and Rich-Cheap Relative Value
Trading
Copyright 1996-2006
Investment Analytics
1
Rich/Cheap Analysis &
Relative Value Trading
Principles of rich/cheap analysis
Relative value concepts
Total return analysis
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 2
Rich-Cheap Analysis
Select the appropriate tax-rate
Identify the tax-efficient bonds
Estimate the spot tax-yield curve using the
efficient bonds
Identify the issues which are low yield
(rich) or high yield (cheap) relative to
the curve
Initiate duration-weighted trade
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 3
Rich-Cheap Graphical Analysis
Yield
Cheap
Issue
Rich
Issues
Maturity
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Slide: 4
Problems with Simple
Approach
Coupon
Issues with different coupons trade at different
yields
Risk-Return
Maturity is an inexact measure of risk
Yield is an inexact measure of return
Liquidity
On-the-run vs off-the-run
Issues on repo special
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 5
Example: Rich/Cheap Analysis
Lab
Simple Example: Worksheet-Rich Cheap Analysis
Work out spot rates
Two 2-year notes:
71/2% trading at par, 15% trading at 113.69
Market Yield
Calculate YTM on both bonds, given market prices
Theoretical Price/Yield
Calculate theoretical price & yield on each note
Conclusion:
What is the relationship between coupon and yield?
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 6
Solution: Rich/Cheap Analysis Lab
7.5% 2-year Note:
Market
Price
Yield
100
7.5%
15% 2-year Note:
Market
Price
Yield
113.69 7.5%
Theoretical
Price
Yield
100.09
7.45%
Theoretical
Price
Yield
113.87
7.41%
Both issues are cheap, high coupon > low coupon
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 7
Impact of Coupon on Bond
Value
YTM calculation
Makes simplifying assumption of constant
reinvestment rate
With rising spot rates:
Low coupon bonds must trade at higher
yields than high coupon bonds to
compensate
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 8
Iso-Coupon Curves
Implication
To judge richness or cheapness of an issue
must take account of coupon
Coupon adjusted yield
Iso-Coupon Yield Curves
Group bonds by coupon
Plot YTM vs Maturity (duration)
Assess value vs appropriate curve
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 9
Iso-Coupon Curves - Example
0%
5%
10%
15%
Yie ld
7%
6%
5%
0
5
10
15
Ma turi ty
20
25
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
30
Slide: 10
Bond Stripping & Repackaging
Trading based on a variant of rich-cheap analysis
Replicate the cash flows of inefficient bonds using
the efficient bonds
Stripping:
Buy cheap bond & sell off the cash flows (as ZCBs)
Repackaging:
Sell rich bond & hedge with replicating cash flows from
efficient bonds
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 11
Relative Value Concepts
Yield curve as a measure of risk-return tradeoff
Maturity as a proxy for risk
Look at yield pickup on extension to identify value
Example
Se ttl e m e nt
Ma turity
15-Feb-15
15-Aug-15
15-Nov-15
15-Feb-16
15-May -16
15-Nov-16
15-May -17
2-Ma y-95
Coupon
11 1/4
10 5/8
9 7/8
9 1/4
7 1/4
7 1/2
8 3/4
Cle a n
Price
139 10/32
133 4/32
125 13/32
118 27/32
97 29/32
100 18/32
113 23/32
Acrrue d
Inte re st
2.3619
2.2307
4.5829
1.9420
3.3646
3.4807
4.0608
Dirty
Price
141.6744
135.3557
129.9891
120.7857
101.2709
104.0432
117.7795
YTM
7.4255%
7.4351%
7.4412%
7.4514%
7.4482%
7.4467%
7.4706%
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Yie l d
Modifie d
Pi ckup (bp) Dura tion
9.3628
0. 96
9.5637
0. 61
9.5491
1. 02
9.9062
-0.32
10.2487
-0.14
10.2782
2. 38
10.0543
Slide: 12
Yield vs. Maturity
YIELD vs. MATURITY
7.48%
15-May -17
7.47%
7.46%
15- Feb- 16
15- May -16
15-Nov - 15
15-A ug- 15
7.45%
7.44%
7.43%
15-Nov -16
15-Feb-15
7.42%
7.41%
7.40%
Dec-14
Jul-15
Jan-16
Aug-16
Mar-17
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Sep-17
Slide: 13
Yield Curve Analysis
Fairly normal yield curve
Yield on the 9 1/4 of Feb 16 looks to be a basis point
too high
2.4bp pickup on the 8 /4% of May 17 indicates value
in this sector
Clear relationship between yield and tenor
What about relationship between yield and risk?
