1

Structure
 Are economic (growth) models useful in setting public discount rates?
 A simple market calibration exercise
 Risk premium information from the stock market
 Summing up
2

Are economic (growth) models useful in setting public discount rates?
 Of course, but with a minimum of market calibration
 But, the models have not been very useful in explaining
(or predicting) the financial markets
Discount rate = Risk free rate (real) + Risk Premium
 Risk Free rate puzzle: too high
 Equity premium puzzle: too low
 Too much degree of freedom in more elaborate models,
 or too complex and unstable for practical use
3

Structure
 Are economic (growth) models useful in setting public discount rates?
 A simple market calibration exercise
 Few long instruments with «risk free» real return matching except for the UK 50-year indexed Giltmarket (excess demand)
 Will instead use the US 100-year corporate bond market
4

100 Year Bonds - Yields 2001 - 2012
Walt Disney 2093 vs 2032
US Treasury 2030
Coca Cola 2098 vs 2036
US Treasury 2030
5

100 Year Bonds – Yield spreads 2001 - 2012
2093 - 2032
WD 2032 vs
Treasury 2030
2098 - 2036
CC 2036 vs

100 Year Bonds – Forward Yields

(TL

RL - TS

RS) / (TL-TS)
WD93 = WD32 +
Fwd purch. WD93 in 2032
CC98 = CC36 +
Fwd purch. CC96 in 2036
7

Uncertain future price and yield (in 2032-36) -
Convexity adjusted forward yield
 Price long bond = Price short bond + E[Future Price]
 Determine forward yield from expected future price
Dybvig, et. Al. (JB 1996;
Weitzman JEEM 1998)
8

100 Year Bonds – Stable 3.2 % Forward Yields
R93

[T32

R32 +
(T93-T32)

3.2% ]/T93
R98

[T36

R36 +
(T98-T36)

3.2% ]/T98
9

Structure
 Are economic (growth) models useful in setting public discount rates?
 A simple market calibration exercise
 Risk premium information from the stock market
10

Two days in the life of Oslo Stock Exhange …..
30. sep. 2008: Down 8.5 %

SELL !!
1. oktober 2008: Up 5.5 %

BUY !!

The stock market is driven by expectations and risk
 Stocks give a w return when investors demand more
(and a higher return when they expect less)
 Stock market and economic growth uncorrelated, across markets and over time (Dimson, Marsh & Staunton)
 (but the stock market is a good predictor for future growth)
 High correlation between long-run stock and bond returns, while short-run returns are negatively correlated
Discount rate = Risk free rate (real) + Risk Premium
12

Pricing of OSE Large Caps Nov vs Aug 2008
OSE Large Caps 04.08.08 vs ROE-estimate for 2008
6
REC
5
4
3
2
1
2,5
2,0
0
0,0
Seadrill
Aker Solutions
Statoil
Yara
Frontline
(7,8 / 13,3)
Hydro
Orkla
Stb
RCL
T hon
DnB Nor
Avg LC ( 2,0 )
T elenor
Krav 11,9% = 4,9% + 1,5
Corr = 0.81
1,0 2,0 3,0
Static P/B (R08* / 11.9%)
4,0
OSE Large Caps 03.11.08 vs ROE-estimate for 2009
Frontline
(3,3 / 0,9)
REC
Statoil
· 4,5%
5,0
Aug 08 : RF 5.0 %
MP 4.5 %

Cost 12 %
1,5
1,0
0,5
0,0
0,0
Seadrill
Avg LC ( 1,2 )
Aker Solutions
Yara
T hon Orkla
Hydro
RCL
Norske Skog
Stb
DnB Nor
T elenor
0,5 1,0 1,5
Static P/B (R09* / 14.5%)
Krav 14,5% = 3,8% + 1,5 · 7%
Corr = 0.40
2,0 2,5
Nov 08 : RF 3.8 %
MP 7 %

Cost 14.5%

Cyclical risk premiums US
2,2
5,3 4,8
2,4
(snitt premie 1,1 %)
-2,2
14

Equity, gov. bonds and GNP-growth Norway / US (deflated, log)
1900 - 2010
NORWAY: 0.60

Equity + 0.40

Bonds = 3.2 %

GNP-growth > 1980
8 %
2.6 %
6,5 %
-GNP: 2.4 %
-Real rate:3.8%
US: 0.60

Equity + 0.40

Bonds = 4.5 % >> GNP-growth
6,5 %
2.5 %
7 %
-GNP: 2.7 %
-Real rate:1.8%

15-yrs geometric real returns Norway / US 1900 – 2011
1900-1959 : 1960-2011 :
Equity: 3,2%
Gov Bonds: 1,1%
Equity: 5,2%
Gov. bonds: 2,9%
Real interest: 1,2% Real interest: 2,5%
NORWAY
1900-1959 :
Equity: 6,9%
Gov. bonds: 1,1%
Real interest: 0,7%
1960-2011 :
Equity: 5,4%
Gov. bonds: 3,3%
Real inteest: 1,1%
US
16

Summing up
 Yes, the risk free (real) rate term structure has a dip at the (very) long end
 But, the the term structure of risk premiums are problably upward bending (e.g. Pastor &
Stambaug, JF 2012)
 Use market calibration (political defense)
 More focus on benefits/cash flows than discount rates in public projects
17