FNCE 4070: FINANCIAL MARKETS AND INSTITUTIONS Lecture 3: Understanding Interest Rates Various Measures of Interest Rates Relationship of Market Interest Rates to Bond Prices Risks in the Bond Markets Real Interest Rate

Where is this Financial Center?

Can you explain this headline? Treasuries Decline as Weekly Jobless Claims Drop  Treasuries declined as first-time claims for unemployment insurance fell to the lowest since July 2008.

Interest Rate Defined “Dual” Definition:  Borrowing: the cost of borrowing or the price (%) paid for the “rental” of funds. A financial liability for “deficit” entities.  Saving: the return from investing funds or the price (%) paid to delay consumption. A financial asset for “surplus” entities. Both concepts are expressed as a percentage per year (Percent per annum; “p.a.”).  True regardless of maturity of instrument of the financial liability or financial asset. Thus, all interest rate data is annualized. See:

Savings and Borrowing Rates: They Move Together, 1977– 2011 Regression analysis: 1964 – 2010 (monthly data, 564 observations); CD rate as dependent variable. R-squared = 88.55%

Regulation Q (Glass Steagall Act, 1933) and Market Interest Rates

Seeds of Disintermediation

Regulation Q Phased out by 1986 (Large denomination CDs exempt in 1970) Monetary Control and Deregulations Act, 1980

The Demise of the S&Ls: Maturity Mismatch of Asset and Liability

Commonly Used Interest Rate Measures There are four important ways of measuring (and reporting) interest rates on financial instruments. These are:  Coupon yield: The “promised” annual percent return on a coupon instrument.  Current Yield: Bond’s annual coupon payment divided by its current market price.  Discount Yield and Investment Yield: The yield on T- bills (and other discounted securities, such as commercial paper) which are selling at a discount of their maturity values.  Yield to Maturity: The interest rate that equates the future payments to be received from a financial instrument (coupons plus maturity value) with its market price today (i.e., to its present value).

Benchmarking with Interest Rates Interest rates can be used for cross-country assessments or changes in individual country assessments over time. The 2 most common benchmark rates are yields to maturity on 10-year Government U.S. Treasuries and German Bunds.  We assume both of these are “default-free.” Thus we can compare other sovereigns to these (and to one another) to assess : Credit ratings risk Inflation risk The market’s overall assessment of country risk  See:

Coupon Yield Coupon yield is the annual interest rate which was promised by the issuer when a bond is first sold.  Information is found in the bond’s indenture. The coupon yield is expressed as a percentage of the bond’s par value. In the United States, all bonds have a par value of $1,000  Example: 3.125% U.S. Treasury bond due November 2041  This bond will pay $31.25 per year in interest ( x $1,000) The coupon yield on a bond will not change during the lifespan of the bond.

Par Values: Other Countries Par values different in other countries:  UK Government bonds (generally £100 par value; called gilts)  Japanese Government bonds (¥10,000 par value; called JGBs)  German Government bonds (minimum amount of €100 par value, called bunds)  Canadian Government bonds (CAD$1,000 par value) Par value is also called the maturity value (or face value). Government bonds generally pay interest semi- annually.

Current Yield Since bond prices are likely to change, we often refer to the “current yield” which is measured by dividing a bond’s annual coupon payment by its current market price.  This provides us with a measure of the interest yield obtained at the current market price (i.e., cost of investing)  Current yield = annual coupon payment/market price So, if our 4.5% coupon bond is currently selling at $900 the calculated current yield is:  $45/$900 = 5.00% And if the bond is selling at $1,100, the current yield is:  $45/$1,100 = 4.09%

Discount and Investment Yield Discount yields and investment yields are calculated for U.S. T-bills and other short term money market instruments (e.g., commercial paper and bankers’ acceptances) where there are no stated coupons (and thus the assets are quoted at a discount of their maturity value). The discount yield relates the return to the instrument’s par value (or face or maturity).  The discount yield is sometimes called the bank discount rate or the discount rate. The investment yield relates the return to the instrument’s current market price.  The investment yield is sometimes called the coupon equivalent yield, the bond equivalent rate, the effective yield or the interest yield.

