Rudimentary errors in Central Bank’s Treasury Bill reports

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

24 August 2025

The weekly treasury bills auction report published by the Central Bank of Kenya (CBK) has some fundamental mathematical errors. I have brought these to the attention of the bank at least twice in the past but it has not corrected them; so, now it’s time to go public.

The report compares the weighted average interest rate for the current and previous auctions and then shows the change between the two. Unfortunately, it does not indicate whether the change is an increment or a decrement. It only shows a number. For example, in the report of 18th August 2025, the average interest rate for the 91-day T-Bill was 8.0107 per cent while the previous week it was 8.0799pc. The change is shown as simply “0.0692”.

But when we work it out the change (8.0107 – 8.0799) we get –0.0692. That is, a negative number – signifying a decrease. But the value in the CBK report is positive which signifies an increment. This is wrong. A very rudimentary mistake!

Furthermore; this change in interest rates is labelled as “variance”. Now, in mathematics, variance is not the same thing as change or difference. Variance is a statistical quantity that gives information about how scattered a set of values is. It is calculated as follows:-

Consider a set comprising of the numbers 79, 80, 81, 82. The mean (average) is 80.5. Now think about another set with 70, 80, 81 90; the mean is also 80.5. But the second set is more widely scattered than the first one.

To find the variance, we start by working out the difference between each number in a set and the mean. In the first set, this comes to 1.5, 0.5, -0.5, -1.5 respectively. Next, we square each of these values; thus, we get, 2.25, 0.25, 0.25, 2.25. Notice that working out the squares removes the negative signs.

Finally, we work out the mean of these squared values. The variance comes to 1.25. Doing similar calculation for the second set yields 55.75. The fact that 55.75 is greater than 1.25 tells us that the second set is more scattered than the first one – a fact that can be ascertained by casual observation. This is not what the CBK T-Bill report is referring to!

I think that this is a case of some one at the CBK trying to sound sophisticated, but messing things up in the process. I therefore suggest that they simplify the wording to read “Change” instead of “Variance”; and don’t forget the positive/negative sign in the answer!