Let's take this example and convert it to a generalized algebraic formula. I'll use these variables:
- TBP = 6 month T-Bill Price ("break even" price compared to a bond unit trust)
- LM = Lost Months of SA interest with bond unit trust-based shielding (either 1 or 2)
- R = CPF SA interest rate (floor rate of 4.00%, currently 4.08%)
That gives us an algebraic equation of:
- TBP * [(7-LM)/12] * R = 1000 - TBP
I assume you are only going to consider 6 month T-bills that only result in the loss of 7 months of SA interest, not 8 months. (A safe assumption!) OK, let's rearrange the equation to solve for TBP:
- TBP + TBP * [(7-LM)/12] * R = 1000
- TBP * [1 + (7-LM)/12 * R] = 1000
- TBP = 1000 ÷ [1 + (7-LM)/12 * R]
Now let's test this algebraic equation using LM = 2 and R = 4.08%:
- TBP = 1000 ÷ [1 + (7-2)/12 * 0.0408]
- TBP = 1000 ÷ (1 + 5/12 * 0.0408)
- TBP = 1000 ÷ (1 + 0.017)
- TBP = 1000 ÷ 1.017
- TBP = $983.28
OK, so that's the "break even"
price for a 6 month T-bill in this scenario (2 months of lost SA interest with the bond unit trust-based shielding method because your birthday is too close to the beginning or end of the calendar month, 4.08% SA interest rate). Let's round that up to $983.50 (add a few cents) because a bond unit trust could wobble in price for the few days you hold it, so you might reasonably prefer to take the "sure deal" of the T-bill even if it's a little more expensive than the "break even" price. Now let's convert that to a Cut-Off Yield (COY) for competitive T-bill bidding purposes. This COY formula may be approximate but will be "close enough," and note there are 366 days this year (2024 is a leap year)....
- (risk-adjusted) TBP = $983.50
- COY = (366÷183) * (1000 - TBP) ÷ 1000
- COY = 366÷183 * 16.50 ÷ 1000
- COY = 3.30%
So
in this example (LM=2, R=4.08%) you should be at least happy enough using a 6 month T-bill with a cut-off yield of 3.30% or higher for your SA shielding purposes.
Someone please double check my algebra!