Use duration as a proxy for risk
Plot yield vs. duration
Makes relative values more distinct
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 14
Yield vs. Duration
YI ELD vs. DURATION
7. 48%
7. 47%
7. 47%
7. 46%
7. 46%
7. 45%
7. 45%
7. 44%
7. 44%
7. 43%
7. 43%
7. 42%
9. 20
May 17
Feb 16
May 16
Nov 16
Nov 15
Aug 15
Feb 15
9. 40
9. 60
9.80
10.00
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
10.20
10. 40
Slide: 15
Yield Enhancement Swap
Because it has higher coupon, the 8 3/4 of May
17 has lower duration than the 7 1/4 of May 16
or the 7 1/2 or Nov 16.
By trading at slightly higher yield, the market
would appear to be underpricing it slightly
Bond Swap:
Action Maturity
Coupon
Price YTM
Sell
15-Nov-16 7 1/2% 100 18/32
Buy
15-May-17
8 3/4% 11323/32
Duration
7.4467% 10.278
7.4706% 10.054
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 16
Limitations to Traditional
Yield Curve Analysis
Yield curve:
A primitive expression of risk/return tradeoff
Drawbacks
Maturity is poor indicator of bond price volatility
YTM is not a measure of potential return
For Buy and Hold investor, assumes coupons are
reinvested at YTM
For Active investor, assumes that if bond is sold
prior to maturity, it is sold at same yield as on
purchase date
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 17
Total Return
Holding Period Return (HPR)
Measures bonds total return over given period
HPR is a time-weighted average return
HPR = ending market value + income receipts -1
beginning market value
Copyright 1996-2006 Investment Analytics Rich-Cheap Relative and Value Trading
Slide: 18
HPR Example
7%, 30Yr T-Bond, priced at par to yield 7%
1-year HPR:
[($1000 + $35 + $35 + $1.23*) / $1000] -1 =
HPR = 7.12%
* $35 x 0.07 x 0.5 = $1.23
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 19
HPR Example
7%, 30yr T-Bond, priced at par to yield 7%
1 Year HPR:
Falling
Rates
6%
HPR
20.78%
Constant
Rates
7%
7.12%
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Rising
Rates
8%
-4.08%
Slide: 20
Components of Total Return
Price return
(ending bond price - beginning bond price)
Excluding accrued interest
Coupon return
Coupon receipts +/- accrued interest
Reinvestment return
Interest earned on reinvested coupons
Total Return = Price Return + Coupon Return
+ Reinvestment Return
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 21
Components of Total Return
100%
80%
60%
40%
Pric e
Coupon
20%
Reinvestment
0%
Short Term
Medium
Term
Long Term
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 22
Realized Compound Yield
Pr ice =
FV
T
RCY
(1+
)
2
RCY is a dollar-weighted average return
FV is the future value of the bond
investment over the holding period
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 23
Reinvestment Rate and
Realized Compound Yield
Return on 30-Year 10% Coupon Bond
RR
RCY
Realiz ed Compound Yield
20%
15%
YTM
10%
5%
0%
0%
5%
10%
15%
20%
Reinvestment Rate
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 24
Characteristics of Total Return
Effect of reinvestment rate on total
return
Low vs. high coupon bonds
Short vs. long maturity issues
Holding period < maturity
Lab: Total Return Analysis
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 25
Total Return vs. Coupon
Total Return
10%
6%
0%
Reinvestment Rate
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Slide: 26
Total Return vs. Horizon
Total Return
10 year
6.23 Year
5 Year
Reinvestment Rate
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Slide: 27
Characteristics of Total Return
- Summary
Coupon
RR has greater effect for higher coupon issues
