By Tim Dulaney, PhD and Tim Husson, PhD
Earlier this month, SLCG finished a short research paper on the ubiquitous, but often overlooked, aspect of interest-bearing investments: day-count conventions. Day-count conventions (DCCs) refer to the various procedures used to compute the amount of time elapsed for the purposes of interest accrual. These conventions effect the payments we receive/pay on everything from mortgages to credit cards, from savings accounts to interest rate swaps.
Usually these conventions are written as a fraction with the numerator denoting the number of days in a month and the denominator denoting the number of days in a year. For example, the day-count convention ACT/360 computes the actual ('ACT') number of calendar days elapsed between two dates and then divides the result by 360 to determine the fraction of a year elapsed.
One may think that the amount of time elapsed between two dates was the same for every type of investment, but this is simply not the case. For example, the fraction of year between January 1, 2012 and February 1, 2012 is given by 0.0820 for 30/ACT and 0.0861 for ACT/360. Two people making interest payments based upon the same interest rate, but using different DCCs will end up paying a different amounts of interest and this effect can become large over the term of the interest-bearing security.
We point out that a person with an interest-bearing obligation would prefer a DCC with a larger denominator (30/ACT is preferred over 30/360) while a person with an interest-bearing asset would prefer a DCC with a larger numerator (ACT/360 is preferred over 30/360) for the same interest rate.
In our research paper, we study the effect of day-count conventions on interest rate swaps in particular since the DCC used on each leg of the agreement depends on the needs of the counterparties, and can therefore differ contract-by-contract. We show that the effect of a misapplied DCC is larger with a longer term of the agreement and that the effect is dependent more on the changes in expected future interest rates rather than the levels. We emphasize that the day-count convention can be used to hide an undisclosed transfer of wealth in a subtle, but important, way.
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