You can compute the capital appreciation using standard bond pricing formula either via duration (duration will do, for first order change, convexity is used for second order effect, which is negligible for < 1 year tenor zero-coupon bonds...) or discounting.

To quote one example, the last 6M T-bill I bid successfully was on 18th of July 2024: BS24106W ( https://www.mas.gov.sg/bonds-and-bills/auct...date=2024-07-23 ) has a cut-off yield of 3.64 p.a. with cut off price of 98.185. It will due next week on 21st Jan 2025 and the current 4-month risk free rate is, let's say somewhere between 12-week (3-month) MAS bill and 6-month T-bill, but closer to the 12-week bill.

6-month T-bill yields 3.03% p.a. from: https://eservices.mas.gov.sg/statistics/fda...ssuePrices.aspx
12-week MAS bill yields 3.18% p.a. from https://eservices.mas.gov.sg/statistics/mas...ssuePrices.aspx

We now linearly-interpolate the yield curve to find a 4-month risk-free rate (in discount rate notation): (3.03-3.18)/(6-3) = (4M rate - 3.18)/(4-3) -> 4M rate = 3.13% p.a.

So today, the same bill will have a price of 100*(1-0.0313*(122/365)) = 98.954 today which is an increment of some 0.79% in 2 month's time. If the yield has stayed at 3.64% p.a., you will expect the price to be 98.783 today, so the price change due to the drop in interest rate is 98.954-98.783 = 0.2%

You can double check this answer with the duration formula for change in zero-coupon bond prices. The Macaulay duration for ZCB is its tenor/time to maturity which is 1/3 years (4 months) in our case here, the modified duration is (1/3)/(1+0.037) = 0.32 (3.7% is the effective rate, converted from 3.64% discount rate*). When the yield drops from 3.64 to 3.13 = 0.51% decline, the price appreciation = 0.51% * 0.32 = 0.16% (which is about the same as the 0.2% price change we found earlier).

*Yield and price calculation Reference: https://williamlsilber.com/images/pdf/hando...easurybills.pdf

*Note: SG treasuries are issued at par value of 1000 SGD (except SSB, which has a minimum subscription of 500 SGD) and follows ACT/365 convention (unlike the 30/360 convention used in US t-bill markets). After adjusting for these discrepancies, the formula remains the same.

*Conversion from discount rate to effective yield can be seen in this paper: https://williamlsilber.com/images/pdf/hando...easurybills.pdf or the Excel spreadsheet attached

 6_Month_SG_T_bill_calculator.zip ( 8.75k ) Number of downloads: 3