LOS 32 - Changing

CFA Level III Derivatives
#1

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

#2

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

Need corrections please

#3

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.

#4

* 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.

#5

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.