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Key rate thresholds turning defensive assets into ordinary assets

Alexander Apokin, CMASF NRU-HSE Conference, April 2-5, 2013

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Research Question

• Do most widespread defensive assets turn into ordinary assets for prolonged time periods?

• Where are the thresholds for risk-free rate on defensive assets?

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Research questions

What is a defensive asset?

• Suppose CAPM holds, thus the yield on asset is:

R i



R rf

 

i

(

R m



R rf

) , where 

i

   

i m

• Defensive assets are assets with 

i

 0 , i.e.

assets that have negative correlation with the market portfolio (usually the stock index)

i

• Anecdotal evidence is that most widespread defensive assets are oil, gold and Swiss frank

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Research questions

Oil, gold and CHF rolling betas*

7.1

2 1 0 -1 -2 -3 5 4 3

Gold WTI

*30-day rolling betas relative to S&P500, kernel smoothing at 0.95

CHF Center for Macroeconomic Analysis and Short-term Forecasting

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Research questions

How defensive asset can transform into an ordinary asset?

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Research questions

How defensive asset can transform into an ordinary asset?

• The case for oil was formulated in Kaufman (2012) based on Pindyck (2001):

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Research questions

How defensive asset can transform into an ordinary asset?

• SML downward shift because

R rf

decreases: – lower rates

R rf



r

mean lower beta – might mean negative rates for negative-beta assets

i

• Futures markets role (

ceteris paribus

): – lower rate means lower convenience yield  – with lower convenience yield, futures price changes from backwardation to contango – i.e. it is better to receive asset later than to buy&store it – stocks decline and spot price rises until contango is eliminated – rates

R i

thus kept positive

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Research questions

How defensive asset can transform into an ordinary asset?

SML r E SML’ r E ’ r F b C ’ r oil financial asset ’ r F ’ r oil b A ’ b = 1

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Research questions

Oil, gold and CHF rolling betas*

10.0

8.0

6.0

4.0

2.0

0.0

-2.0

-4.0

-6.0

-8.0

-10.0

1995-2008

Gold

2003-2004

*Kernel smoothing at 0.95

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Research questions

Oil vs. gold rolling betas*

10.0

8.0

6.0

4.0

2.0

0.0

-2.0

-4.0

-6.0

-8.0

-10.0

1995-2008

Gold

2009-2013

*30-day rolling betas relative to S&P500

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The Literature

Defensive assets in the literature

• Macroeconomic variables and oil shocks, based on Hamilton (1983) – Hamilton (2003), Kilian and Park (2009), Conrad et al.

(2012) • Financial markets and investment management, based on Jaffe (1989) and Jones and Kaul (1996) : – Oil: Nandha and Faff (2008), Huang et al. (1996) – Gold: Jaffe (1989), Lawrence (2003), Baur et al (2006), Fang et al (2012)

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The Data

Variable description

WTI oil London gold fixing beta Swiss frank beta Federal funds rate $/bbl $/troy ounce $/CHF %

Source

FRED FRED FRED Fed

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1. Individual asset rate thresholds

1. Individual asset rate thresholds

Individual asset rate thresholds

•

Time-series self-exciting threshold models (SETAR) for each asset separately

• 1) 2)

Fed funds rate as exogenous regime switching variable:

FF rate clearly can influence financial markets (e.g. betas) FOMC is practically unconcerned by betas in its rate decisions

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1. Individual asset rate thresholds

Estimation results (WTI SETAR)

Lconst

Estimate

0.52

0.55

SE

0.23

0.09

t-stat

2.31

6.02

phiL.1

phiL.2

0.15

0.10

1.44

phiL.3

Hconst -0.07

-0.05

0.09

0.18

-0.81

-0.31

phiH.1

phiH.2

-0.19

-0.10

0.10

0.10

-1.91

-0.95

phiH.3

Threshold: 2.61% -0.27

0.10

SETAR vs. Linear test

1vs2 1vs3 2vs3 19.71 31.88 11.13

-2.67

Pval

0.5

0.0

0.0

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Pr(>|t|)

0.02

0.00

0.15

0.42

0.75

0.06

0.34

0.01

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1. Individual asset rate thresholds

ACF/PACF (WTI SETAR) Threshold variable used

th 1 0 trim= 0.1

th 1 50 100 Time 150

Ordered threshold variable

200 0 50 100 150 200

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1. Individual asset rate thresholds

Estimation results (Gold SETAR)

