Yield and Duration Financial Markets, Day 3, Class 1 Jun Pan - PowerPoint PPT Presentation

Yield and Duration Financial Markets, Day 3, Class 1 Jun Pan Shanghai Advanced Institute of Finance (SAIF) Shanghai Jiao Tong University April 20, 2019 Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 1 / 29

Outline for Day 3 Class 1: Yield and duration. Class 2: Factors infmuencing the yield curve. Class 3: Modeling the yield curve. Class 4: Interest rate swaps. Class 5: Corporate bonds and credit risk. Class 6: Review and quiz. Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 2 / 29

Outline for Class 1 From equity to fjxed income. Bond price and yield: duration and convexity. The universe of fjxed income securities. Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 3 / 29

From Equity to Fixed Income So beta in equity, and duration in fjxed income. Jun Pan Yield and Duration Financial Markets, Day 3, Class 1 So Black-Scholes implied vol in options and yield in fjxed income. of yields to maturity. The cheapness and richness of a bond is often measured in the space swaps: difgerent in structure but same as vehicles for duration . So how are things difgerent? (Michael Lewis: Equities in Dallas.) This becomes quite useful when moving from bonds to interest-rate Very often, we will refer to buying bonds as buying duration. duration . Its key risk factor: interest rate exposure, which is measured by Before maturity, it has scheduled coupon payments. A bond matures. At maturity, the bond pays back the principal. 4 / 29

Monthly Returns Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 5 / 29

Monthly Returns Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 6 / 29

Monthly Returns Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 7 / 29

Stock and Bond Returns -0.06 -0.06 10Y Bond 0.57 1.99 0.16 -6.68 8.54 0.07 1.00 1.00 5Y Bond 0.50 1.24 0.20 -3.38 4.52 0.01 11.41 0.15 (%) min max correlation with 1990-2014 (%) (%) ratio (%) -16.70 Stock TBill 10Y Stock (CRSP VW) 0.87 4.22 0.15 -0.10 0.93 std 0.34 -0.00 0.68 0.01 1.00 0.07 CPI 0.21 -1.92 0.25 1.22 -0.04 0.18 -0.16 Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 0.19 1M TBill 2Y Bond 0.74 0.39 0.54 0.26 -1.30 2.07 -0.11 0.41 1Y Bond 0.51 0.33 0.31 0.26 -0.33 1.31 -0.03 0.72 Sharpe mean Returns of Stock and Bond and Infmation 2.00 -21.58 16.81 1.00 -0.05 0.10 10Y Bond 0.47 0.08 4.16 -6.68 10.00 0.10 0.12 1.00 5Y Bond 0.46 0.17 1.03 0.10 1942-2014 Monthly Returns mean std Sharpe min max correlation with (%) Stock (CRSP VW) (%) ratio (%) (%) Stock TBill 10Y 1.38 -5.80 Monthly Returns 0.12 1M TBill 0.32 0.26 -0.00 1.52 -0.05 1.00 CPI 0.59 0.31 0.45 -1.92 5.88 -0.07 0.26 -0.07 0.62 0.08 10.61 -3.69 0.07 0.19 0.90 2Y Bond 0.42 0.77 0.13 8.42 5.61 0.08 0.37 0.76 1Y Bond 0.40 0.50 0.16 -1.72 8 / 29

Bond and Equity Funds Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 9 / 29

Yield to Maturity y and Bond Price P c Jun Pan Yield and Duration Financial Markets, Day 3, Class 1 Decreasing interest rate after issuance turns the bond into premium rate is good news for bonds. Increasing interest rate is bad news for bonds and decreasing interest At issuance, a Treasury bond has the following terms fjxed: 10 / 29 Treasury bonds pay coupon semi-annually, and, at issuance, the face value = $100; coupon rate = c ; maturity = T years. Later, with interest rate fmuctuations, both P and y change and there is a deterministic , inverse relationship between the two: coupon rate c is chosen so that the bond is priced at par: P = $100 and c = y . 2 T 2 × 100 100 ∑ P = ) n + ) 2 T . ( 1 + y ( 1 + y n =1 2 2 P > $100 , and increasing interest rate turns it into discount P < $100 .

Fixed-Rate Coupon Bonds Financial Markets, Day 3, Class 1 Jun Pan Yield and Duration 11 / 29 c 2 T 2 × 100 100 ∑ P = ) n + ) 2 T . ( 1 + y ( 1 + y 2 n =1 2

Treasury Yield Curve A typical yield curve (also called the term structure of interest rate): A yield curve can be created for any specifjc segment, from triple-A rated mortgage-backed securities to single-B rated corporate bonds. The Treasury bond yield curve is the most widely used. The normal shape of the yield curve is upward, but, occasionally, it slopes downward, or inverts. Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 12 / 29

Treasury Yield Curve on November 8, 1994 (Noise=2.60) Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 13 / 29

Treasury Yield Curve on September 15, 2008 (Noise=6.64) Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 14 / 29

Treasury Yield Curve on December 11, 2008 (Noise=20.4) Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 15 / 29

Treasury Constant Maturity Yields Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 16 / 29

