Key rate thresholds turning defensive assets into ordinary assets

Center for Macroeconomic Analysis and Short-term Forecasting1

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Key rate thresholds turning defensive assets into ordinary

assets

Key rate thresholds turning defensive assets into ordinary

assets

Alexander Apokin, CMASF

NRU-HSE Conference, April 2-5, 2013

Center for Macroeconomic Analysis and Center for Macroeconomic Analysis and Short-term forecastingShort-term forecasting

Tel.: 7-499-129-17-22, Fax: 7-499-129-09-22, e-mail: [email protected], http://www.forecast.ru


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Research QuestionResearch QuestionResearch QuestionResearch 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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• Suppose CAPM holds, thus the yield on asset i is: , where

What is a defensive asset?What is a defensive asset?What is a defensive asset?What is a defensive asset?

Research questions

( )i rf i m rfR R R R

• Defensive assets are assets with , i.e. assets that have negative correlation with the market portfolio (usually the stock index)

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

,i m mi

i

0i


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Research questions

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

Oil, gold and CHF rolling betas*Oil, gold and CHF rolling betas*Oil, gold and CHF rolling betas*Oil, gold and CHF rolling betas*

-3

-2

-1

0

1

2

3

4

5

1995

1997

1999

2001

2003

2005

2007

2009

2011

2013

Gold WTI CHF

7.1


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How defensive asset can transform How defensive asset can transform into an ordinary asset?into an ordinary asset?


Research questions


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



Research questions


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• SML downward shift because decreases:

– lower rates mean lower beta

– might mean negative rates for negative-beta assets

• 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 thus kept positive



Research questions

,rf F tR r

,t T

iR

iR

rfR


8



Research questions


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Research questions

*Kernel smoothing at 0.95

Oil, gold and CHF rolling betas*Oil, gold and CHF rolling betas*Oil, gold and CHF rolling betas*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

-4.0

-3.0

-2.0

-1.0 0.0

1.0

2.0

3.0

4.0

1995-2008 2003-2004

WT

I

Gold


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Research questions

Oil vs. gold rolling betas*Oil vs. gold rolling betas*Oil vs. gold rolling betas*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

10.0-4

.0

-3.0

-2.0

-1.0 0.0

1.0

2.0

3.0

4.0

1995-2008 2009-2013

Gold

WT

I

*30-day rolling betas relative to S&P500


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Defensive assets in the literatureDefensive assets in the literatureDefensive assets in the literatureDefensive 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)

The Literature


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Variable descriptionSource

WTI oil $/bbl FRED

London gold fixing beta $/troy ounce FRED

Swiss frank beta $/CHF FRED

Federal funds rate % Fed

The Data


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1. 1. Individual asset rate Individual asset rate thresholdsthresholds

1. 1. Individual asset rate Individual asset rate thresholdsthresholds

Центр макроэкономического анализа и краткосрочного прогнозирования13

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Individual asset rate thresholdsIndividual asset rate thresholds Individual asset rate thresholdsIndividual asset rate thresholds

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

• Fed funds rate as exogenous regime-switching variable:

1) FF rate clearly can influence financial markets (e.g. betas)

2) FOMC is practically unconcerned by betas in its rate decisions

1. Individual asset rate thresholds


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Estimation results (WTI SETAR)Estimation results (WTI SETAR)Estimation results (WTI SETAR)Estimation results (WTI SETAR) Estimate SE t-stat Pr(>|t|)

Lconst 0.52 0.23 2.31 0.02

phiL.1 0.55 0.09 6.02 0.00

phiL.2 0.15 0.10 1.44 0.15

phiL.3 -0.07 0.09 -0.81 0.42

Hconst -0.05 0.18 -0.31 0.75

phiH.1 -0.19 0.10 -1.91 0.06

phiH.2 -0.10 0.10 -0.95 0.34

phiH.3 -0.27 0.10 -2.67 0.01


Threshold: 2.61%

SETAR vs. Linear test Pval1vs2 19.71 0.51vs3 31.88 0.02vs3 11.13 0.0


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ACF/PACF ACF/PACF (WTI (WTI SETAR)SETAR)ACF/PACF ACF/PACF (WTI (WTI SETAR)SETAR)


