T-Rex Math
Are You Curious About T-Rex Math?
“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it” —Albert Einstein
The following illustration demonstrates the simple math behind T-Rex Scores.
You Invest: $100
Annual Rate of Return: 8%
Annual Fee: 2%
Reinvestment: All returns are reinvested at the same rate.
We will look at longer term numbers next, but first here are the cumulative results over 5 years:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Pre-fee Investment Value | $108.00 | $116.64 | $125.97 | $136.05 | $146.93 |
| Pre-Fee Gain | $8.00 | $16.64 | $25.97 | $36.05 | $46.93 |
| Investment Value You Keep | $106.00 | $112.36 | $119.10 | $126.25 | $133.82 |
| Gain You Keep | $6.00 | $12.36 | $19.10 | $26.25 | $33.82 |
| Fees Paid | $2.00 | $4.12 | $6.37 | $8.75 | $11.27 |
| Diminished Compounding Loss | $0.00 | $0.16 | $0.50 | $1.05 | $1.84 |
| Total Lost to Fees | $2.00 | $4.28 | $6.87 | $9.80 | $13.11 |
| T-Rex Score | 75.0% | 74.3% | 73.5% | 72.8% | 72.1% |
Total Loss to Fees
Your Pre-Fee Investment Value increases by 8% annually. Increasing $100 by 8% produces $108 (Year 1 gain of $8), increasing $108 by 8% produces $116.64 (Year 2 gain of $8.64), increasing $116.64 by 8% produces $125.97 (Year 3 gain of $9.33) and so on. While the rate of growth in percentage terms remains constant at 8%, the rate of growth in dollar terms constantly accelerates. This magical effect is known as compounding.
Given annual fees amounting to 2% of your investment balance are deducted by your investment provider, the Investment Value You Keep increases by only 6% annually. Increasing $100 by 6% produces $106 (Year 1 gain of $6.00), increasing $106 by 6% produces $112.36 (Year 2 gain of $6.36), increasing $112.36 by 6% produces $119.10 (Year 3 gain of $6.74) and so on. This constant 6% growth rate also produces an accelerating rate of growth in dollar terms. But it is a slower rate of acceleration. The difference between the pre-fee and post-fee rates of growth is your “Diminished Compounding Loss (DCL)”.
Cumulative Fees Paid + DCL = Total Lost to Fees
In other word, the the total amount you lose to fees includes not just actual fees paid but your DCL as well. T-Rex Scores capture the DCL effect.
Your T-Rex Score represents the percentage of your total investment returns you actually get to keep (Gain You Keep / Pre-Fee Gain). At the end of Year 1, your T-Rex Score is 75% ($6/$8). But, driven by an accelerating DCL, your T-Rex Score declines relentlessly over time.
Looking at T-Rex math for longer terms makes this abundantly clear.
| Year | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| Pre-fee Investment Value | $215.89 | $466.10 | $1,006.27 | $2,172.45 | $4,690.16 |
| Pre-Fee Gain | $115.89 | $366.10 | $906.27 | $2,072.45 | $4,590.16 |
| Investment Value You Keep | $179.08 | $320.71 | $574.35 | $1,028.57 | $1,842.02 |
| Gain You Keep | $79.08 | $220.71 | $474.35 | $928.57 | $1,742.02 |
| Fees Paid | $26.36 | $73.57 | $158.12 | $309.52 | $580.67 |
| Diminished Compounding Loss | $10.45 | $71.81 | $273.80 | $834.36 | $2,267.47 |
| Total Lost to Fees | $36.81 | $145.38 | $431.92 | $1,143.88 | $2,848.15 |
| T-Rex Score | 68.2% | 60.3% | 52.3% | 44.8% | 38.0% |
Total Lost to Fees
Notes:
Over long periods of time, compounding magic really kicks in. In this illustration, with an average rate of return of 8%, your Pre-Fee Investment Value more than doubles every 10 years. After 30 years, your Pre-Fee Investment Value is worth 10 times your original investment! But your T-Rex Score is just over 50%. Almost half your gains are lost to fees. Note that your 30 year DCL comprises the great majority of your Total Loss to Fees.
- Depending on actual rates of return, investments can produce astonishing results over long time horizons. But remember that, in addition to fees, you need to need to overcome the impact of taxes and inflation to produce real gains!
- T-Rex Scores demonstrate the impact of fees on investment performance. T-Rex Scores do not predict investment performance or future fee levels.
- For clarity and ease of understanding T-Rex math is simplified. The mathematical model assumes fees are deducted at the end of each year based on the your investment value at the beginning of that year. In practice, investment fees are calculated as a percentage of current value and deducted more frequently. As a result, T-Rex Scores are approximations which, assuming increasing investment values, will generally be slightly overstated.
- What happens to the DCL? Where does the money go? Your investment provider may use a portion of your fees to cover expenses or pay your advisor. But if your provider invested all fees upon receipt at the same rate (8%) for the same time period, their incremental investment gain would exactly match your DCL amount and their total income (fees + investment gain) would exactly match your Total Lost to Fees.