Relationship between ‘beta’ and stock returns

Mayur AgrawalVarun Agrawal

Debabrata MohapatraVikas Yadav

Experimental Setup

1st Jan 1962 31st Dec 2008Current Time

K monthsN months

Obtain daily fluctuations on beta portfolios. Obtain Sharpe ratios after each portfolio readjustment.

Default Parameters: N = 60, K = 12, P = 10

Long versus Long-Short Portfolio

Long Long-Short

Borrow $1 at 0% and invest in low beta portfolio

Borrow $1 and invest in low beta portfolio

Return $1 to the lender after N days

Return $1 worth of today’s high beta portfolio to lender after N days

Loss is limited to invested amount

Unlimited loss can occur

PNL Plot for Beta Portfolio

PNL Plot for Long Short Portfolio

19691231

19711221

19731214

19751208

19771130

19791121

19811113

19831104

19851029

19871021

19891012

19911004

19930927

19950919

19970910

19990903

20010828

20030828

20050823

20070820

-3

-2

-1

0

1

2

3

4

5

LowHigh

19691231

19711221

19731214

19751208

19771130

19791121

19811113

19831104

19851029

19871021

19891012

19911004

19930927

19950919

19970910

19990903

20010828

20030828

20050823

20070820

-3

-2

-1

0

1

2

3

4

5

LowLow High

Sharpe Ratio for Beta Portfolios

19691231

19711221

19731214

19751208

19771130

19791121

19811113

19831104

19851029

19871021

19891012

19911004

19930927

19950919

19970910

19990903

20010828

20030828

20050823

20070820

-3

-2

-1

0

1

2

3

4

SnP500Low High

Sharpe Ratio for Long-Short and SnP