You manage a Pension Fund with a $9 billion portfolio that is 80% US equity with a beta of 1.05 to the S&P 500 and 20% Bonds with a duration of 3.0 years. Your tactical asset allocation model dictates you should reduce your portfolios equity exposure and increase fixed income exposure by 5%

How could you immediately reduce the funds equity exposure using the December S&P500 and the December 5-yr Treasury Bond futures?

What time period should you execute your trades over so as not to exceed 25% of the average volume?

December S&P 500 Future (ESM1)

Last Price = 3948.25

Multiplier = 50 x the Index

Average Volume 1.6 million contracts daily (6.5 trading hours)

December 5-yr Treasury Bond future (FVM1)

Last Price = 123.50

Contract Size = 100,000

Duration = 5.4

Average Volume = 970,000 daily (6.5 trading hours)

Hedge Quantities = ?

Order execution times to not exceed 25% of the average volume = ?

HINT:

Stock Index Futures:

Optimal Hedge Quantity = b * $Value hedged b = Portfolio Beta

Index Value * Multiplier

Bond Futures:

Optimal Hedge Quantity = (Portfolio Duration / Bond Future Duration) * $Value hedged

Bond Contract $Value