Calculating the Discount Yield Discount yield = [(PV - MP)/PV] * [360/M] PV = par (or face or maturity) value MP = market price M = maturity of bill.  For a “new” three-month T-bill (13 weeks) use 91, and for a six-month T-bill (26 weeks) use 182.  For outstanding issues, use the actual days to maturity. Note: 360 = is the number of days used by banks to determine short-term interest rates.

Discount Yield Example What is the discount yield for a 182-day T-bill, with a market price of $ (per $1,000 par, or face, value)? Discount yield = [(PV - MP)/PV] * [360/M] Discount yield = [(1,000) - (965.93)] / (1,000) * [360/182] Discount yield = [34.07 / 1,000] * [ ] Discount yield = = 6.74%

Investment Yield The investment yield is generally calculated so that we can compare the return on T-bills to “coupon” investment options.  The calculated investment yield is comparable to the yields on coupon bearing securities, such as long term bonds and notes. As noted: The investment yield relates the return to the instrument’s current market price. In addition, the investment yield is based on a calendar year: 365 days, or 366 in leap years. Investment yield = [(PV - MP)/MP] * [365 or 366/M]

Investment Yield Example What is the investment yield of a 182-day T- bill, with a market price of $ per $1,000 par, or face, value? Investment yield = [(PV - MP)/MP] * [365/M] Investment yield = [(1,000 – ) / (965.93)] * [365/182] Investment yield = [34.07] / ] * [ ] Investment yield = = 7.07%

Comparing Discount and Investment Yields Looking at the last two examples we found:  Discount yield = [(PV - MP)/PV] * [360/M] Discount yield = [(1, )] / (1,000) * [360/182] Discount yield = [34.07 / 1,000] * [ ] Discount yield = = 6.74%  Investment yield = [(PV - MP)/MP] * [365/M] Investment yield = [(1,000 – )] / (965.93) * [365/182] Investment yield = [34.07 / ] * [ ] Investment yield = = 7.07% Note: The discount formula will tend to “understate” yields relative to those computed by the investment method, because the market price is lower than the par value ($1,000).  However, if the market price is very close to the par value, the yields will be similar. See: management/interest-rate/daily_treas_bill_rates.shtmlhttp:// management/interest-rate/daily_treas_bill_rates.shtml And:

Bloomberg and Reported Yields on T-Bills Go to Go to Market Data Go to Rates and Bonds You will see for “U.S. Treasuries” the following data (note: this is an example from the Feb 4, 2011 site): Coupon Maturity Current Date Price/Yield 3-month /05/ /.15 6-month /04/ / month /12/ /.28 Key: These are T-bills, thus the coupon is 0% (recall they are sold at a discount). At maturity date they will pay the holder $1,000. The current price is the discount yield (bank discount yield) and the current yield is the investment yield (bond or coupon equivalent yield).

Yield to Maturity The yield to maturity uses the concept of present value in its determination. Yield to maturity is the interest rate which will discount the incomes (i.e., cash-flows) of a bond to produce a present value which is equal to the bond’s current market price (or produce a net present value = 0). Yield to maturity (i) is calculated as: MP = Market price of a bond (i.e., present value) C = Coupon payments (a cash flow) PV = Par, or face value, at maturity (a cash flow) n = Years to maturity  Note: i is also the internal rate of return

Yield to Maturity Example Assume the following given variables: C =$40 (thus a 4.0% coupon issue; paid annually) N =10 PV =$1,000 MP =$1,050 (note: bond is selling at a premium of par) 1050 = 40/(1 + i) /(1 + i) /(1 + i) /(1 + i) 10 Solve for i, the yield to maturity Note: The “i" calculated using this formula will be the return that you will be getting when the bond is held until it matures and assuming that the periodic coupon payments are reinvested at the same yield. In this example, the “i" is 3.4%.

