Analyzing the Effect of a Market Jump on an Equity’s Returns

Junior Research Seminar

Economics 201FS

Outline

• Objective

• Procedure

• Summation of Results

• Timeline

Capital Asset Pricing Model

Return of Equity = Risk-free rate

+ (Beta * Market Premium)

Beta = Cov(Market Return, Equity Return) / Var(Market Return)

Assumptions:

(i) Market return and residual are uncorrelated

(ii) Residuals are mutually uncorrelated

(iii) Residuals are difference between actual return and predicted return

Objective

• Introduce a dummy variable (Jmt), that depends on if the market (SPY) jumped– Lee/Mykland

• rcmt = (1-Jmt)(rmt)

• rjmt = (Jmt)(rmt)

rit = αi + βic (1-Jmt)(rmt) + βij (Jmt)(rmt) + εit

Procedure

• Lags/Leads for Beta Calculation

• Lee/Mykland test– Flagged 1318 jumps in SPY– Separated “flagged jump returns” and

“continuous returns”

ritc = αi + βic(rmtc) + εit

ritj = αi + βij(rmtj) + εit

Summation of Results

Standard CAP-M

Beta

1 Lag/Lead 1.0592

2 Lags/Leads 0.6932

3 Lags/Leads 0.2169

Results

Dep. Variable

Indep.

Variable

Coeff. SE t P>t 95% CI

Corres.

Equity

Returns

Flagged

Jump Returns

(Mkt)

0.12006 0.00182 65.917 0 0.1144-0.1257

Dep. Variable

Indep.

Variable

Coeff. SE t P>t 95% CI

Corres.

Equity

Returns

Cont. Returns

(Mkt)

0.3671 0.00106 346.51 0 0-0.7344

Timeline

• April 25th

– Model:• Formalize statistical analysis• One-equation model• Extend to other 40 stocks

– Other Areas:• Lag/Leads for Beta Calculation• Shifting Beta