=7% and 2R1 = 8% but 0R3=5% The average of the short term one year rates is 7%, but the three year rate is only 5%. One could borrow any given amount such as $1000 for the full three years and invest that money one year at a time and rolling over the investment for three years. The borrowing cost per year is 5% and the average rate of return is 7%. This is a riskless arbitrage under the given assumptions that would force the three year rate and the average of the one year rates to converge. For a series of holding period returns (HPRs) the geometric average can be found as: N 1/N Geometric Average (1 HPR ) T 1 T 1 For example if we have a time series of three returns of 10%, 15% and 12% the arithmetic and geometric averages are 2.33% and 1.55% respectively: (10%15%12%) Arithmetic Average 3 2.33% 1/3 Geometric Average 1.10 0.85 1.12 1 1.55% The critical concept to understand is that under the UET an investor is indifferent between how one arrives at an N year investment. For example, one can invest for N years all at once, or invest for 1 year and roll the investment over N1 times. 210 Chapter 02 – Determination of Interest Rates b. Liquidity Premium Theory If investors prefer shorter maturities to long, they will require a premium to invest for N years all at once instead of investing for 1 year and rolling the investment over N1 times. In other words, the long term rate cannot be the average of the expected short term rates. The long term rate must equal the average of the short term rates plus what is illogically called a ‘liquidity premium.’ (It is an illiquidity premium.) The rationale for the shorter maturity preference is that with uncertainty about future rates, it is riskier to invest long term rather than investing for a shorter time and rolling the investment over because it is harder to forecast rates further in the future and longer term investments are more price volatile. This is a modification of the UET, but it does not invalidate the logic of the UET. It does imply that long term rates are biased forecasters of expected future short term rates. We don’t know very much about the size of the liquidity premiums. They 1 increase with maturity, and probably do not get much over 100 to 200 basis points. c. Market Segmentation Theory Market segmentation or preferred habitat theory claims that there are two or three distinct maturity segments (the segments are illdefined) and market participants will not venture out of their preferred segment, even if favorable rates may be found in a different maturity. A less extreme version posits that a sufficient interest rate premium may induce investors to switch maturity segments. The idea behind segmentation is that institutions naturally have liabilities of a distinct maturity, e.g., life insurers have long term liabilities, so they will not invest short term. Hence, there is no or only a very weak relationship between interest rates of different maturities and supply and demand of a given maturity sets the individual interest rates. By inference, there is no reason to construct a term structure as there is no relationship between long term rates and expected future short term rates. This is unlikely to strictly hold because it suggests that opportunities to take advantage of mispricing of securities will not be exploited. For example if the 10 year bond rate is much higher than warranted by expectations, one could buy the 10 year bond and short a 9 year bond. If the rates on different maturities get far enough out of line with expectations, some entity will seek to exploit the profit opportunity. If existing investors will not exploit the opportunity, new investors will emerge to do so in a capitalist system. On the other hand, daily changes in supply and demand and changes in nonprice conditions can certainly cause long term rates to diverge from the average of expected future short term rates. These create profit opportunities for astute bond traders. If bond markets are reasonably efficient, these profit opportunities should not last long. 1 Although not often recognized, it is possible for liquidity premiums to be negative. If investors have long investment horizons it is actually less risky for them to hold long duration bonds (as opposed to short duration) to minimize their interest rate risk. If the majority of investors have long time horizons then it would be riskier to hold short term, low duration investments. This could make long term investments preferable to short term, implying that the liquidity premium would have to be negative. 211 Chapter 02 – Determination of Interest Rates 7. Forecasting Interest Rates A forward rate is a rate that can be imputed from the existing term structure. It is a mathematical tautology that given a set of long term spot rates one can find the set of individual one year forward rates. For instance using the books terminology: (1+ 1 )6 = (1+ R1) 5* (1+ F 5 1 6 4 (1+ 1 )5 = (1+ R1) 4* (1+ F 4 1 where R1a6 R 1ar5 the long term spot rates from today to year 6 and 5 respectively and F stands for a forward rate. The first subscript refers to the loan origination date, but the textbook confusingly uses 1 instead of 0 as is normal to represent today. The second subscript refers to the term to maturity. Since all the spot rates are known one can construct the full set of forward rates, F i 1,m them. Teaching Tip: The text’s terminology is very confusing to me and to students. I use R 0 N to mean a spot rate on a loan originated today at time 0 and maturing in year N so that the loan term is N0. Forward rates such as F a4 6then understood to be the implied rate on a 2 year loan originated in time period 4 that matures in time period 6. Students have no trouble grasping my terminology. The test bank responses use this terminology as well. Interpreting the forward rates If the UET strictly holds then forward rates are an unbiased estimate of expected future annual rates. If there are liquidity premiums, one should subtract the liquidity premium from the forward rate before using it as an estimate of the expected future spot rate. If segmentation strictly holds, the forward rate has no economic meaning. IV. Web Links http://www.ft.com/ Financial Times, won two Espy awards for best new site and best non U.S. news site. Outstanding coverage of global events and markets http://www.wsj.com/ The Wall Street Journal website has excellent data sources and articles on finance and economics. The Wall Street Journal’s international coverage is also outstanding. http://www.ustreas.gov/ Treasury data on U.S. national debt http://www.federalreserve.gov/ Board of Governors of the Federal Reserve System homepage, breaking news, monetary policy data and careers with the Fed http://www.moodys.com/ A leading provider of independent credit ratings, research and financial information to the capital markets 212 Chapter 02 – Determination of Interest Rates http://www.standardandpoors.com/ A leading provider of independent credit ratings, research and financial information to the capital markets 213 Chapter 02 – Determination of Interest Rates Financial Systems Discussion Question 2.1 Discuss your viewpoints on the current situation of social security benefits. See article below. Social Security is meant to assist older Americans, disabled workers, and families in where a spouse or parent dies. The article describes how someone can maximize their total use of their social security benefits simply by delaying the time that you receive them. There are many benefits to delaying your benefits once you reach the age of retirement. From what I have read, it seems as if social security will be around for a long time, and it sounds like the majority of people will be around longer than they believe. Most people are eager to receive a Social Security check but the best thing that you can do is to delay it. If you receive the checks early you may not receive some of the benefits that the government provides. It also goes into detail as to when the best time the elderly should begin to withdraw their funds for the maximum amount of benefits while still attempting to work. There are ways that you can still maximize your benefits if you receive Social Security early. Some of these ways would be the benefits of waiting, by this you can avoid penalty. Financial Systems Discussion Question 2.2 Share your experience related to reading "good debt vs bad debt" posted under Chapter 2. http://finance.yahoo.com/bankingbudgeting/article/109993/gooddebtvsbaddebt?mod=oneclick Most Americans live in debt, whether its good debt or bad debt, and most will fail to recognize the difference between the good and bad debt. This article does a great job at not only explaining the difference between good and bad debt, but also is a great example of how to maintain your money without going into debt all the time. Good debt creates value where as bad debt is borrowing money to buy things that aren’t necessities. Good debt, should you need to go into debt, is always the better, and of course anything you go into debt for, should not diminish in its value but grow. Student loans are a fantastic example of good debt. 214
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