Question: I highly appreciate your enlightening and inspirational writeups in the Punch Newspaper. I have come across the term ‘true yield’ in treasury bills which is usually higher than the actual rate. Please can you through more light on this?
Answer: Thanks for your question. To understand true yield in treasury bills, you need to place it side by side with other money market instruments like fixed deposits whereby you earn interest upon maturity. With treasury bills, you earn interest upfront, which means what you actually invest is less than the face value, hence your true yield calculation is based on the actual amount invested.
To further clarify, I will illustrate with an investment of N1Million for 364 days, fixed deposit vs treasury bills, assuming a 10% rate of return.
Starting with fixed deposits, your interest (I) in one year amounts to:
I = P x T x R/100 (where P is your sum invested, T is time in years and R is the interest rate)
So here goes:
I = 1,000,000 x 1 x 10/100 = 100,000.
In addition, you will be charged a withholding tax of 10% bringing your true yield to 9% (90,000)
For treasury bills, your upfront internet comes to the same thing:
I = 1,000,000 x 1 x 10/100 = 100,000.
This will be returned to you as interest while 900,000 will be booked for one year, so in effect, you are investing 900,000, and not 1,000,000 if you received a cashback of 100,000.
From the formula:
I = P x T x R,
R = I x 100/(P x T)
So your true yield becomes
R = 100,000 x 100/(900,000 x 1) = 11.11%
Please note that the actual time is 364/365 days. I used 1 to simplify the calculations. If you were calculating for a 91-day tenor, the time T would be 91/365, and for a 182 days tenor, 182/365.
Your yield becomes even higher if you reinvest your upfront interest instead of consuming it.
