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Calculating an ACT/360 Money Market Forward Rate

Article Quant Q&A · Author: Winodd Dhamnekar
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Summary

The document explains how ACT/360 day-count conventions enter a money market forward-rate calculation. Under this convention, simple interest accrues using the actual number of days in the period divided by 360. The example equates growth from investing for 92 days at 8% and then for 182 days at an unknown forward rate with growth from investing for 274 days at 8%. Solving that relationship gives a forward rate of 7.84%.

The result does not match any of the multiple-choice options, so the answer choices or the stated answer appear inconsistent with the calculation shown. The discussion also clarifies that day-count conventions are technical conventions for measuring accrual, rather than a test of general financial aptitude. The example assumes the quoted rates use simple money market interest and the same ACT/360 convention throughout; it does not address other compounding or discounting conventions.

Key ideas

  • ACT/360 interest uses actual accrual days divided by a 360-day year.
  • A forward rate can be derived by equating compounded growth across sequential periods with growth over the full period.
  • The example's implied forward rate is 7.84%, which is absent from the listed choices.
  • The calculation assumes simple money market accrual for each rate period.

Tags

Fixed incomeDerivatives pricingStatistics
Full text
# Money market yield question


# Money market yield question












Assuming the 92-day and 274 day interest rate is 8% (act/360, money market yield) compute the 182- day forward rate starting in 92 days (act/360, money market yield).

1)7.80%

2)8.00%

3)8.20%

4)8.40%

Answer provided is 7.20%.

I don't understand the term act/360 given in this question. What is its meaning? How is this computation made? To answer this question, study of which topic in quantitative finance is necessary?

In my opinion, this question is useful for testing the financeIQ of the readers of this "Quantitative Finance stack exchange". Isn't it?

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/60992

Daycount conventions are rather a technical topic that does not test anyone’s ‘finance IQ’. Moreover, the readers of the site aren’t here to be tested, we are here to help those that wish to learn (site moderator can more clearly opine).

To answer your question, Act/360 is a daycount convention whereby the actual amount of interest paid equals the interest rate times a fraction equal to (number of days in the interest accrual period)/360. So in the question, if the forward rate to be found is $f$, we must have that a dollar invested for 92 days at 8pct, with the proceeds reinvested at the forward rate for 182 days, must give the same amount as investing for 274 days at 8pct. Thus, $$(1+0.08(92/360))(1+f(182/360))=(1+0.08(274/360))$$. Hence $ f=7.84pct $ which does not exactly match any of your answers.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.