Yield to Maturity Second Example Now assume the following:  C =$40 N =10 PV =$1,000 MP =$ (note: bond is selling at a discount of par) 900 = 40/(1 + i) /(1 + i) /(1 + i) ,000/(1 + i) 10 Solve for i, the yield to maturity Note: The “i" calculated in this example is 5.315%. What one factor accounts for the yield to maturity difference when compared to the previous slide, with its i of 3.4%?

Useful Web Site for Calculating a Bond’s Yield to Maturity While yields to maturity can be determined through a book of bond tables or through business calculators, the following is a useful web site for doing so: zine.com/Calculators/Investment- Calculators/Bond-Yield-Calculator/ zine.com/Calculators/Investment- Calculators/Bond-Yield-Calculator/

The Yield to Maturity Think of the yield to maturity as the “required return on an investment.” Since the required return changes over time, we can expect these changes to produce inverse changes in the prices on outstanding (seasoned) bonds. Why will the required return change over time?  Changes in inflation (inflationary expectations).  Changes in the economy’s credit conditions resulting from change in business activity.  Changes in central bank policies. Impact on shorter term maturities.  Changes in the credit risk (i.e., risk of default) associated with the issuer of the bond. On Governments, also changes in credit ratings risk.

Illustrating the Relationship Between Interest Rates and Bond Prices Assume the following:  A 10 year corporate Aaa bond which was issued 8 years ago (thus it has 2 years to maturity) has a coupon rate of 7%, with interest paid annually.  Thus, 7% was the required return when this bond was issued. This bond is referred to as an outstanding (or seasoned) bond.  Question: How much will a holder of this bond receive in interest payments each year?  This bond has a par value of $1,000. Question: How much will a holder of this bond receive in principal payment at the end of 2 years?

What Happens when Interest Rates Rise? Assume, market interest rates rise (i.e., the required return rises) and now 2 year Aaa corporate bonds are now offering coupon returns of 10%.  This is the “current required return” (or “i” in the present value bond formula) Question: What will the market pay (i.e., market price) for the outstanding 2 year, 7% coupon bond noted on the previous slide?  PV = $70/(1+.10) + $1,070/(1+.10) 2  PV = $ (this is today’s market price) Note: The 2 year bond’s price has fallen below par (selling at a discount of its par value). Conclusion: When market interest rates rise, the prices on outstanding bonds will fall.

What Happens when Interest Rates Fall? Assume, market interest rates fall (i.e., the required return falls) and now 2 year Aaa corporate bonds are now offering coupon returns of 5%.  This is the “current required return” (or “i” in the present value bond formula) Question: What will the market pay (i.e., market price) for the outstanding 2 year, 7% coupon bond?  PV = $70/(1+.05) + $1,070/(1+.05) 2  PV = $1, (this is today’s market price) Note: The 2 year bond’s price has risen above par (selling at a premium of its par value). Conclusion: When market interest rates fall, the prices on outstanding bonds will rise.

Bond Price Sensitivity to Changes in Market Interest Rates (YTM)

Change in Market’s Required Return Versus Change in Market Demand The examples on the previous slides demonstrated the impact of a change in the market’s required return on bond prices.  Observation: Cause – effect relationship runs from changes in required return to changes in market prices (which produce the market’s new required return). However, it is possible for a change in market demand to produce changes in bond prices and thus in market interest rates.  For example: Safe haven effects result in changes in demand for particular assets.  Observation: Cause – effect relationship runs from changes in demand to changes in prices (which have an automatic impact on yields).

What if the Time to Maturity Varies? Assume a one year bond (7% coupon) and the market interest rate rises to 10%, or falls to 5%.  = $1,070/(1.10)  PV = $  $1,070/(1.05)  PV = $1, Now assume a two year bond (7% coupon) and the market interest rate rises to 10%, or falls to 5%  = $70/(1+.10) + $1,070/(1+.10) 2  PV = $  = $70/(1.05) + $1,070/(1+.05) 2  PV = $ Conclusion: For a given interest rate change, the longer the term to maturity, the greater the bond’s price change.

