Bonds Part 3

1. Bond Prices and YieldsBond Prices and Yields
Part 3Part 3
Under redevelopmentUnder redevelopment

2. Reinvestment RiskReinvestment Risk
• Consider a $1000 bond with a coupon rate of 10% paid annually for 10 years.
Initially, the yield is 11%, the price is $941.11, and the yield curve is flat. Prior to
the payment of the next coupon, we consider three scenarios
1. the yield curve shifts parallel down to 9%
2. the yield curve remains flat at 11%
3. the yield curve shifts parallel up to 12%
What are the actual yields?
$1,000 F
10.00% c nominal Year CF DF DCF 9% 11% 12%
11.00% y nominal 1 100$ 0.9009 90.09$ 217.19$ 255.80$ 277.31$
2 100$ 0.8116 81.16$ 199.26$ 230.45$ 247.60$
3 100$ 0.7312 73.12$ 182.80$ 207.62$ 221.07$
4 100$ 0.6587 65.87$ 167.71$ 187.04$ 197.38$
5 100$ 0.5935 59.35$ 153.86$ 168.51$ 176.23$
6 100$ 0.5346 53.46$ 141.16$ 151.81$ 157.35$
7 100$ 0.4817 48.17$ 129.50$ 136.76$ 140.49$
8 100$ 0.4339 43.39$ 118.81$ 123.21$ 125.44$
9 100$ 0.3909 39.09$ 109.00$ 111.00$ 112.00$
10 1,100$ 0.3522 387.40$ 1,100.00$ 1,100.00$ 1,100.00$
Sum 941.11$ 2,519.29$ 2,672.20$ 2,754.87$
Yield To Maturity 10.35% 11.00% 11.34%
Bond Price Calculation Future Value of Coupon Reinvestment
2

3. Bond Price QuotesBond Price Quotes
• Dirty and clean prices
o Dirty price
• Price from DCF formula
• Transaction price
• When the seller sells at this price she gets the prorated
share (accumulated interest) of the next coupon
o Clean price
• Price quoted by bond dealer
• Excludes accumulated interest on next coupon payment
o Clean price = Dirty price – accumulated
interest
• Accumulated as simple interest using applicable day
count convention 3

4. Clean and Dirty Bond PricesClean and Dirty Bond Prices
Bond purchased just after its 8/15/2008 coupon Bond purchased 6/12/2009
From 8/15/08 to 8/15/09 is 365 days From 8/15/08 to 6/12/09 is 301 days or .825 yrs
From 6/12/09 to 8/15/09 is 64 days or .175 yrs
Payment
Date
t CF DF DCF
15-Aug-08 0 $0 1.000 $0.00
15-Aug-09 1 $5 0.962 $4.81
15-Aug-10 2 $5 0.925 $4.62
15-Aug-11 3 $5 0.889 $4.44
15-Aug-12 4 $5 0.855 $4.27
15-Aug-13 5 $5 0.822 $4.11
15-Aug-14 6 $105 0.790 $82.98
Sum $130.00 P $105.24
Payment
Date
t CF DF DCF
12-Jun-09 0 $0 1.000 $0.00
15-Aug-09 0.175 $5 0.993 $4.97
15-Aug-10 1.175 $5 0.955 $4.77
15-Aug-11 2.175 $5 0.918 $4.59
15-Aug-12 3.175 $5 0.883 $4.41
15-Aug-13 4.175 $5 0.849 $4.24
15-Aug-14 5.175 $105 0.816 $85.71
Sum $130.00 P $108.70
F=$100, c=5%, y=4%, m=1
4

5. Closed Form FormulasClosed Form Formulas
.825 .175
last coupon next coupon
e=64 days d = 365 days
e/d=.175
8/15/08 8/15/09 8/15/10 8/15/11 8/15/12 8/15/13 8/15/14
6/12/09
F=$100
y=4% annual
c=5% annual
y & c are effective & nominal
Clean and Dirty Price example (p. 7.10) using closed form
$100
$101
$102
$103
$104
$105
$106
$107
$108
$109
$110
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Time
Price
5
70.108$
)%4(1
1
)%4(1
$100
)%44%(1
1
4%
1
15$P
365
6455
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6. $100
$101
$102
$103
$104
$105
$106
$107
$108
$109
$110
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Time
Price
Dirty and Clean PricesDirty and Clean Prices
15
Aug
2008
Clean price @ 6/12/09 = Dirty price – accumulated interest
= $108.70 – $5 · 301 / 365
= $108.70 - $4.12 = $104.58
15
Aug
2009
6
12 June 2009

7. Bond Price QuotesBond Price Quotes
• Bid and ask prices
o The clean price is quoted for bid and ask prices
• The dealer will buy a bond at the bid price
• The dealer will sell a bond at the ask (offer) price
• Bond prices are quoted relative to 100
regardless of actual par value
o Price is quoted as a percent of par
• Example
7