# Ⅱ Definition of bull and bear market Bull and bear markets are

Document Sample

```					                     Ⅱ. Definition of bull and bear market

Bull and bear markets are often heard from financial analysts, stock market

commentators, and the press, but there is no generally accepted formal definition of

bull and bear markets. The followings are several definition discussed in previous

literatures. Each definition is listed below.

1. Fabozzi and Francis (1977) gave three alternative definitions of bull and bear

market conditions.

(1) Bull and Bear (BB) Markets are the months which were designated as bull

and bear markets by a popular investment textbook.

(2) Up and Down (UD) Markets. Months of non-negative market return are

classified as Up months, while months of negative market return are placed

in Down category.

(3) Substantial Up and Down (SUD) Months. Substantial-up (Substantial-down)

movements are defined as months when market returns were larger (smaller)

than half of one standard deviation of the markets returns over the sample

period, for example, rmt > 0.5σ M for substantial-up movements. Months not

classified in substantial-up or -down categories are not used.

2. Kim and Zumwalt (1979) introduced another measure to determine what

constituted an “up-” or “down-” market. An “up-” market was defined as

months when the rate of return on the market portfolio exceeded (1) the average

market return, (2) the risk free rate, or (3) zero. Otherwise, the market was

defined as a “down-” market.

3. Lunde and Timmermann (2004) provided a more mathematically demanding

definition to capture long-run dependencies in the underlying stock prices. First,

let I t be a market indicator variable equals to 1 at time t if the stock market is

5
in a bull state and 0 otherwise. Pt is the stock price at the end of period t. Let

λ1 be the a scalar defining the threshold of the movements in stock prices

triggering a switch from a bull to a bear market, and λ2 be the threshold for

shifts from a bear to a bull market. Suppose at t0 , the stock market is at a local

maximum ( I t0 = 1 ) and set Pt0max = Pt0 .

τ max ( Pt max , t0 | I t = 1) = inf{t0 + τ : Pt +τ ≥ Pt max }
0          0                           0        0

τ min ( Pt max , t0 , λ2 | I t = 1) = inf{t0 + τ : Pt +τ < (1 − λ2 ) Pt max }
0                   0                       0                  0

where τ max and τ min are stopping variables. If τ max < τ min , then we update the

local maximum in the current bull market state, Pt0maxmax = Pt0 +τ max
+τ                                          which

continued from           t0 + 1 to         t0 + τ max : I t0 +1 = ... = I t0 +τ max = 1 . Conversely, if

τ min < τ max , the stock price at t0 + τ min has declined by a fraction λ2 from its

local peak, Pt0 +τ min < (1 − λ2 ) Pt0max , implying that the bull market has switched to

a bear market that prevailed from t0 + 1 to t0 + τ min : I t0 +1 = ... = I t0 +τ min = 0 . In

this case, we set Pt0minmin = Pt0 +τ min .
+τ

If the starting point of a bear market state is t0 , then the stopping times are

defined as

τ min ( Pt min , t0 | I t = 0) = inf{t0 + τ : Pt +τ ≤ Pt min }
0           0                           0        0

τ max ( Pt min , t0 , λ1 | I t = 0) = inf{t0 + τ : Pt +τ > (1 + λ1 ) Pt min }
0               0                           0                 0

Although UD markets and SUD markets suggested by Fabozzi and Francis (1977)

and that “up-” or “down-” market defined by Kim and Zumwalt (1979) are mutually

exclusive and easily applied by others, these methods view every month

independently and do not reflect long-run dependencies in stock prices. In this paper, I

6
categorized bull and bear markets by adopting the definition of Lunde and

Timmermann (2004). The threshold scalars ( λ1 , λ2 ) are chosen as (15, 15) expressed

in percentage terms. By this criterion, I identify 24 bear markets in Taiwan stock

market from January 1971 to December 2006. Table 1 provides the periods of bear

markets of the TAIEX index of peak and trough. Figure 1 shows the TAIEX index and

bear markets highlighted by shaded areas.

Table 1. Details of bear markets: from January 1971 to December 2006
Peak                                   Trough                    Duration
Date              Index                Date             Index            (month)
June 71                  141.14        October 71               118.8              4
November 73              499.22        May 74                  323.44              5
July 74                  376.77        December 74             193.06              5
August 75                387.37        November 75             306.53              3
March 76                 415.64        September 76            287.17              6
January 77               391.15        April 77                 322.2              3
September 78             679.17        February 79             531.31              5
April 79                 659.19        June 80                 480.38             14
February 81              582.36        January 83              442.73             23
April 84                  938.3        July 85                 637.14             15
September 87            4459.01        December 87            2339.86              3
September 88            8402.93        December 88            5119.11              3
January 90             12054.35        September 90           2705.01              8
April 91                5921.29        November 91             4378.5              7
January 92              5391.63        January 93             3374.56             12
March 93                4825.29        September 93           3832.69              6
December 94             7124.66        January 96              4763.4             13
July 97                10066.35        October 97              7313.4              3
February 98             9202.56        December 98            6418.43             10
March 00                9854.95        December 00            4739.09              9
January 01               5936.2        September 01           3636.94              8
March 02                6167.47        October 02             4579.14              7
January 03              5015.16        April 03               4148.07              3
February 04             6750.54        July 04                5420.57              5

7

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 10 posted: 3/20/2010 language: English pages: 3