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Interest Rate Risk Management and Tax-Loss Harvesting of Municipal Bonds
Seattle, Washington
May 3, 2013
2
Genesis of After-Tax Analysis of Munis
AKA provides debt management advisory services Municipal clients include the Commonwealth of Massachusetts and
the City of Chicago
Corporations consider taxes in debt management decisions In the early ‘90’s AKA developed after-tax valuation framework
Perspective differs from issuer to investor
Municipal bond issuers don’t pay taxes, however investors do Interest is tax-exempt, but gains and losses are taxable
Challenge: incorporate tax treatment into contemporary bond
valuation model
3
Key Concepts for Tax-Exempt Munis
Capital gains and losses are taxable Details follow
Investors are in the highest tax bracket Taxes on tax-exempt bonds, Journal of Finance, 2010
Arbitrage-free bond valuation in use since the mid-’80’s ‘Option Adjusted Spread’
AKA’s MuniOAS™ incorporates tax treatment Applicable to interest rate risk management and to pricing
OAS framework amenable to analyze tax-loss harvesting Determine optimum strategy
Applicable to asset management
4
Bird’s Eye View of MuniOAS™
OAS-based valuation of tax-exempt bonds Thorough tax treatment
Patent pending
Built on BondOAS™ Widely used, extensively tested over 20 years
2 million callable bonds per minute (Intel Core i7-2600-3.4 Ghz)
Click on Speed or Accuracy demos at bottom of kalotay.com
5
Tax Treatment of Tax-exempt Bonds Held to Maturity – Simple Version
* Marginal tax rate implied by EMMA prices is ‘very high’
** 0.25 x the number of remaining years to maturity (e.g. 2.50 for a 10-year bond)
Purchase Price Treatment Tax Rate*
At a premium Premium amortized to zero N/A
At a de minimis**
discount
Taxed as capital gain 20%
At a non-de minimis
discount
Taxed as ordinary income 40%
6
Historical Muni Yields
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
1991 1996 2001 2006 2011
Yie
ld (
%)
Bloomberg GO 20yr AAA
Bloomberg GO 10yr AAA
7
Key Concept: Tax-Neutral Value*
Defined as the price that equals the PV of after-tax cashflows
under ‘buy-and-hold’ (Hold To Maturity) PV of tax on gain depends on purchase price and discount rate
Determined by iterating price until PV and price converge Lattice needed for callable bonds
Yield curve is a required input Either issuer-specific, or benchmark shifted by tax-neutral OAS
Tax-neutral OAS can be calculated from market price
* The after-tax ‘fair price’
8
Assumptions for Following Exhibits Unless Stated Otherwise
Tax Rates
Income 40%
Short-term capital gains/losses 40%
Long-term capital gains/losses 20%
Issuer Par Optionless Yield Curve
Mty (yrs) 1 2 5 10 20 30
Rate (%) 1.0 1.5 2.0 3.0 4.0 4.5
Interest Rate Volatility
20%
Transaction Cost
0.50% par
9
Price Response to Rising Rates More Pronounced Than Expected
Single-A
Par Bonds
Rates Rise 100bps
Other Systems MuniOAS™
Price Yield Price Yield Δ Yield (bps)
2-yr 0.90% 98.05 1.90 96.82 2.54 64
5-yr 1.65% 95.35 2.65 92.84 3.21 56
10-yr 3.00% 91.87 3.99 88.94 4.38 39
Relevant tax rate: Income 40%
10
Pre-Tax Fair Price of 10NCL
93
94
95
96
97
98
99
100
101
2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10
Valu
e (
% P
ar)
Coupon (%)
Pre-Tax
11
Taxes Depress Prices of Discounts 10NCL Based on Buy-and-Hold
93
94
95
96
97
98
99
100
101
2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10
Valu
e (
% P
ar)
Coupon (%)
Pre-Tax
Tax-Neutral Buy-and-Hold
MuniOAS™ can smooth
out discontinuity
12
Duration of 10-Year NCL Bonds
8
9
10
11
12
13
2.0 2.2 2.4 2.6 2.8 3.0 3.2
Du
rati
on
(yrs
)
Coupon (%)
13
Takeaways
When rates rise, prices of discount munis will decline more than
predicted by standard systems Reported performance, based on mark-to-market, could suffer unduly
Investing in premium bonds mitigates adverse effect of higher rates 5% coupon is the norm for institutional deals
Market price less likely to decline below par
14
Tax Loss Harvesting: Overview
Compare after-tax proceeds from sale to HTM value Both depend on investor-specific purchase price and date
Reinvestment strategy may be relevant
Need yield curve and tax rates to determine: HTM value
PV of remaining after-tax flows
Future ‘market prices’ in different states of the world Tax-neutral values
After-tax OAS framework provides sell signal
83
84
85
86
87
88
89
90
91
92
93
80 85 90 95 100 105 110 115 120
% P
ar
Purchase Price 5 Years Ago (% par)
Sale Price
A/T Proceeds
15
Tax Loss Harvesting 2% Bond, 10 Years to Maturity
Current 10y rate 3%
Sale price reduced by
0.5% transaction cost
83
84
85
86
87
88
89
90
91
92
93
80 85 90 95 100 105 110 115 120
% P
ar
Purchase Price 5 Years Ago (% par)
Sale Price
A/T Proceeds
HTM Value
16
Tax Loss Harvesting 2% Bond, 10 Years to Maturity
Current 10y rate 3%
Sale price reduced by
0.5% transaction cost
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
80 85 90 95 100 105 110 115 120
% P
ar
Purchase Price 2 Years Ago (% par)
Net Benefit from Sale
17
Tax Loss Harvesting 2% Bond, 10 Years to Maturity
Current 10y rate 3%
Sale price reduced by
0.5% transaction cost
18
When to Sell?
