Gross Equivalent Yield Example
This example compares the strcture of payoffs for the bonds against a regular and fixed-term savings account, displays what is meant by Gross Equivalent Yield (GEY) in a more rigorous sense.
For the purposes of this example, the tax rate is set at 45% (additional rate).
Note: we have rounded values to 2dp, so may not add up correctly.
Bond
The bond here is free of capital gains tax, so could be a UK Government
Bonds (Gilt) or Qualifying Corporate Bond (QCB).
For technical people, coupons are not reinvested here, meaning this is a lower bound for GEY
(the actual return will be even better).
- Price: £85.51
- Face Value: £100.00
- Coupon: 0.250%
- Time to Maturity: 3 years
| Year | Gross Gain (£) | Net Gain (£) |
|---|---|---|
| Year 1 | 0.25 (Coupon) | 0.14 (Coupon) |
| Year 2 | 0.25 (Coupon) | 0.14 (Coupon) |
| Year 3 | 0.25 (Coupon) + 14.49 (Capital Gain) | 0.14 (Coupon) + 14.49 (Capital Gain) |
| Total | 15.23 0.75 (Coupon) + 14.49 (Capital Gain) |
14.90 = 0.41 (Coupon) + 14.49 (Capital Gain) |
| Net Return | 14.90/85.50 | 17.43% |
Regular Savings Account
The regular savings account is what one would typically hold in a bank. The interest earnt per year is increasing as it is compounding.
- Holding time: 3 years
- Annual Earning Rate (AER): 10.00%
| Year | Gross Gain (£) | Net Gain (£) |
|---|---|---|
| Year 1 | 8.55 (Interest) | 4.70 (Interest) |
| Year 2 | 9.02 (Interest) | 4.96 (Interest) |
| Year 3 | 9.52 (Interest) | 5.24 (Interest) |
| Total | 27.10 (Interest) |
14.90 (Interest) |
| Net Return | 14.90/85.50 | 17.43% |
Fixed-Term Savings Account
This is when you lock your money away in a savings account for a certain amount of time. All interest income is taxed at the end of the term, hence the net gain column is empty. As in the regular savings account, interest earnt per year is increasing as it is compounding.
- Holding time: 3 years
- Annual Earning Rate (AER): 9.61%
| Year | Gross Gain (£) | Net Gain (£) |
|---|---|---|
| Year 1 | 8.22 (Interest) | - |
| Year 2 | 9.01 (Interest) | - |
| Year 3 | 9.87 (Interest) | - |
| Total | 27.10 (Interest) |
14.90 (Interest) |
| Net Return | 14.90/85.50 | 17.43% |
All three investments (bonds, regular savings, fixed-term savings) achieve the same net
of 17.43% (equivalent to 5.50% net AER).
This is precisely the concept of GEY, the equivalent interest rate required
in a savings account to achieve the same return as a bond with specific parameters.
The effecive tax rate for the bond is (15.23-14.90)/15.23=2.17%
and for both savings accounts it is (27.10-14.90)/27.10=45%, the marginal tax rate of the individual.