Time

0 50 100 150 200

01

23

45

6

Threshold variable used

th 1

0 50 100 150 200

01

23

45

6

Ordered threshold variable

trim= 0.1th 1


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Estimation results (Gold SETAR)Estimation results (Gold SETAR)Estimation results (Gold SETAR)Estimation results (Gold SETAR)


Estimate SE t-stat Pr(>|t|)

Lconst 0.25 0.08 2.99 0.00phiL.1 0.11 0.12 0.88 0.38phiL.2 -0.24 0.11 -2.09 0.04phiL.3 -0.11 0.11 -0.95 0.34Hconst -0.13 0.06 -2.10 0.04phiH.1 0.09 0.08 1.03 0.31phiH.2 -0.04 0.09 -0.49 0.63phiH.3 0.14 0.09 1.66 0.10

Threshold: 1.81%



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ACF/PACF ACF/PACF ((GoldGold SETAR)SETAR)ACF/PACF ACF/PACF ((GoldGold SETAR)SETAR)



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Estimation results (CHF SETAR)Estimation results (CHF SETAR)Estimation results (CHF SETAR)Estimation results (CHF SETAR)


Estimate SE t-stat Pr(>|t|)

Lconst 0.28 0.10 2.83 0.01phiL.1 0.36 0.15 2.41 0.02phiL.2 -0.07 0.15 -0.47 0.64phiL.3 -0.08 0.14 -0.59 0.56Hconst -0.23 0.06 -3.78 0.00phiH.1 0.16 0.08 2.14 0.03phiH.2 0.03 0.08 0.32 0.75phiH.3 0.19 0.08 2.40 0.02

Threshold: 1.00%



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ACF/PACF ACF/PACF ((CHFCHF SETAR)SETAR)ACF/PACF ACF/PACF ((CHFCHF SETAR)SETAR)



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Individual asset rate thresholdsIndividual asset rate thresholds Individual asset rate thresholdsIndividual asset rate thresholds

• Fed funds rate threshold for beta dynamics is in range of 1.0%-2.6%, tests indicate threshold models are specified correctly

• WTI and CHF exhibit no mean reversion under the threshold

• Regime change in dynamics is most pronounced in oil



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2. 2. Common threshold Common threshold dynamicsdynamics

2. 2. Common threshold Common threshold dynamicsdynamics


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Common thresholdCommon threshold Common thresholdCommon 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

2. Common threshold dynamics


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Estimation results (TVAR)Estimation results (TVAR)Estimation results (TVAR)Estimation results (TVAR)


$Bdown C Trend beta_WTI(-1)

beta_gold (-1)

beta_CHF(-1)

beta_WTI(-2)

beta_gold (-2)

beta_CHF(-2)

beta_WTI(-3)

beta_gold (-3)

beta_CHF(-3)

beta_WTI -3.41 0.03 0.46 -0.21 -0.80 0.10 0.11 -0.58 -0.05 -0.49 -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 -0.11 0.31 0.03 -0.02 -0.02 -0.03 0.20 0.06

$Bup

beta_WTI 0.05 0.00 -0.11 0.20 -0.58 -0.04 0.03 0.65 -0.28 0.04 0.14

beta_gold 0.14 0.00 -0.03 -0.21 0.06 -0.02 -0.04 -0.05 -0.03 0.00 -0.03

beta_CHF -0.12 0.00 0.02 0.03 0.13 0.01 -0.12 0.09 -0.04 -0.09 0.18

Threshold value: 1.82LR test: 1vs2 1vs3Test 82.4 134.1P-Val 0.0 0.0


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Impulse response (Low regime)Impulse response (Low regime)Impulse response (Low regime)Impulse response (Low regime)



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Impulse response (High regime)Impulse response (High regime)Impulse response (High regime)Impulse response (High regime)



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33. . ConclusionsConclusions33. . ConclusionsConclusions


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“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

4. Conclusions


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Future research directions Future research directions Future research directions 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 financialization and producer-speculator structure– Oil market financialization

– Non-commercial trader positions for each market

– Endogenize futures convenience yields

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

Testing structural break vs. regime-switching model

Key rate thresholds turning defensive assets into ordinary assets

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