creating synthetic cash formula & question his, currently, following, creating

soddy1979

An investor has a $100 million stock portfolio with a beta of 1.1. He would like to hedge his portfolio using S&P 500 futures contracts, which are currently trading at 596.70. The futures contract has a multiple of 250. Which of the following is the CORRECT trade required to create a synthetic T-bill?
A) Sell 670 contracts.
B) Buy 670 contracts.
C) Sell 737 contracts.
Your answer: A was incorrect. The correct answer was C) Sell 737 contracts.
The position created by risk-minimizing hedging is essentially the creation of a synthetic T-Bill. The number of futures contracts required for the risk-minimizing hedge is computed as follows:
Number of contracts = Portfolio value / Futures contract value

tobeornottobe

Wow no idea how I screwed this one up. Thanks everyone for your help.
Using bpdulog’s formula to alter the portfolio beta to zero makes sense to me.
Just one question on mcap11’s point. If what he said is true (“only time you use the interest rate is for SYNTHETIC transactions”), then why is the question/answer saying you have created synethetic t-bill, if we just alter the beta here?

OmarAdnan

c is correct 100*1e6*1.1/( 250*596.70) = 737

meghanjackson

The formula used to create a synthetic t-bill V(1+rfr)/q*f can be used ONLY if the portfolio is the same as the underlying of the index future. CFAI is very clear on that. Look at page 363 of the derivative book. In this case, the portfolio is clearly not the S&P 500 because the beta is 1.1, so that formula cannot be used. The right answer should be A.

IAmNeil

only time you use the interest rate is for SYNTHETIC transactions.
bpdulog is 100% right
this is a NO EXCUSES topic!!

LBriscoe

How can you use that formula if no interest rate is given? That means we have to use this formula:
((0-1.1)/1)*(100,000,000/(596.70*25)) = -737

jcfa2011

Just checked CFAI book (volume 5 pg 361 top of page) and the formula is the same as schweser, so i am fairly certain schweser is wrong here and there is no need for beta and needs to be a time horizon and rfr disclosed