Question regarding synthetic position with future constract

CFA Level III
#1

In Scheweser on derivative session, there is a content like as below to explain effective beta, 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: (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% ?

#2

2 * 0.8 = 1.6 2 * 1.05 = 2.1

#3

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

#4

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.