Presentation is loading. Please wait.

Presentation is loading. Please wait.

V: Bonds 15: Duration. Chapter 15: Duration © Oltheten & Waspi 2012 Duration Concept Calculation Duration and Price Volatility.

Similar presentations


Presentation on theme: "V: Bonds 15: Duration. Chapter 15: Duration © Oltheten & Waspi 2012 Duration Concept Calculation Duration and Price Volatility."— Presentation transcript:

1 V: Bonds 15: Duration

2 Chapter 15: Duration © Oltheten & Waspi 2012 Duration Concept Calculation Duration and Price Volatility

3 Chapter 15: Duration © Oltheten & Waspi 2012 Fundamental Risk Reinvestment Risk: The risk that coupons, paid out of the bond, cannot be reinvested at the same YTM. Price Risk: The risk that the price of the bond will fall Note that this is a risk only if we sell the bond before it matures. There is no price risk if we hold the bond to maturity.

4 Chapter 15: Duration © Oltheten & Waspi 2012 Duration Duration: Weighted by Net Present Value average term to maturity. Duration can be calculated on any cash flow structure.

5 Chapter 15: Duration A Tale of Two Bonds $1000 5% Annual Coupon $50 Price: $ $1000 9% Annual Coupon $90 Price: $1, © Oltheten & Waspi 2012

6 Chapter 15: Duration A Tale of Two Bonds © Oltheten & Waspi 2012 Income Yield: 5.45% Income Yield: 8.32% Capital Gain 1.73% Capital Gain -1.56% Yield to Maturity: 7.00% 5 year capital gain = 8.93% Annual capital gain = 1.73% 5 year capital gain = % Annual capital gain = %

7 Chapter 15: Duration A Tale of Two Bonds $50 $1050$50$90 $1090$90 How much of my investment faces a reinvestment risk every year? © Oltheten & Waspi 2012

8 Chapter 15: Duration Calculating Duration I 5 year 5% Annual Coupon Bond at 7% TCash Flow NPVNPV/P 1 year$50$ % 2 years$50$ % 3 years$50$ % 4 years$50$ % 5 years$1050$ % Total NPV =$ % © Oltheten & Waspi 2012

9 Chapter 15: Duration © Oltheten & Waspi 2012 A Tale of Two Bonds How much of each bond must be reinvested after 1,2,3,4 and 5 years? © Oltheten & Waspi 2012

10 Chapter 15: Duration Calculation 5 year 5% Annual Coupon Bond at 7% TCash Flow NPVNPV/PDuration T*NPV/P Convexity D*(T+1) 1 year$50$ % years$50$ % years$50$ % years$50$ % years$1050$ % Total NPV =$ %4.523 yrs yrs 2 © Oltheten & Waspi 2012

11 Chapter 15: Duration A Tale of Two Bonds © Oltheten & Waspi 2012

12 Chapter 15: Duration © Oltheten & Waspi 2012 Duration & Price Risk Volatility: Change in the price of the bond due to a change in market yield.

13 Chapter 15: Duration Duration & Volatility 5% annual bond: yrs * 1% = 4.227% 1.07 Modified Duration is years If Yd 1% then P 4.227% 9% annual bond: yrs * 1% = 3.993% 1.07 Modified Duration is years If Yd 1% then P 3.993% © Oltheten & Waspi 2012

14 Chapter 15: Duration © Oltheten & Waspi 2012 Price Yield Curve

15 Chapter 15: Duration © Oltheten & Waspi 2012 Price Yield Curve 5 year 5% annual coupon 7% yield

16 Chapter 15: Duration © Oltheten & Waspi 2012 Price Yield Curve 20 year 6% semi-annual coupon 8% yield

17 Chapter 15: Duration © Oltheten & Waspi 2012 Calculating Duration II Calculate the duration and convexity of a semi-annual bond $10,000 6% coupon December 31, 2017 Settles March 2,

18 Chapter 15: Duration Calculating Duration II Base Price: 62/180 days Accrued Interest: Invoice Price: YTM: % $10, $ $10, © Oltheten & Waspi 2012

19 Chapter 15: Duration Calculating Duration II © Oltheten & Waspi 2012

20 Chapter 15: Duration © Oltheten & Waspi 2012 Exercise Calculate the duration and convexity of a semi-annual bond $1000 6% coupon 2.5 years to maturity Priced to yield 8%

21 Chapter 15: Duration Semi-Annual Bonds 1 1/2 year 6% Semi-Annual Coupon Bond at 8% TCash Flow NPVNPV/PDuration T*NPV/P Convexity D*(T+1) © Oltheten & Waspi 2012

22 Chapter 15: Duration © Oltheten & Waspi 2012 Volatility Duration: First derivative of the Price Yield Curve.D = dP/dY Slope of the Yield Curve Convexity: Second derivative of the Price Yield Curve.C = dP2/d2Y Curvature of the Yield Curve

23 Chapter 15: Duration © Oltheten & Waspi 2012 Volatility Taylor Expansion: Modified Duration Modified Convexity Yield at which duration was calculated

24 Chapter 15: Duration Volatility $1000 6% semi-annual coupon 2 ½ years to maturity Priced to Yield 8% Duration: yrs Modified D: =2.264 (1.04) Convexity:6.922 yrs 2 Modified C:6.922 = (1.04) 2 © Oltheten & Waspi 2012

25 Chapter 15: Duration Δ Yield +200 basis points Duration onlyConvexity Correction Total (+.02) (+.02) 2 = (1.04)2(1.04) 2 © Oltheten & Waspi 2012

26 Chapter 15: Duration Δ Yield -200 basis points Duration onlyConvexity Correction Total (-.02) (-.02) 2 = (1.04)2(1.04) 2 © Oltheten & Waspi 2012

27 Chapter 15: Duration © Oltheten & Waspi 2012 Price Yield Curve Convexity corrections are always positive Price effect is asymmetric

28 Chapter 15: Duration © Oltheten & Waspi 2012 Volatility Yields increase by 2% % % = % Yields decrease by 2% % % = % Convexity corrections are always positive Price effect is asymmetric

29 Chapter 15: Duration © Oltheten & Waspi 2012 Spreadsheet Exercise

30 Bonds IV © Oltheten & Waspi 2012


Download ppt "V: Bonds 15: Duration. Chapter 15: Duration © Oltheten & Waspi 2012 Duration Concept Calculation Duration and Price Volatility."

Similar presentations


Ads by Google