Daily Changes in Treasury Yields -33 20080917 -81 4.94 3M 2008-2015 19940404 32 20011031 4.99 20080919 30Y 19940404 39 19950613 -23 5.78 10Y 19940404 76 2Y 20010913 30Y Jun Pan Yield and Duration Financial Markets, Day 3, Class 1 20110811 28 20081120 -32 6.12 20080930 4.86 24 20090318 -51 6.42 10Y 20080919 38 20080915 -45 36 -54 Daily Changes in Treasury Yields 3M -84 6.86 2Y 19820201 169 19820222 -104 7.63 1982-2015 80 (bp) (bp) (bp) max min std maturity sample 19871020 19820201 6.05 19820201 2Y 20001226 58 20070820 -64 5.18 3M 1990-2008 42 10Y 19871020 -76 6.30 30Y 19820201 44 19871020 -75 6.80 17 / 29

Dollar Duration (DV01) and Modifjed Duration which is the negative of $ change in bond price per unit change in Jun Pan Yield and Duration Financial Markets, Day 3, Class 1 change in bond price (i.e., bond return) per unit change in yield. which is efgectively a weighted sum of semi-annual coupon payment c c n Dollar Duration: P Modifjed Duration: DV01 = Dollar Duration/10000 ($ per 1 basis point change in yield): yield. 18 / 29 c n [ 2 T ] 2 × 100 − ∂ P 1 100 ∑ ∂ y = ) n + T × , 2 × ) 2 T 1 + y ( 1 + y ( 1 + y 2 2 n =1 2 2 × 100 ∑ 2 T 100 n + T × 2 × n =1 ( 1+ y 2 ) 2 T − 1 1 ∂ P ( 1+ y 2 ) ∂ y = , 1 + y 2 × 100 ∑ 2 T 100 n + 2 n =1 ( 1+ y 2 ) 2 T ( 1+ y 2 ) dates: 6 m , 1 y , 1 . 5 y , . . . , and T years. It captures the percentage

Modifjed Duration 5.81 7.71 7.79 9.02 4.95 5.46 5.51 5.65 5.85 7.21 6.50 3.86 4.16 4.18 4.27 4.36 4.38 7.44 7.11 2.54 14.46 Jun Pan Yield and Duration Financial Markets, Day 3, Class 1 9.46 12.47 13.39 13.84 15.45 6.23 22.48 8.58 10.68 11.13 11.56 12.12 12.55 16.42 Modifjed Duration 4.74 2.66 2% 0.99 10% 7% 7.2% 6% 4.8% 5% coupon c 0.96 10% 7% 6% 6% 6% 5% 2% yield y 0.96 0.96 0.95 1.86 2.68 2.71 2.74 2.75 2.90 1.77 1.84 1.84 19 / 29 1.87 1.88 1.95 0.93 0.95 T = 1 T = 2 T = 3 T = 5 T = 7 T = 10 T = 20 T = 30

Calculating Modifjed Duration c Jun Pan Yield and Duration Financial Markets, Day 3, Class 1 c 20 / 29 n 2 × 100 ∑ 2 T 100 n + T × 2 × n =1 2 T ( 1+ y 2 ) 1 ( 1+ y 2 ) D mod = 1 + y 2 × 100 ∑ 2 T 100 n + 2 n =1 ( 1+ y 2 ) 2 T ( 1+ y 2 )

Bond Price, Yield, and Duration Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 21 / 29

Duration and Convexity Duration and convexity are meaningful only because we work in the Jun Pan Yield and Duration Financial Markets, Day 3, Class 1 Bonus from positive convexity, not ofgered by a security linear in y . The relation between price and yield is not linear, but convex: 22 / 29 yield space (for convenience), and the profjt/loss is in the dollar space. Duration is a bridge that connects the two: ▶ Dollar Duration: ∆ P t = P t − P t − 1 ≈ − D $ × ( y t − y t − 1 ) = − D $ × ∆ y t ▶ Modifjed Duration: R t = ∆ P t = P t − P t − 1 ≈ − D mod × ( y t − y t − 1 ) = − D mod × ∆ y t P t − 1 P t − 1 ▶ With decreasing y , duration increases: profjts amplifjed. ▶ With increasing y , duration decreases: losses dampened.

The Universe of Fixed Income Securities US treasuries: bills, notes, bonds. Treasury infmation protected securities (TIPS). Muni’s Agencies, government sponsored enterprises (GSE) Mortgage-backed Corporate bonds Emerging market bonds LIBOR and swaps Fixed income derivatives Credit derivatives Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 23 / 29

Key Risk Factors in Fixed Income Yield curve uncertainties: Credit risk (e.g., yield spread between US investment grade and US Treasury bond of similar maturity). Counterparty risk and other interesting spreads: LIBOR-OIS, swap spread, old bond and new bond spread, CDS-bond basis. Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 24 / 29 ▶ level of interest rates. ▶ the slope of the yield curve (long-term yield minus short-term yield). ▶ interest rate volatility (e.g., swaption implied vol).

Outstanding US Bond Market Debt in $ Billions Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 25 / 29

Issuance in the US Bond Markets (USD Billions) Financial Markets, Day 3, Class 1 Yield and Duration Jun Pan 26 / 29