Lecture205

# Lecture205 - Lecture 5 Valuation of Debt Contracts and...

This preview shows pages 1–3. Sign up to view the full content.

Lecture 5 Valuation of Debt Contracts and Their Price Volatility Characteristics Continued. I. Valuation continued. A) Recall the formula for modified duration: MD =(P -1 )*[(1+y) -1 ]*{[a 1 /(1+y)] + [2a 2 /(1+y) 2 ] + [3a 3 /(1+y) 3 ] +…+ [T(M+ a T )/(1+y) T ]}. Where y is the yield to maturity measured at the same frequency as the coupon payments. Thus, if a 1, a 2, a 3, …, a T are paid at a semi-annual frequency y = semi-annual yield. Likewise, if a 1, a 2, a 3, …, a T are paid at a monthly frequency y = monthly yield. Generally we quote bonds in terms of their annual yield. Therefore, we need a method to transform y at any frequency into an annual yield. Let y (1/n) denote the (1/n)-annual yield. Then y annual = (1+ y (1/n) ) n –1. Example: Suppose we have a bond with a \$1000 face value that matures in 10 years. This bond pays a semi-annual 7% coupon (\$35) 6-months from now and every 6-months thereafter until the maturity date. This bond’s current price is \$1050. The semi-annual yield can be found by solving our present value equation for y: P= [a 1 /(1+y)] + [a 2 /(1+y) 2 ] + [a 3 /(1+y) 3 ] +…+ [(M+ a T )/(1+y) T ] 1050 = [35/(1+y)] + [35/(1+y) 2 ] + [35/(1+y) 3 ] +…+ [(1000+ 35)/(1+y) 20 ] y = .03159 or a 3.159% semi-annual yield solves this equation. To convert this to an annual yield note that n = 2 and plug y (1/n) = .03159 into y annual = (1+ y (1/n) ) n –1 to find y annual . y annual = (1+ .03159) 2 –1 = .064178 or 6.4178% annual yield

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
II. Duration and Convexity Again consider a bond with a \$1000 face value that matures in 10 years. This bond pays a semi-annual 7% coupon (\$35) 6-months from now and every 6-months thereafter until the maturity date. The bond’s current price is \$1050. The semi-annual yield y = .03159 and y annual = (1+ .03159) 2 –1 = .064178. Definition: Basis Point: 1/100 th of an annual yield percentage point. Example: The bond with a 6.4178% yield is said to have a yield of 641.78 basis points. A) The bond’s price is \$1050 and its yield is 641.78 basis points. Suppose you hold a number of these bonds. Their yield is a
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/12/2008 for the course ECON 435 taught by Professor Chabot during the Winter '08 term at University of Michigan.

### Page1 / 6

Lecture205 - Lecture 5 Valuation of Debt Contracts and...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online