Estimate SE Lconst

0.25

0.08

phiL.1

0.11

0.12

phiL.2

-0.24

0.11

phiL.3

-0.11

0.11

Hconst

-0.13

0.06

phiH.1

0.09

0.08

phiH.2

-0.04

0.09

phiH.3

Threshold: 1.81% 0.14

0.09

SETAR vs. Linear test

1vs2 6.91 1vs3 2vs3 18.70 11.41

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t-stat

2.99

0.88

-2.09

-0.95

-2.10

1.03

-0.49

1.66

Pval

0.5

0.0

0.0

Pr(>|t|)

0.00

0.38

0.04

0.34

0.04

0.31

0.63

0.10

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1. Individual asset rate thresholds

ACF/PACF (Gold SETAR)

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1. Individual asset rate thresholds

Estimation results (CHF SETAR)

Estimate SE t-stat Lconst

0.28

0.10

2.83

phiL.1

0.36

0.15

2.41

phiL.2

-0.07

0.15

-0.47

phiL.3

-0.08

0.14

-0.59

Hconst

-0.23

0.06

-3.78

phiH.1

0.16

0.08

2.14

phiH.2

0.03

0.08

0.32

phiH.3

Threshold: 1.00% 0.19

0.08

SETAR vs. Linear test

1vs2 8.79 1vs3 2vs3 14.32 5.31

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2.40

Pval

0.5

0.0

0.0

Pr(>|t|)

0.01

0.02

0.64

0.56

0.00

0.03

0.75

0.02

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1. Individual asset rate thresholds

ACF/PACF (CHF SETAR)

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1. Individual asset rate thresholds

•

Individual asset rate thresholds

Fed funds rate specified correctly threshold for beta dynamics is in range of 1.0%-2.6%, tests indicate threshold models are • WTI and CHF exhibit no mean reversion under the threshold • Regime change in dynamics is most pronounced in oil

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2. Common threshold dynamics

2. Common threshold dynamics

•

Common threshold

Asset prices are apparently interweaved, and so are betas

•

Thus, threshold VAR approach (Lo and Zivot, 2001) needed:

1) FF rate stays an exogenous variable 2) Test rejects hypothesis of common unit root for defensive asset betas

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1. Individual asset rate thresholds

Estimation results (TVAR)

$Bdown C beta_WTI

-3.41

Trend

0.03

beta_W TI(-1)

0.46

beta_gol d (-1) -0.21

beta_CH F(-1)

-0.80

beta_WT I(-2) 0.10

beta_gol d (-2) 0.11

beta_CH F(-2) -0.58

beta_WT I(-3) -0.05

beta_gol d (-3)

-0.49

beta_CH F(-3) -0.05

beta_gold 0.22

0.00

-0.06

-0.18

0.25

-0.01

0.07

0.09

-0.01

0.19

-0.02

beta_CHF

-0.85

0.01

0.00

$Bup beta_WTI 0.05

0.00

-0.11

-0.11

0.20

0.31

-0.58

0.03

-0.04

-0.02

0.03

-0.02

0.65

-0.03

-0.28

0.20

0.04

0.06

0.14

beta_gold 0.14

0.00

-0.03

-0.21

beta_CHF -0.12

0.00

0.02

0.03

0.06

0.13

-0.02

0.01

-0.04

-0.12

-0.05

0.09

-0.03

-0.04

0.00

-0.09

-0.03

0.18

LR test: Threshold value: 1.82

Test P-Val

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1vs2 82.4

0.0 1vs3 134.1

0.0

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1. Individual asset rate thresholds

Impulse response (Low regime)

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1. Individual asset rate thresholds

Impulse response (High regime)

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3. Conclusions

4. Conclusions



“Defensive assets” are not defensive per se, some additional conditions (like relatively high rates) needed



The thresholds for asset betas exist and are in the range 1.0-2.6%



There were two distinct periods of low rates, i.e.

“low” beta regime with positive betas, and we are in the one since 2008



Change in beta is the most pronounced for oil market, while in gold and CHF it is still volatile

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

Future research directions Expanding the list of defensive assets to gov’t bonds



Testing the role of macro shocks vs. risk-free rate shocks

– Integrating yield forecasts into threshold multi-factor APT model 

Accounting for speculator structure financialization

– Oil market financialization – Non-commercial trader positions for each market – Endogenize futures convenience yields

and producer-



Building on level data (cointegrated) instead of yield data (stationary)



Testing structural break vs. regime-switching model

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