Implication of growth option on the term structure of
equity
Wah Yip Chu
BI Norwegian Business School
30 Jun 2017
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Quick Summary
van Binsbergen, Brandt, and Koijen (2012) empirically show that the
term structure of equity is downward sloping, i.e. short-term assets
have higher yields (returns) than the long term assets.
I show ...
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New empirical finding:
The term structure of returns for the growth stock is downward
sloping, while that for the value stock returns is flat.
The term structure of cash flow betas for the growth stocks is
downward sloping, while that for the value stocks is flat.
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Theoretical implication: consistent with the real/growth option theory,
because the real option can be riskier in the short-run than in the
long-run.
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Literature review
Theories:
1 Modifying preferences, e.g. Curatola, (2015), Eisenbach and Schmalz
(2016), Andries, Eisenbach, and Schmalz (2017).
No cross sectional implications, e.g. value and growth would exhibit
the same term structure patterns, according to law of one price.
2
Production-based
1
Operating leverage, Marfe(2017), Favilukis and Lin (2016)
implies that firms with high operating leverage (e.g. value firms) should
exhibit downward sloping term structure
2
This paper proposes real option theory
implies that firms with more growth options (e.g. growth firms) should
exhibit downward sloping term structure
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Real option theory
Vi,t = Ai,t + Gi,t .
(1)
Gi,t = N (d1 )Ai,t − N (d2 )Ie −rT
(2)
where
√
ln(Ai,t /Ie −rT ) + 0.5(σ T )2
√
d1 =
σ T
√
and d2 = d1 − σ T
(3)
and N(.) is the cumulative distribution function for the standard normal
distribution.
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Real option theory
β i,t =
Ai,t A
Gi,t G
β i,t +
β
Vi,t
Vi,t i,t
(4)
β i,t =
Ai,t
(1 + δi,t ) βAi,t
Vi,t
(5)
∂Gi,t
∂Ai,t
(6)
where
δi,t =
The delta channel:δi,t ↑⇒ β i,t ↑⇒ E [Ri,t ] ↑
How can this explain the downward sloping term structure of equity?
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Real option theory
Interesting property of option delta: for an in-the-money option, the
shorter the time-to-maturity, the higher the option delta.
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∂ G
Option charm or commonly known as the delta decay, − ∂A∂τ
,
measuring the sensitivity of delta to time-to-maturity (τ ).
According to the option charm property, short term growth options
are riskier (higher delta), because they are soon to be exercised
(closed to maturity)
Testable hypothesis:
Downward sloping term structure of equity is mainly driven by growth
stocks.
Short term growth stocks have more short term growth options, which
are riskier according to the option charm property.
Value firms have more assets-in-place, which behave the same in
response to the shocks for both long and short-run.
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Empirical test
Methodology: Weber (2017), Dechow, Sloan, and Soliman (2004):
DURi,t =
s
∑T
s =1 s × CFi,t +s / (1 + r )
Pi,t
(7)
Double-sorting by BM and DUR, or profitability and DUR
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Asset pricing
Exactly how much of the return spread over the term structure can be
explained by variation in risk exposures?
Asset pricing test (2 stage regression):
Two factors model (Campbell and Vuolteenaho, 2004).
DR DR
E [Ri ] = λCF βCF
βi
i +λ
(8)
Test assets: two sets of decile portfolios single-sorted by BM and DUR.
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Price of risk
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Model performance
Such asset pricing test implicitly assumes a constant price of risk over
the term structure.
The fact that such model is able to generate a large fraction of return
spread suggests the importance of the growth option mechanism.
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Conclusion
I show that ...
Theoretically, the real option theory can explain the downward sloping
term structure of equity.
Empirically, firms with more growth options exhibit steeper downward
sloping term structure of returns.
Asset pricing test with constant price of risks can already account for
a large fraction of the duration spread.
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