(Thinking About) Hedging Municipal Portfolios

with DerivativesCadmus Hicks

February 20, 2003

2003 by Nuveen Investments

Why is duration so long?

Municipal Yield Curve

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Maturity

Why is duration so long?

Municipal Yield Curve

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 18.00

Duration

The Challenge

• To reduce the price volatility of a fund to match that of a benchmark.

Moving Target, Moving Train

Parallel Shift: Durations of Fund vs. Benchmark

5

6

7

8

9

10

11

12

125i

100i 75

i

50i

25i

Baseli

ne -25i

-50i

-75i

-100i

-125i

paralle l s hift yie ld s ce nario

dura

tion

Benchmark Fund

Moving Target, Moving Train

D ifference in D urations of Fund - B enchmark

0.4

0.9

1.4

1.9

2.4

2.9

3.4

3.9

4.4

125i

100i 75

i

50i

25i

Baseli

ne -25i

-50i

-75i

-100i

-125i

paralle l s hift yie ld s ce nar io

dura

tion

diffe

renc

e

The Bond Buyer 40

TV = Theoretical value of the contract

I = Index valueSMR= Short-term municipal rateLMR = Long-term municipal rateDR = Days remaining until expirationCGTR= Capital gains tax rate

The Bond Buyer 40

CGTR

DRLMRSMRIITV

−

−+=

1360

)(

The Bond Buyer 40

Advantages:In use for many years.No counterparty risk.

Disadvantages:Low trading volume, low liquidity.Underlying Index subject to manipulation.

MMD Rate Locks

• Maturity: 2023 Yield:4.65%

• Value of 1 bp per $1 million: $1,289

• 5 bp spread x DV01/$1MM: $6,443

• Effect of spread on return: 64 bp

• Annualized effect: 258 bp.

MMD Rate Locks

Assume:

Portfolio = $100MM

Average Life = 15 Years

Average Duration = 11 years

DV01 = $110,000

MMD Rate Locks

Assume Target:

Average Life = 10 Years

Average Duration = 8.25 years

DV01/$MM = $825

Target DV01 of Portfolio = $82,500

MMD Rate Locks

Actual DV01 = $110,000

Target DV01 = $ 82,500

Hedge Need =$ 27,500

DV01/$MM of 10 year MMD = $825

$27,500 / $825 = 33 contracts

MMD Rate Locks

Hedge Need =$ 27,500

DV01/$MM of 15 year MMD = $1,100

$27,500 / $1,100 = 25 contracts

DV01/$MM of 20 year MMD = $1,300

$27,500 / $1,300 = 21 contracts

Moving Target, Moving Train

Parallel Shift: Durations of Fund vs. Benchmark

5

6

7

8

9

10

11

12

125i

100i 75

i

50i

25i

Baseli

ne -25i

-50i

-75i

-100i

-125i

paralle l s hift yie ld s ce nario

dura

tion

Benchmark Fund

MMD Rate Locks

Advantages:Can take position on specific maturity.Simple to track value.

Disadvantages:Counterparty risk.Large bid/ask spread.

BMA Swaps

Advantages:Can take position on specific maturity.Bid/Ask spread of 3 basis points.

Disadvantages:Counterparty risk.Negative carry lowers tax-exempt income.Less liquid than LIBOR swaps.

Forward Starting BMA Swaps

R1 = 1-year BMA rate = 1.26%R20 = 20-year BMA rate = 4.20%F19 = Rate on 19-year swap that starts in

1 year.

(To simplify, illustration assumes annual compounding.)

Forward Starting BMA Swaps

To simplify, illustration assumes annual compounding

2020

1919

11 )1()1(*)1( RFR +=++

201919

1 042.1)1(*0126.1 =+ F

Forward Starting BMA Swaps

=+

0126.1277.2)1( 19

19F

191

19 0126.1277.2)1(

=+ F

Forward Starting BMA Swaps

0435.1)1( 19 =+ F

%35.419 =F

Forward Starting BMA Swaps

Advantages:Can take position on specific maturity.Capital gains/losses do not affect income.

Disadvantages:Counterparty risk.Less liquid than LIBOR swaps.Forward start costs more.

(Thinking About) Hedging Municipal Portfolios

with DerivativesCadmus Hicks

February 20, 2003

2003 by Nuveen Investments