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## Economics 173A

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**Economics 173A**Comprehensive (excluding MPT) Slide Deck**To help to finance Companies**Annual Working Capital increases = $ 150 Billion Annual Capital Expenditures “CAPEX” = $ 900 Billion = $ 1,050 Billion Source of funds: Annual Earnings = ($ 800 Billion) GAP $ 250 Billion 2. Annual Debt issued ($ 300 Billion) ( $ 50 Billion) Equity -this represents repurchases of Equity Capital Markets**The Assets**Fixed Income Bonds Real Estate Equity Shares Units Derivatives Options Futures The Process Asset Allocation Equity/Fixed 60/40 80/20 120/20 ? Security Selection Security Analysis Assets & Investing Risk Return Trade-off**Prices and Coupon Rates**Risk and expected Return Return Risk**Money Market**Certificates of Deposit U.S. Treasury Bills Money Market Funds Bond Market U.S Treasury Notes, Bills, and Bonds U.K. Gilts and Consols Municipal Bonds Corporate Bonds Equity Market Common Stock Preferred Stock Derivative Market Options Futures Other Swaps Pass-throughs Financial Instruments**Banks**Commercial Banks Investment Banks Funds Mutual Hedge Pension Private Equity Foreign Exchange Commodity Securitization GNMA CMOs, CDOs Bundling (Un) STRIPS Engineering Custom-tailored Risk/Return Synthetics – derivative hedges – mimic something Intermediation and Innovation**Fixed**CDs – bank time-deposits Paper – unsecured, trade-able company debt Acceptances – bank promises Eurodollars - $ denominated foreign bonds Repos, Reverse Repos – of treasury debt Treasuries – bills, notes, bonds Rates Prime Fed Funds LIBOR TED Spread : the 3-month Treasury less LIBOR Fixed Securities & Rates**TED Spread**Originally calculated as the difference between interest rates on 3-month T-bills and 3-month Eurodollar contracts w/ identical expiration. Acronym is derived from the “T” for “Treasuries" and the ticker symbol for Eurodollars, which is “ED”.Today, the TED spread is calculated as the difference between interest rates on 3-month T-bills and 3-month LIBOR (London Interbank Offered Rate).**TED Spread**Denominated in basis points (bps). Historically 10 to 50 bps – average 30 bps A rising TED spread indicates shrinking liquidity –an indicator of perceived credit risk: T-bills are considered risk-free LIBOR reflects the credit risk of lending banks. Widening TED spread is a sign that lenders believe default risk on interbank (counterparty) loans is increasing.]**Historically 20 to 30 bps**2007 Average 150 – 200 bps September 2008 > 300 bps; and on October 8th 465 bps**Bonds**• Characteristics • Pricing • Yields • Sensitivity to Time, i.e. maturity • Sensitivity to interest rates Economics 175**Bond Characteristics**• Debt Security – related to borrowing • Also called a Fixed Income security • Covenants or Indenture define the contract (this can be complex) • 2 types of Payments: interest & principal • Interest payments are the Coupon • Principal payment is the Face**Bond Basics**• Fixed Income Securities: A security such as a bond that pays a specified cash flow over a specific period. Fixed Income Securities vs. Common Stock Fixed Claim Residual Claim High Priority on cash flows Lowest Priority on cash flows Tax Deductible Not Tax Deductible Fixed Maturity Infinite life No Management Control Management Control Bonds Hybrids (Combinations Common Stock of debt and equity)**The bond indenture usually lists:**Amount of Issue, Date of Issue, Maturity Denomination (Par value) Face Annual Coupon, Dates of Coupon Payments Security Sinking Funds Call Provisions Covenants Features that may change over time: Rating Yield-to-Maturity Market price Bond Basics • The indenture is a written agreement between the corporate debt issuer and the lender.**Types of Bonds (Fixed Income Instruments)**• Convertibles (into Equity) • Callable Bond (buy-back by Issuer) – shorten the term • Putable Bond (sell-back by Owner) – extend the term • Floating-rate & Inverse Floaters • Asset-backed (like CMOs) • Zeros – no Coupons • Strips – no Face • Senior versus Subordinated Economics 175**Treasury Bonds, Bills, & Notes**• Notes – up to 10 year term • Bonds – to 30 years • Face (denomination) of $1,000; quotes in $100’s • Coupon (rate) paid semi-annually • Prices quoted in points (of face) + 1/32 • No default / credit risk**Bond Pricing**As with all Financial Assets The price is a Present Value of the expected cash flows discounted at the appropriate (relative to risk) discount (interest) rate.**Coupon Payments**• Relative to other types of securities, bonds produce cash flows that an analyst can predict with a high degree of precision. • Fixed rate • Variable rate • Zero coupons • Consols – consolidated annuities - perpetuities introduced in 1751.**Annual percentage yield (APY)**The effective, or true, annual rate of return. The APY is the rate actually earned or paid in one year, taking into account the affect of compounding. The APY is calculated by taking 1+r … the periodic rate and raising it to the number of periods in a year. For example, a 1% per month rate has an APY of 12.68% (1.01^12).**Bond Pricing**• DCF Technique PB = Price of the bond Ct = interest or coupon payments T = number of periods to maturity r = semi-annual discount rate or the semi-annual yield to maturity**20**S 40 1 = + P 1000 B t 20 (1+.03) (1+.03) t =1 Bond Pricing • Example (annual coupon paid SA). Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000 in a 6% risk-adjusted market. Ct = 40 (SA), F = 1000, T = 20 periods, r = 3% (SA) PB = $1,148.77**Three Bonds in a 10 percent world …**Insert Figure 4-6 here.**Bond Pricing**• Zero Coupon Bonds • Consols – Zero Face Bonds**Bond Yields**• Yield to Maturity: The discount rate that makes the present value of a bond’s payments equal to its price. • Internal rate of return from holding bond till maturity. • Example3 year bond with interest payment of $100, principal of $1,000 and current price of $900 • Assume coupon proceeds are reinvested at the YTM.