Return reversals and the compass rose:
Insights from high frequency options data
Thanos Verousis (Swansea University)
Owain ap Gwilym (Bangor University)
The compass rose pattern architecture
Conditions:
– Sufficient price level volatility
– Price discreteness
– Small price changes
Arithmetic derivation:
Rt 1
( P  Pt ) / Pt
( P  Pt ) nt 1h nt 1
 t 1
 t 1


Rt
( Pt  Pt 1 ) / Pt 1 ( Pt  Pt 1 ) nt h
nt
(Crack and Ledoit, 1996 JF)
Rt 1
nt 1 h / Pt
nt 1 
nt h 




1

Rt
nt h /( Pt  nt h)
nt 
Pt 
(Szpiro, 1998 JBF)
Are we able to increase returns’ predictability?
 Crack and Ledoit, 1996 JF:
“an artefact of market microstructure”
 Lee et al. (2005, EJoF):
“...may help in improving forecasts...”
 Batten and Hamada (2008, EFMA):
“may suggest [...] an arbitrage opportunity for some investors”
Return reversal architecture and predictability
 Gosnell (1995, JBFA) “a price change in the opposite direction to
the previous price change”
 Linked with new information (Buckle et al., 1998 JBFA)
 In a compass rose plot, reversals (continuations) are found in the
NW and SE (NE and SW) quadrants
Where do we stand and the setup
 Study occurrence/visibility of the compass rose pattern in options
 Leverage effect
 Price level effect
 Lee et al (2005, EJoF):
“the tick/volatility ratio is a determinant of the compass rose pattern”
 Show return reversals embedded in the compass rose plot
Data
 Intraday LIFFE
 28 firms (> 133m obs.)
 Returns on options:
 Sheikh and Ronn (1994, JF): at-the-money, nearest-to-mature
 Bollerslev and Melvin (1994, JIE): stale pricing problem – asks
 UHF, 15-min, 30-min, trades
The compass rose in options contracts
 WRT Crack and Ledoit, 1996 JF: The assumption of continuity is
not valid
 WRT Szpiro, 1998 JBF: formula is not universal
,Sk = Sk-1, Si = Si-1,
Since
, then
Lee et al (2005, EJoF, p 103): “the pattern appears only if the
tick/volatility ratio is above some threshold level”
 The above implies that:
 The pattern’s visibility increases with decreasing volatility (ceteris paribus)
 Contracts with same tick/volatility ratios produce a similar pattern
 Table 1: Ratio consistent when changes in frequency of observations…
 Quality is not an increasing function of the ratio
 Even at high tick/volatility, the ratio not a consistent measure
 Figure 3: Ratio may give inconclusive results on the strength of the
pattern
The compass rose and return reversals
 At UHF, certain assets exhibit a “pattern within the pattern”
 Explanations found in literature:
 Park (1995, JFQA): bid-ask bounce
 Christie and Schultz (1994, JF): speed of adjustment
 Figure 6: control for duration
 and the non-linearity?
Continued...
 Buckle et al (1998, JBFA): news dissemination (local minima), scheduled
macroeconomic announcements (global minima) and day trading
strategies (global maxima)
42
41
40
39
38
37
36
35
34
33
32
Expected
Sign
Intercept
Pr
TS
Liq
OD
Time
15
:3
0:
00
14
:3
0:
00
13
:3
0:
00
12
:3
0:
00
11
:3
0:
00
10
:3
0:
00
09
:3
0:
00
CD
08
:3
0:
00
08
:0
0:
00
Percentage
Variable
DMM
TTM
FV
R-Square
No. of Obs.
+
-
Call
Put
53.67***
56.83***
4.96***
4.55***
-3.00***
-2.70***
0.02***
0.01**
5.46***
6.05***
1.10***
1.07***
-3.79***
-3.44***
-0.02**
-0.01
-2.10***
-2.42***
0.10
0.09
54,235
54,410
Conclusions
 Compass rose in options: non-linearities
 Tick/volatility ratio consistent at high sampling frequencies
 Trading frequency key element
 Inconclusive results on the strength of the pattern
 Visual inspection only comparable measure
 Return reversals embedded in the compass rose
 Market opening and news announcements
 Price discovery