Question regarding synthetic position with future constract content, index, regarding, effective, following

RepoToronto

In Scheweser on derivative session, there is a content like as below to explain effective beta,
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We can hypothesize the following scenario:
- the reference index (used to calculate the betas) increased in value by 2%
- the value of the equity position increased by 1.6%
- the value of the futures price increased by 2.1 %.
(These values correspond exactly to what we would expect with the provided betas of 0.8 - existing portfolio beta, and 1.05- future beta)
Had the leveraged position worked as desired (i.e. achieved an effective beta of 1.1) , the value of the portfolio would have increased 1.1*(0.02) = 2.2% to $ 5,110,000:
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(p. 148 in book4)
In here I have difficulty with understanding the phrase,
” (These values correspond exactly to what we would expect with the provided betas of 0.8 - existing portfolio beta, and 1.05- future beta) ”
How could it be related with the equity position increase 1.6% & future position increase 2.1% ?

cjs238

2 * 0.8 = 1.6
2 * 1.05 = 2.1

infinitybenzo

just understand vaguely by seeing after writing .. 2% x .8 & 2% x 1.05
appreciate if explained in detail

bchadwick

2% was change in the index
1.6% was change in the equity position.
so beta of the equity position must be 1.6 /2 = 0.8
same for the bond position.