Summary: The Interest Rate Bond Price Relationship #1: When the market interest rate (i.e., the required rate) rises above the coupon rate on a bond, the price of the bond falls (i.e., it sells at a discount of par). #2: When the market interest rate (i.e., the required rate) falls below the coupon rate on a bond, the price of the bond rises (i.e., it sells at a premium of par) IMPORTANT: There is an inverse relationship between market interest rates and bond prices (on outstanding or seasoned bonds). #3: The price of a bond will always equal par if the market interest rate equals the coupon rate.

Summary: The Interest Rate Bond Price Relationship Continued #4: The greater the term to maturity, the greater the change in price (on outstanding bonds) for a given change in market interest rates.  This becomes very important when developing a bond portfolio-maturity strategy which incorporates expected changes in interest rates.  This is the strategy used by bond traders: What if you think interest rates will fall? Where should you concentrate the maturity of your bonds? What if you think interest rates will rise? Where should you concentrate the maturity of your bonds?  See Appendix 1 for Excel Calculation of bond prices.

Interest Rate (or Price) Risk on a Bond Defined: The risk associated with a reduction in the market price of a bond, resulting from a rise in market interest rates. This risk is present because of the “inverse” relationship between market interest rates and bond prices. The longer the maturity of the fixed income security, the greater the risk and hence the greater the impact on the overall return. For a historical examples, see the next slide.

Relationship of Maturity to Returns Note: Return = coupon + change in market price

Price Risk:

Reinvestment Risk on a Bond Reinvestment risk o ccurs because of the need to “roll over” securities at maturity, i.e., reinvesting the par value into a new security. Problem for bond holder: The interest rate you can obtain at roll over is unknown while you are holding these outstanding securities. Issue: What if market interest rates fall? You will then re-invest at a lower interest rate then the rate you had on the maturing bond. Potential reinvestment risk is greater when holding shorter term fixed income securities. With longer term bonds, you have locked in a known return over the long term.  For a historical example, see the next slide

Reinvestment Risk:

Concept of Bond Duration Issue: The fact that two bonds have the same term to maturity does not necessarily mean that they carry the same interest rate risk (i.e., potential for a given change in price). Assume the following two bonds:  (1) A 20 year, 10% coupon bond and  (2) A 20 year, 6% coupon bond. Which one do you think has the greatest interest rate (i.e., price change) risk for a given change in interest rates?  Hint: Think of the present value formula (market price of a bond) and which bond will pay off more quickly to the holder (in terms of coupon cash flows).

Solution to Previous Question Assume interest rates change (increase) by 100 basis points, then for each bond we can determine the following market price. 20-year, 10% coupon bond’s market price (at a market interest rate of 11%) = $ year, 6% coupon bond’s market price (at a market interest rate of 7%) = $ Observation: The bond with the higher coupon, (10%) will pay back quicker (i.e., produces more income early on), thus the impact of the new discount rate on its cash flow is less.

Duration and Interest Rate Risk Duration is an estimate of the average lifetime of a security’s stream of payments.  Duration rules:  (1) The lower the coupon rate (maturity equal), the longer the duration.  (2) The longer the term to maturity (coupon equal), the longer duration.  (3) Zero-coupon bonds, which have only one cash flow, have durations equal to their maturity. Duration is a measure of risk because it has a direct relationship with price volatility. The longer the duration of a bond, the greater the interest rate (price) risk and the shorter the duration of a bond, the less the interest rate risk.

