# LOS 32 - Changing

hi all

i am a bit confused with the practice problem 8 of the CFA book.

the question is as follows :

a Manager holding 350M of US Equities with beta of 1.1

The manager would like to Create a synthetic cash position by temporarily converting the US equity exposure in the fund into cash for a period of three months.

below are the market information:

S&P 500 futures Treasury bond futures Quoted futures price 2157 Quoted futures price \$105,200 Multiplier \$250 Duration 6.20 Beta 0.90 Yield beta 0.95 Maturity of futures 3 months Maturity of futures 3 months Other US market data Risk-free rate 0.50% S&P 500 dividend yield 3.00%

The proposed solution by the CFA book

The number of S&P 500 futures contracts needed to be sold to execute Strategy 2 is calculated as follows.

Nf=(βT−βSβf)(Sf)

while i would have thought that

Nf = 350M x (1+RFR)^0.25/Nq

Can somebody tell me where is the mistake in my reasoning? shouldn’t we always look at the FV of the cash that we are synthesizing?

Thank you

This is NOT a case where the manager expecting a cashflow in 3 months. So your PV=350M not 350 discounted RFR. In this case, you lend this cash and get your RFR interest payment along with 350M in 3 months.

However, if you are expecting a cashflow IN 3 months, you want to adjust for RFR.

--------------------- on a seperate subject,

I believe Futures do not reflect dividends, unlike your portfolio.

So your hypothetical # of futures should be adjusted the dividends out of them.

However, though your actual# of futures shorted would walk up to the index value, the dividend adjustment will allow you to see your effective stocks you’d have shorted

Interesting because the curriculum explains the difference btw the 2 formulas (the one used in EOC No 2 and the one in EOC No 8) with the issue if the synthetic equity position perfectly matches the index or if there is a difference in the betas.

I’m not comfortable either with when to use the value increased by the RFR and when not.

* This portfolio is meant to track the performance of US large-cap stocks, not to exactly replicate the performance of the S&P 500 Index.

This footnote was in the problems set. This means you use “beta formula.”

If the equity portfolio was exactly indexed to the S&P500, you use the “risk free rate formula.”

That is my interpretation and I am sticking with it. CFAI is terrible at explaining it.

Yes, that was my understanding re these two EOC questions (No. 2 and 8).

However I’ve just came across an AM question (Exam 2016 I think - I’m not at home) where the RFR was given (maybe as a distractor?) and it was NOT needed in the calculation. There were different betas given but there was no statement about whether to match fully or not the index.