No effect for ZCBs
Holding period
For long holding periods
Total return rises with RR
Reinvestment of coupon cash flows dominates return
For short holding periods
Total return falls with RR
Bond price at horizon dominates return
Greater RR implies lower price, hence return falls
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 28
Immunized Portfolios and
Total Return
Portfolio with Horizon = Duration
Coupon reinvestment effect balances pricediscount effect
Total return is approximately the same
regardless of reinvestment rate
Central concept of portfolio management
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 29
Breakeven Reinvestment Rate
RR at which TR on two bonds is the same
over given horizon
Used to decide which of two bonds is more
attractive
For some bonds, may not be a breakeven RR
One bond totally dominates the other
Total return is always greater
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 30
Breakeven RR - Example
Total Return
Total Return
15%
13%
11%
10 year, 5% coupon priced at $94
Breakeven RR
9%
10 year, 10% coupon priced at $113
7%
5%
0%
5%
10%
15%
20%
Reinvestment Rate
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 31
The Total Return Curve
Project returns for a given holding period
Plot HPR against duration
Return vs. Risk
Assumptions
Interest rates
Sector spreads (quality, maturity, coupon, issuer)
Reinvestment rate
Baseline Total Return Curve
1 Year horizon, yield curve shape unchanged
All reinvestments made in the middle of the curve
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 32
Total Return Curve Example
Yield an d Baseline T otal Return Curv es
8.0%
Yield
7.5%
YTM
7.0%
HP R
6.5%
6.0%
0
2
4
6
8
10
12
14
Duratio n
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 33
YTM vs. HPR Pickup
Difference due to yield curve roll factor
As bond ages, it rolls down to new, lower
yield
Also, moves from on-the-run to off-the-run
Long duration bonds are especially
sensitive to roll factors:
% change in price: (P/P) = -D* x Y
D* is modified duration
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 34
Yield and Total Return Pickup
Ma turi ty Dura ti on
2
1.91
3
2. 56
4
3. 49
5
4.23
7
5.6
10
7. 07
30
12.12
YTM
6.29%
6. 42%
6. 62%
6.68%
6. 98%
7. 16%
7. 47%
30-year sector preferred on
YTM basis
YTM
Pickup on
Ex te nsion
13
20
6
30
18
31
1-Year
HPR
6. 72%
6. 81%
7. 10%
6.91%
7. 48%
6. 96%
6. 67%
Tota l Re turn
Pickup on
Ex te nsi on
9
29
-19
57
-52
-29
7-year sector preferred on
HPR basis
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 35
On-the-Run vs. Off-the-Run
HPRs
HPR f o r On-the-Run vs. Of f -the-Run Treasuries
9.0%
8.5%
HPR
8.0%
Off-the-run
7.5%
7.0%
On-the-run
6.5%
6.0%
0
2
4
6
8
10
12
14
Duration
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 36
Relative Value & Risk-Return
Tradeoff
Market does not seem to appraise risk in a
consistent fashion
Attractive issues:
Off the run issues with 4-5 years and 8-9 years in
duration
6-yr, 8-yr, 15-yr maturities
Overvalued sectors:
All the current coupon issues
5-yr, 7-yr and 29-yr off-the-runs
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 37
Factors Affecting Relative
Value Trading in Practice
Coupon
Low coupon issues trade at higher yields to give fair
value (with an upward sloping yield curve)
Tax effects
Liquidity
On-the-run vs. off-the run treasuries
Issues on special in repo market
Call provisions (& other option features)
Transaction costs, shorting restrictions
Copyright 1996-2006 Investment Analytics Rich-Cheap and Relative Value Trading
Slide: 38