 # Derivatives Question - CFAI Derivative TT #53

Can someone help me with this one - it is question 53 of the derivatives section on CFAI

Ndlovu is also evaluating the forward contract in Zulu Mineral Mining (Zulu) stock to determine if an arbitrage opportunity exists. The South African 12-month prime rate is 3.25%. The spot price for Zulu is ZAR 60.50. Zulu pays an annual dividend of ZAR3.00 on a semiannual basis, and the next dividend is paid in three months. Interest compounds annually.

Q. The three-month forward price for Zulu stock is closest to:

1. ZAR63.99.
2. ZAR59.47.
3. ZAR57.99.

Forward price of an equity forward contract: FP = (S - PVD)*(1+Rf)t

in which S is the spot price

PVD = present value of dividends if it is paid within the timeframe of the contract

t = contract time

So in this problem, you want to find the PV of div first. DIV is 3 in 3 months, PV of div (discount back 3 months) is 2.976108. You plug everything into the formula FP = (60.5 - 2.976108)*(1.0325).25 = 57.9857

Thank you. On the dividends, why don’t you use 1.5? If they pay semi-annually, and the next one is in 3 months (same time-frame as the forward), shouldn’t you use PV of 1.5 in three months?

You’re right. My mistake.

But that’s the problem - CFAI has it calculated basically the way you did. But it makes no sense based on the facts in the case, right? Or am I missing something?

Bumping this back up - anyone have any thoughts? The answer according to CFAI is 3. ZAR57.99, but this assumes you subtract the full ZAR3 dividend.

S2000Magician - any chance you could weigh in on this one? It’s throwing me for a loop as the way CFAI calculated it is contrary to what I’ve understood all this time…

Hi, I’ve been looking at this example by Tuchsford. Can it be that CFA made a mistake here? I’m confused whether the annual or semi-annual dividend should be subtracted. Did anyone have maybe a Heureka moment and figured it out? Thank you.

Can someone point me to where I can find this problem?

OP says it is “question 53 of the derivatives section on CFAI” but I only see 36 derivatives questions in the CFAI q-bank.

Hi , It’s in the afternoon session of CFAI Mock 2019, Question 47 in the Derivatives section;)

This question assumes that the dividends are paid right before the contract matures. In other words that the stock that would be delivered by the short would be ex-dividend. If so, the computations by sig make sense. Else, we would just ignore them dividends. Question should specify very clearly!

Hi CMLSML,

Your explanation make sense, however, I still do not understand why you would subtract the whole dividend amount. If a stock is paying 3 USD on a semiannual basis, i.e. 1.5 every 6 months, then (I would assume) the stock price would decrease only by 1.5 USD and not 3 USD after the dividend is paid. Any thoughts anyone?

Thanks:)