 # THE FUTURE: HUURLY INTEREST RATES?

Suppose that sometime in the not-so-distant future the fastest-growing financial institution in the world is Bank 24/7/52. Its success owes to pioneering use of hourly interest rates for loans and deposits, an idea borrowed from the success of the hourly car rental businesses. Its (add-on) rates on shortterm large time deposits (>\$1,000,000) are shown in Table 1.2. The APR quoted by Bank 24/7/52 assumes a 364-day year. For instance, 3.4944% is calculated as 0.0004% * 24 * 7 * 52.

TABLE 1.2 Hourly Interest Rates

 Time Period Rate per Hour APR 1-8 hours 0.0004% 3.4944% 9-24 hours 0.0005% 4.3680% 25-72 hours 0.0006% 5.2416%

To see how hourly interest rates might work, suppose a corporation makes a 52-hour, \$5,000,000 time deposit at Bank 24/7/52. The redemption amount on the deposit can be calculated using an hourly version of equation 1.3. The corporation will receive \$5,001,560 when the deposit matures. The fraction of the year no longer is the number of days divided by the assumed number of days in the year; it becomes the number of hours for the transaction divided by the assumed number of hours in the year.

Now suppose that 30 hours after making the time deposit, the corporation has sudden need for liquidity. Bank 24/7/52's policy is to buy back time deposits as a service to its regular corporate customers. The redemption amount is fixed once the deposit is issued. The present value of the time deposit after 30 hours have passed and 22 hours remain is again based on equation 1.3 but now solving for TV. Assuming no change in the bank's rates, the corporate customer receives \$5,001,010. Notice that this neglects the bank's bid-ask spread on money market transactions. In fact, Bank 24/7/52 likely would buy the deposit at a slightly higher rate (and lower price).

How did the corporation do on its short-term investment? The realized rate of return for its 30-hour holding period can be calculated with an hourly version of equation 1.4. That turns out to be 5.8822% on a 364-day add-on basis. Suppose that, for consistency, the money manager likes to convert all rates of return to a semiannual bond basis. Equation 1.9 can be used to convert that AOR to an SABB, but first one additional step is needed.

In general, interest rates should be put on a full-year, 365-day basis before carrying out the periodicity conversion. That is because an SABB having a periodicity of 2 implicitly assumes two evenly spaced periods in the 365-day year, each period having 182.5 days. (Notice that this assumption is implicit in equation 1.13.) So, first we need to convert 5.8822% to an addon rate for 365 days in the year by multiplying by 365/364. This rate is now an APR for 292 periods in the year: (365 * 24)/30 = 292. The holding-period rate of return converted to an SABB is 5.9856%. # CONCLUSION

There are a number of factors that can account for the difference between any two money market interest rates. Usually the rate spread is explained by differences in credit risk, liquidity, taxation, and time to maturity. This chapter has emphasized more technical and mathematical factors, such as the method of rate quotation, the assumed number of days in the year, and the manner in which the rate per time period has been annualized. Many interest rates reasonably summarize the two cash flows on a money market security – and a significant subset of those many rates actually are used in practice.

Money market interest rates can be misleading and confusing to those who do not know the differences between add-on rates, discount rates, and interest rates in textbook time-value-of-money theory. Some rates are relics of an era when interest rate and cash flow calculations were made without computers and use arcane assumptions such as 360 days in the year. Knowing only the quoted interest rate on a money market security is not sufficient. You must also know its quotation basis, its day-count convention, and its periodicity. Only then do you have enough information to make a meaningful decision. 