Calculate benefit from sale over HTM As illustrated above
Positive outcome not sufficient reason to sell More favorable opportunities may arise in the future
Need to value of ‘tax option’ Depends on interest rate volatility and transaction cost
Reinvestment strategy is also relevant ‘Like’ bond eliminates future rate risk
Can acquire a new tax option, if desired
19
Sell Efficiency Calculator
Compares net benefit from sale to forfeited option value Similar to Refunding Efficiency Calculator for callable bonds
Nested options require ‘generalized efficiency’ approach
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =𝐴𝑓𝑡𝑒𝑟-𝑡𝑎𝑥 𝐵𝑒𝑛𝑒𝑓𝑖𝑡 𝑜𝑓 𝑆𝑎𝑙𝑒
∆𝑇𝑎𝑥 𝑂𝑝𝑡𝑖𝑜𝑛 𝑉𝑎𝑙𝑢𝑒
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
95 97 99 101 103 105 107 109
% P
ar
Purchase Price 2 Years Ago (% par)
Sell-HTM
20
Net Benefit From Sale
2.5% coupon
20 years left to maturity
Current 20y rate 4%
Sale price 73.30
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
95 97 99 101 103 105 107 109
% P
ar
Purchase Price 2 Years Ago (% par)
Option Value
Sell-HTM
21
Net Benefit From Sale vs. Value of Tax Option
2.5% coupon
20 years left to maturity
Current 20y rate 4%
Volatility 20%
Sale price 73.30
-20
0
20
40
60
80
100
120
95 97 99 101 103 105 107 109
Eff
icie
ncy
(%)
Purchase Price 5 Year Ago (% par)
22
Sell Only Near 100% Efficiency
2.5% coupon
20 years left to maturity
Current 20y rate 4%
Volatility 20%
Sale price 73.30
23
Value of Embedded Tax Option
The tax option is a ‘real’ option Active managers can optimally exercising it
Let’s monitor bond from cradle to grave, as it migrates among active
managers Each manager optimally exercises option
How much tax benefit can be extracted from the bond over its
lifetime?
24
Embedded Tax Option in 3% 10NCL
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 5 10 15 20 25 30 35 40 45
Val
ue
of
Tax
Op
tio
n (
% P
ar)
Interest Rate Volatility (%)
Zero Transaction Cost
TC = 0.5
TC = 1.0
25
Embedded Tax Option in 30-Year 4.25% NC10
0
2
4
6
8
10
12
14
0 5 10 15 20 25 30 35 40 45
Val
ue
of
Tax
Op
tio
n (
% P
ar)
Interest Rate Volatility (%)
Zero Transaction Cost
TC = 0.5
TC = 1.0
26
Short-term Capital Loss
Short-term capital gains rate is currently 40% Applicable within the first year of purchase
Active managers can enhance performance by trading tax options Value of new tax option may compensate for otherwise
uneconomical trade
Assumes off-setting short-term gain
Conservative assumption: losses are deductible at long term rate
Eliminates trades driven purely by tax-option
27
Effect of Short-Term Capital Gains Rate 30-Year 4.25% Non-Call 10
0
2
4
6
8
10
12
0 5 10 15 20 25 30 35 40 45
Val
ue
of
Tax
Op
tio
n (
% P
ar)
Interest Rate Volatility (%)
Short-Term Gain Rate 40
Short-Term Gain Rate 20
28
Tax-Loss Harvesting: Summary
Can significantly enhance after-tax return over buy-and-hold By as much as 25 bps annually
Short-term losses can be particularly valuable Current applicable rate is 40%
Optimum sell decision requires sophisticated option-based
analysis Depends on interest rate volatility and transaction cost
29
References
“The Interest Rate Sensitivity of Tax-Exempt Bonds under Tax-neutral
Valuation” – Working paper
“The Tax Option in Municipal Bonds” – Working paper
“Managing the Tax Option in Municipal Bonds” – Working paper
"Taxes on Tax-Exempt Bonds“, A. Ang, V. Bhansali, Y. Xing. Journal of
Finance, Vol. 65, No. 2 (2010)
“What Makes the Municipal Yield Curve Rise”, A. Kalotay,
M. Dorigan, Journal of Fixed Income (Winter 2008)
Bond Buyer:
“The Allure of 5% Bonds: Coupon Levitation Creates Magical
Savings” – January 27, 2012
“For Investors, Stress-Testing Munis Is Easier Said Than Done”
– March 18, 2013