Calculated Durations Duration for a 10 year bond assuming different coupons yields:  Coupon 10%Duration 6.54 yrs  Coupon 5%Duration 7.99 yrs  Zero CouponDuration 10 years Duration for a 10% coupon bond assuming different maturities:  5 yearsDuration 4.05yrs  10 yearsDuration 6.54 yrs  20 yearsDuration 9.00 yrs Note: See Appendix 2 for Excel calculations

Using Duration in Portfolio Management Given that the greater the duration of a bond, the greater its price volatility (i.e., interest rate risk), we can apply the following: (1) For those who wish to minimize interest rate risk, they should consider bonds with high coupon payments and shorter maturities (also stay away from zero coupon bonds).  Objective: Reduce the duration of their bond portfolio. (2) For those who wish to maximize the potential for price changes, they should consider bonds with low coupon payments and longer maturities (including zero coupon bonds).  Objective: Increase the duration of their bond portfolio

The Real Interest Rate Real interest rate:  This is the market (or nominal) interest rate that is adjusted for expected changes in the price level (i.e., inflation) and is calculated as follows: i rr = i mr - p e Where: i rr = real rate of interest (% p.a.) i mr = market (nominal) rate of interest (% p.a.) p e = expected annual rate of inflation, i.e., the average annual price level change over the maturity of the financial asset (% p.a.)

Real Interest Rate Impacts on Borrowing and Investing We assume that real interest rates more accurately reflect the true cost of borrowing and true returns to lenders and/or investors.  Assume: i mr = 10% and p e = 12% then  i rr = 10% - 12% = -2% When the real rate is low (or negative), there should be a greater incentive to borrow and less incentive to lend (or invest).  Assume: I mr = 10% and p e = 1% then  I rr = 10% - 1% = 9% When the real rate is high, there should be less incentive to borrow and more incentive to lend (or invest).

3-48 U.S. Real and Nominal Interest Rates:

Real Interest Rate as an Indicator of Monetary Policy The real interest rate (on the fed funds rate) is also assumed to be a better measure of the stance of monetary policy than just the market interest rate.  Why: Real rate affects borrowing decisions.  If the real rate is negative, or very low, monetary policy is very accommodative and borrowing will be encouraged.  If the real rate high, monetary policy is very tight and borrowing will be discouraged.  A neutral monetary policy occurs when the real rate is zero.

Example of Nominal Versus Real Rate Economic Background U.S. experiences the 2000 “dot-com” stock market crash and “terrorist- attack” induced recession of 2001:  March 11, 2000 to October 9, 2002, Nasdaq lost 78% of its value. In response the Fed pushed the fed funds rates to 1.0% (levels not seen since the 1950s) Nominal Fed Funds Rate

Real Fed Funds Rate Real Rate Goes Negative 2003/04 Where is it today? Effective Rate: ______ Go to: pps/quote?ticker=FEDL01%3 AIND pps/quote?ticker=FEDL01%3 AIND Latest Inflation: ______ Go to: n.htm Your analysis of monetary policy and credit conditions in the economy?

Another Web Site for Calculating Yields Visit the web site below. It allows you to calculate the current yield and yield to maturity for specific data you input on:  Current Market Price  Coupon Rate  Years to Maturity It also allows you to calculate present values. Use this web site to test your understanding of the relationship between bond prices and interest rates.  See what happens to the calculated interest rates when you change the bond price above and below the par value.  Note the inverse relationship.

Internet Source of Interest Rate Date Historical and Current Data for U.S.  Real Time Data (U.S. and other major countries)  Go to Market Data and then to Rates and Bonds Other Countries:  Economist.com (both web source or hard copy)

Appendix 1 Using Excel to Calculate the Market Price (Present Value) of a Bond

Using Excel to Calculate Bond Price Go to Formulas in Microsoft Excel Go to Financial Go to Price Insert Your Data:  Example for 20 year, 10% coupon bond with market rate of 11%: Settlement: DATE(2009,2,1) Assume, Feb 1, 2009 Maturity: DATE(2029,2,1) Note: 20 years to maturity Rate: 10% (this is the coupon yield) Yld: 11% (this is the yield to maturity) Redemption: 100 (this is the price per $100) Frequency: 2 (assume interest is paid semi-annually) Basis: 3 (this basis uses a 365 day calendar year)  Formula result (i.e., price per $100 face value) = (or $919.77)