**20**S 40 1 = + P 1000 B t 20 (1+.03) (1+.03) t =1 Bond Pricing • Example (annual coupon paid SA) in a 6 percent world.Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000 Ct = 40 (SA), P = 1000, T = 20 periods, r = 3% (SA) PB = $1,148.77**Approximate Yield to Maturity**Bond Yields • Approximating YTM Using the earlier example Avg. Income = 80 + (1000-1149)/10 = 65.10 Avg. Price = (1000 + 1149)/2 = 1074.50 Approx. YTM = 65.10/1074.50 = 0.0606 Actual YTM = 6.00%**Bond Yields**• Prices and Yields (required rates of return) have an inverse relationship • When yields get very high the value of the bond will be very low • When yields approach zero, the value of the bond approaches the sum of the cash flows**Prices and Coupon Rates**Bond Yields Price Yield**Yield Curve**• A plot of interest rates against time to maturity. yield maturity**Daily Treasury Yield Curve Rates**http://www.ustreas.gov/**Daily Treasury Yield Curve Rates**http://www.ustreas.gov/**Bond Yields**• Current or Annual Yield: Annual coupon divided by bond price. • Different from YTM! • Accrued Interest • Interest is earned for each day that a bond is held, although interest payments are generally made twice a year only. • A bond buyer must pay the accrued interest to the seller of the bond. • dirty price = bond price + accrued interest • clean price = bond price • By convention, accrued interest is calculated using a 360-day year.**Bond Pricing: Accrued Interest**• Example • Consider a bond that is paying a six percent annual coupon rate in semiannual payments with a yield to maturity of 10 percent and two years and ten months until its maturity. • What is the quoted price or clean price? • What is the dirty price?**Bond Pricing: Accrued Interest**• What is the quoted price or clean price? Step One: Calculate the present value of a bond that has 2.5 years until it matures and pays semiannual interest coupons. Step Two: The $30 coupon is added to $913.39. The sum is $943.19. Step Three: The value $943.19 is discounted back 4 months to the purchase date.**Bond Pricing: Accrued Interest**• What is the dirty price? Calculate the accrued interest for two months. There are 180 days between semiannual coupon payments and 30 days in a month. Therefore 60/180 is the fraction of the coupon payment earned by the seller. In other words the accrued interest is $10 and the dirty price is $923.16.**Bond Risks**• Price Risks • Default risk • Interest rate risk • Convenience Risks • Call risk • Reinvestment rate risk • Marketability risk**Default Risk**• The income stream from bonds is not riskless unless the investor can be sure the issuer will not default on the obligation. • Rating companies • Moody’s Investor Service • Standard & Poor’s • Duff and Phelps • Fitch**Default Risk**• Rating Categories • Investment Grade Bonds • Speculative Grade Bonds S&P Moody’s Very High Quality AAA, AA Aaa, Aa High Quality A, BBB A, Baa Speculative BB, B Ba, B Very Poor CCC, CC, C, D Caa, Ca, C, D**Forward Rates**term yearsrat year One-year rate one year from now One-year rate two years from now**Linear measure of the sensitivity of a bond's price to**fluctuations in interest rates. Measured in units of time; always less-than-equal to the bond’s maturity because the value of more distant cash flows is more sensitive to the interest rate. “Duration" generally means Macaulay duration. Bond Duration**For small interest rate changes, duration is the approximate**percentage change in the value of the bond for a 1% increase in market interest rates. The time-weighted average present value term to payment of the cash flows on a bond. Macaulay Duration**The proportional change in a bond’s price is proportional**to duration through the yield-to-maturity Macaulay Duration**A 10-year bond with a duration of 7 would fall approximately**7% in value if interests rates increased by 1%. The higher the coupon rate of a bond, the shorter the duration. Duration is always less than or equal to the overall life (to maturity) of the bond. A zero coupon bond will have duration equal to the maturity. Macaulay Duration**Duration x Bond Price: the change in price in dollars, not**in percentage, and has units of Dollar-Years (Dollars times Years). The dollar variation in a bond's price for small variations in the yield. For small interest rate changes, duration is the approximate percentage change in the value of the bond for a 1% increase in market interest rates. Dollar Duration**Modified Duration – where n=cash flows per year.**Modified Duration and**Modified Duration**What will happen to the price of a 30 year 8% bond priced to yield 9% (i.e. $897.27) with D* of 11.37 - if interest rates increase to 9.1%?**Duration Characteristics**• Rule 1: the duration of a zero coupon bond is equal to its time-to-maturity. • Rule 2: holding time-to-maturity and YTM constant, duration is higher when the coupon rate is lower. • Rule 3: holding coupon constant, duration increases with time-to-maturity. Duration always increases with maturity for bonds selling at par or at a premium. • Rule 4: cateris parabus, the duration of coupon bonds are higher when its YTM is lower. • Rule 5: duration of a perpetuity is [(1+r)/r].**Bond Convexity**• Bond prices do not change linearly, rather the relationship between bond prices and interest rates is convex. • Convexity is a measure of the curvature of the price change w.r.t. interest rate changes, or the second derivative of the price function w.r.t. relevant interest rates. • Convexity is also a measure of the spread of future cash flows. • Duration gives the discounted mean term; convexity is used to calculate the discounted standard deviation of return.