Interest rates of Savings Bonds - A technical explanation

Determining Step-up Coupon Rates

Coupon rates for each issuance of Savings Bonds are determined such that the return over an investor’s investment period is linked to long-term Singapore Government Securities (SGS) yields. The investor’s average annual compounded return over a holding period (e.g. 5 years) should correspond to yield to maturity of a corresponding SGS (e.g. 5 year SGS). There may be two exceptions to this:

  1. The first exception is due to very small rounding differences of up to +/- 0.03% that may arise in the computation of average returns for Savings Bonds.
  2. The second exception may arise from time to time if the shape of the SGS yield curve does not allow the interest rates to step-up. In such instances, the design of the Savings Bond prioritises the “step-up” feature of the interest rates over the matching to SGS yields for a given year (explanations below). This is because the objective of the Savings Bond programme is to encourage and facilitate long-term savings and investment. An adjustment is made so that the interest payments do not step down in any year. This adjustment does not affect the return on the Savings Bond if it is held for the full 10 years.

For the purpose of calculating the Step-up Coupon rates for Savings Bonds, the 1, 2, 5 and 10-year benchmark SGS yields are used as reference. These reference yields will be based on the simple average of the respective daily SGS benchmark yields from the month before the public notice of issuance (the “reference SGS yields”), as provided on the “Daily SGS Prices” page of the SGS website . Reference SGS yields for tenors between the benchmark issuances are interpolated using a hermite spline function.

The coupon rate for each year of the Savings Bond’s tenor shall be derived from the SGS reference yields as follows:

Savings Bond coupons satisfy the no-arbitrage rule, in that (i) the bond can be redeemed at any point of time at a face value of 1, (ii) the bond pays the same effective yield as a SGS bond for the same holding period.

Simplifying assumptions: Assume one coupon paid at the end of each year (In practice, there are two coupons each year, which are half of the coupon rate as determined by the calculation below).

Step-up formula

Adjustments to Coupon Rates to Maintain Step-Up Interest Feature

Depending on the shape of the prevailing SGS yield curve, there may be certain occasions where the reference SGS yields do not allow a particular Savings Bond issue to have a monotonically increasing step-up interest feature (i.e. the implied coupon rates based on the reference SGS yields may decrease over part or all of the issue’s tenor). These occasions could occur when:

  1. Some or all of the longer-dated reference yields are lower than shorter-dated reference yields (an “inverted yield curve”); and/or
  2. A particular reference yield is much higher than the one immediately before it, but not much lower than the one immediately after (e.g. the five-year yield is much higher than the two-year yield, but not far below the ten-year yield). This is known as a “highly convex yield curve”.

Should the reference yields not allow for step-up coupons, MAS shall lower the coupon rates by the minimum amount necessary (subject to the mathematical programming function below), to maintain a weakly monotonically increasing step-up coupon schedule. This is in line with the intent of Savings Bonds, which are to encourage long-term savings. This adjustment is akin to reducing the size of the coupons in earlier years, and increasing the size of the coupons in later years, while adjusting for the time value of money based on the risk-free discount rates.

Adjusted coupon formula

These adjustments may cause the average annual compounded return on the particular Savings Bond issue over 1, 2 or 5 years to be less than the 1, 2 and 5-year reference yields. However, the adjustments will not affect the issue’s return if held to maturity, which shall always equal the 10-year reference yield (subject to slight differences of up to +/- 0.03% due to rounding in the computation of the step-up coupons).

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