MM Exam 1: PM Question - Equity Future Contracts

CFA Level III Derivatives
#1

Hi all,

Question 37 on in Exam 1, PM - we are required to convert cash to equity exposure via futures. The first part of the answer uses the current portfolio beta (1.15) as the target beta opposed to the stated target beta (1.25). Why are they using current portfolio beta instead of target beta?

From answer:

To increase her equity exposure, Ruiz is effectively converting GBP 50 million from cash to equity, so the number of equity contracts that Ruiz needs to execute is:

where:

Nsf = βT − βE × P βf fs

Nsf = number of equity index futures contracts βT = target beta (1.15 for the current portfolio) βE = existing beta (0.0 for cash) βf = futures beta (1.04)

P = market value of portfolio to be reallocated (GBP 50,000,000) fs = equity index futures price (GBP 240,000)

Nsf = βT − βE × P βf fs

= 1.15 − 0.0 × GBP 50,000,000 = 230.37 1.04 GBP 240,000

To increase the equity beta from 1.15 to 1.25 (on the new equity allocation of GBP 300,000,000 (= GBP 250,000,000 + GBP 50,000,000)), the number of equity contracts that Ruiz needs to execute is:

Nsf = βT − βE × P βf fs

= 1.25 − 1.15 × GBP 300,000,000 = 120.19 1.04 GBP 240,000

The total number of equity contracts that El Mohamady needs to execute is: 230.37 + 120.19 = 350.56

Therefore, Ruiz should buy (i.e. take the long position in) 351 equity futures contracts.

thanks

#2

Cause we wanna increase allocation to equities and we don’t wanna modify the beta.

#3

The problem states - Ruiz wants to increase UK equity exposure and adjust UK equity beta to 1.25

#4

You could arrive at the same solution by using either the target beta or the current beta, you’d just have to change your numbers.

Using the target beta: ((1.25 - 0 / 1.04) X (50m/ 240k)) + ((1.25 - 1.15 / 1.04) X (250m/240k)) = 350.56

The solution given simply sets the target portfolio (current 250m plus 50m) equal to the current beta first, then changes the full 300m to the target beta of 1.25.

It’s the same thing. Try both ways for yourself to verify.

#5

You use target beta when you’re adjusting beta of entire portfolio as beta on the entire holding needs to be adjusted not just the change in allocation. Once you get the no of contracts you buy/sell on allocation/deallocations, then you ise target formula as the beta onnthe entire asset holding needs to be adjusted. Using target beta just on 10MN allocation/deallocation won’t be accurate.