Index=1350, rf = 4%, dividend yield/quarter = 1.25%, what’s the 90-day equity forward contract price?
~ 1353.23?
it is not correct, can you show your work?
1346.7
1359.185 if using continuous compounding
No credit for not showing your work, sorry that’s AF’s policy.
Sorry: 1350 x e^(4%-1.25% x 90/365). Correct?
assume rf is pa, per q 1 pct 1350 x 1.01 / 1.0125 = 1346.7
discrete not continuous.
Just noticed that you listed divs as quarterly not annually, so new formula would be: 1350 x e^(-1.25%) x e^(4% x 90/365) = 1346.44.
------- assume rf is pa, per q 1 pct 1350 x 1.01 / 1.0125 = 1346.7 -------- So, yo are saying that F = S0 (1+rf*(90/365)) / (1+dy)?
Or discrete = (1350 - 16.875) x (1+.04)^(90/365) = 1346.08
jcasey, that’s the exact answer.
Thanks. Back to studying for me. Still not finished with the curriculum - have futures, swaps, options, and PM to go.
jcasey, Obviously the timeing of the dividend payout matters . If you’re getting the 16.875 dividend today , then your answer is correct. But say I get the payout 90 days from now , I’d have to discount it to 16.226 and the FP is larger then You can get a range of values ( that differ very little from each other ) in between paying out today and paying out X days from now where X lies between 0 and 90
This is an index with many stocks paying dividends at different times. The assumption is that on average you are getting 1.25% of the index price in divided. A more interesting question is why base the dividend yield on the future value of the index and not on its current value?
what do you mean by base it on the future value of the index? the div is base on the current value 1350 since 1350 * 0.0125 = 16.875
For the record, if this problem had been based on a continuous compounding the answer I gave would be correct: Continuous rf = ln(1+.04) = 0.0392 Contiuous dividend yield = ln(1+(.0125*4)) = 0.0488 FP on Index = 1350 * e^(.0488 - .0392)*(.25) = 1,353.24 Just an FYI.
That’s nice…it can be viewed two different ways, but I like your interpretation. 1) 1350 x (1.04)^90/365 - 1350 x (1.04)^90/365*0.0125 so, it’s like calculating the dividend based on FV of S0, we are subtracting the dividend based on the future price. 2) 1350 x (1.04)^90/365 - (1350x0.125) x (1.04)^90/365 Which is the correct way of viewing it: FV of S0 - FV of dividends. Thanks for the insight!
jdane416 Wrote: ------------------------------------------------------- > For the record, if this problem had been based on > a continuous compounding the answer I gave would > be correct: > > Continuous rf = ln(1+.04) = 0.0392 > Contiuous dividend yield = ln(1+(.0125*4)) = > 0.0488 > > FP on Index = 1350 * e^(.0488 - .0392)*(.25) = > 1,353.24 > > Just an FYI. you switched the rates, fwd must be below spot…