Appendix 2 Using Excel to Calculate the Duration of a Bond

Using Excel to Calculate Duration Go to Formulas in Microsoft Excel Go to Financial Go to Duration Insert Your Data:  Example for 10 year, 10% coupon bond with market rate of 10%: Settlement: DATE(2009,2,1) Assume, Feb 1, 2009 Maturity: DATE(2019,2,1) Note: 10 years to maturity Rate: 10% (this is the coupon yield) Yld: 10% (this is the yield to maturity) Frequency: 2 (assume interest is paid semi-annually) Basis: 3 (this basis uses a 365 day calendar year)  Formula result =

Appendix 3 The Real Interest Rate during a period of deflation

What if the Rate of Inflation is Negative (i.e., Deflation) Assume the following: i mr = 3% and p e = -2% Then the calculated real rate would be: i rr = 3% - (-2%) = 5% Issues: 1. What will be the economy’s incentive to borrow?  High or low. 2, What are the issues facing the central bank when the economy is experiencing deflation?  How can borrowing be encouraged?

Appendix 4 Types of Debt Instruments and Lending Terms

2 Basic Types of Debt Instruments Discount Bond (Zero-coupon Bond):  A bond whose purchase price is below the face (or par) value of the bond (i.e., at a discount)  The entire face (par) value is paid at maturity.  There are no interest payments.  U.S. Treasury bills are an example of a discount security (as is commercial paper and bankers’ acceptances). Coupon Bond:  A bond that pays periodic interest payments (stated as the coupon rate) for a specified period of time after which the total principal (face or par value) is repaid. In the United States and Japan, interest payments are typically made every six months and in Europe typically once a year. coupon bonds can sell at either a discount or premium (of par value). These bonds are generally callable.  Issuer can “retire” them before their stated maturity date.  Why do you think they might do this?

Important Terms in Lending (Loan) Principal: the amount of funds the lender provides to the borrower. Maturity Date: the date the loan must be repaid or refinanced. (Loan) Term: the time period from initiation of the loan to the maturity date. Interest Payment: the cash amount that the borrower must pay the lender for the use of the loan principal. (Simple) Interest Rate: the annual interest payment divided by the loan principal.  In bond terminology, the coupon interest rate is the annual interest payment divided by the par value.

Types of Loans Simple Loan: Principal and all interest both paid at maturity (i.e., date when loan comes due).  Borrow $1,000 today at 5% and in 1 year pay $1,050  Commercial bank loans to businesses are usually simply loans. Fixed-payment Loan: Equal monthly payments representing a portion of the principal borrowed plus interest. Paid for a set number of years, at which time (maturity date) the principal amount is fully repaid.  Referred to as an amortized loan.  Home mortgages (conventional), automobile loans.

Amortization Loan Example: Real Estate Mortgage Loan  Principal Amount: $500,000  Years To Maturity: 30 years (with monthly payments)  Interest rate: 7% (fixed rate mortgage) Monthly Payment  $3, (for 360 months, i.e., 30 years) First Month Payment (n = 1):  Principal: $409.84; Interest: $2, (or, $3,326.51) Last Month Payment (n = 360):  Principal: $3,307.22; Interest: $19.29 (or, $3,326.51)

Appendix 5 Quoting Treasury Notes and Bonds

Treasury Prices in 32nds Treasury note and bond prices are quoted in dollars and fractions of a dollar. By market convention, the normal fraction used for Treasury security prices is 1/32 (of $1). In a quoted price, the decimal point separates the full dollar portion of the price from the 32nds of a dollar, which are to the right of the decimal.  Thus a quote of means $105 plus 8/32 of a dollar, or $100.25, for each $100 face value of the note.  Note: the symbol + refers to ½ of 1/32 nd. Change data is the difference between the current trading day's price and the price of the preceding trading day. It, too, is a shorthand reference to 32nds of a point.  For example, a +16 refers to a change of 16/32 or 50 cents from the previous day.