Finance Review
Autor: Jannisthomas • March 3, 2018 • 2,030 Words (9 Pages) • 525 Views
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• EAY = (1+r )2 –1 = (1+YTM /2 )2 –1 = 12.44%
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Link between week 2 and week 8
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Same concepts, but once from perspective of borrower (week 2) and once from perspective of lender (week 8)
- APR corresponds to YTM (calculated as IRR)
- EAY corresponds to EAR
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Realized Return vs. YTM
- Suppose that you buy a bond.
- Will the return on your investment be equal to the YTM ?
- Realized return = YTM if and only if :
- you hold the bond until maturity, and
- you can re-invest the coupons at a rate equal to YTM
- In most cases it will be different because :
- you must re-invest the coupons at a different rate, or
- you sell the bond before maturity at a price that corresponds to a different yield-to-maturity. (Market yields can change.)
- Lesson: Bonds are risky!
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YTM of ZCB
3.5[pic 22]
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Markets: Current Yield Curve
11/6/2015
3[pic 23]
2.5
2
1.5
1
0.5
0
1 Mo 3 Mo 6 Mo 1 Yr 2 Yr 3 Yr 5 Yr 7 Yr 10 Yr 20 Yr 30 Yr
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Engineering Forward Rates
- A bank has 2 ways of bringing money from today to 2 years from now.
- Case 1: Buying 2-year zero coupon bond
- Case 2: Buying a 1-year zero coupon bond, and re-investing at the forward rate
- yt(n) = YTM for a zero coupon bond with n-period maturity
- Bank has to be indifferent between the two ways (no arbitrage)
Case 1:
Case 2:
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Invest in 2-year ZCB
[pic 24]
t=0 t=1 t=2[pic 25]
[pic 26]
Invest in 1-year ZCB Invest 1-year at forward rate
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Case 1:
Case 2:
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Invest in 2-year ZCB
[pic 27]
t=0 t=1 t=2[pic 28]
[pic 29]
Invest in 1-year ZCB Invest 1-year at forward rate
(1+[pic 30]
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y (2))2
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= (1+
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yt (1))(1+
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ft (1))
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Forward rate = interest rate that would need to prevail in second year to make the long- and short-term investments equally attractive.
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Forward Rates
f (n) =
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(1+
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yt (n +1))
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n+1
−1[pic 31]
t (1+ y (n))n[pic 32]
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The forward rate is determined by no-arbitrage.
- NB: To calculate the 20 year forward rate, you need information on the 21-year zero coupon bond, and the 20-year zero coupon bond.
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Shape of Yield Curve
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