How PT and YT are priced

This page walks through the maths behind PT and YT with one example, from the first split to maturity. You do not need any finance background.

Note

The main example uses a 50% yield so the numbers are easy to follow. Real gold yields are far lower (the Gold Term Curve uses about 2–3%). The logic is identical at any rate. For simplicity, 1 PAXGy is treated as worth 1 PAXG at the start.

Step 1 — From a rate to a growth factor

A yield of 50% written as a number is 50 ÷ 100 = 0.50.

After one year you have what you started with plus 50% of it:

10 + (10 × 0.50) = 10 + 5 = 15
10 × (1 + 0.50)  = 10 × 1.50 = 15

So 1.50 = 1 (what you had) + 0.50 (the yield). In general:

growth factor = 1 + rate ÷ 100

Yield	Rate ÷ 100	Growth factor	10 PAXG become
50%	0.50	1.50	15
10%	0.10	1.10	11
2%	0.02	1.02	10.20
2.80%	0.028	1.028	10.28

• Multiplying by the factor moves a value forward one year (today → maturity).
• Dividing by the factor moves a value back one year (maturity → today).

Step 2 — Without Aureus

You hold 10 PAXGy yielding 50% a year. After one year you have the equivalent of 15 PAXG:

• 10 PAXG of principal (the gold);
• 5 PAXG of yield earned during the year.

Aureus separates these two pieces today, before the year passes:

• the 10 PAXG of principal become 10 PT;
• the 5 PAXG of future yield become 10 YT.

Step 3 — The price of PT

10 PT pay exactly 10 PAXG in one year. Their value today is the amount that, growing at 50%, becomes 10:

PT today × 1.50 = 10   →   PT today = 10 ÷ 1.50 = 6.67 PAXG

Check: 6.67 × 1.50 = 10. Whoever buys the 10 PT at 6.67 and waits a year receives 10: a 50% return, fixed in advance.

For maturities other than one year, the factor is raised to the fraction of a year:

PT price = 1 ÷ (1 + rate) ^ (days ÷ 365)

180 days at 2.55%:  1 ÷ 1.0255 ^ (180 ÷ 365) ≈ 0.9877
1 year at 2.80%:    1 ÷ 1.028                 ≈ 0.9728

Reading it the other way round gives the implied rate that Aureus shows on the curve:

rate = (1 ÷ PT price) ^ (365 ÷ days) − 1

Step 4 — The price of YT

10 PT and 10 YT come from 10 PAXGy, which are worth 10 PAXG today. So YT is what is left:

10 YT = 10 − 6.67 = 3.33 PAXG

The same result another way: the 10 YT will collect 5 PAXG in one year, and 5 ÷ 1.50 = 3.33.

So 3.33 is today’s price of 5 PAXG of future yield. It is not 5 because you pay today and collect later: nobody would pay 5 now to receive 5 in a year when holding PAXGy would turn that 5 into 7.50.

With the realistic 1-year rate of 2.80% the same steps give PT ≈ 9.73 and YT ≈ 0.27 for 10 PAXGy, which is the example used on the Aureus website.

Step 5 — Why the market lands on these prices

Aureus does not set these prices. They are the prices at which PT and YT trade in the pools. What keeps them consistent is that anyone can split PAXGy into PT + YT, or merge PT + YT back into PAXGy. So PT + YT must be worth about the same as PAXGy, otherwise there is free money:

• If 10 YT traded at 5: deposit 10 PAXGy, sell 10 YT for 5 and 10 PT for 6.67, and collect 11.67 for something worth 10. People would keep doing this, selling YT until its price falls.
• If 10 YT traded at 1: buy 10 PT for 6.67 and 10 YT for 1 (7.67 in total), merge them into 10 PAXGy worth 10. People would keep buying YT until its price rises.

Prices settle where this free profit disappears. The implied rate on the curve is then simply read from the PT price.

Step 6 — How the values move over time

If the yield stays at 50% all year:

Moment	Vault value (10 PAXGy)	10 PT price	10 YT price	Yield already collected by YT	Total
Split (today)	10.00	6.67	3.33	0	10.00
After 6 months	12.25	8.16	1.84	2.25	12.25
Maturity (1 year)	15.00	10.00	0	5.00	15.00

• PT rises from 6.67 to 10: its discount closes as maturity approaches.
• The YT price falls from 3.33 to 0, because less and less future yield is left to collect.
• The yield collected by whoever holds YT rises from 0 to 5.
• The total always matches the PAXGy. Aureus does not add or remove value; it only separates it.

Why 2.25 after six months and not 2.50? The 50% is an annual, compounding rate. Over half a year the factor is √1.50 ≈ 1.225, so 10 PAXGy grow by about 2.25. It would be 2.50 only if yield accrued in a straight line.

For someone holding the 10 YT, the value is collected yield + current YT price: 3.33 today, about 4.08 after six months (2.25 + 1.84), and 5 at maturity. That is the same 50% growth.

Step 7 — When the actual yield differs from the price

Prices reflect what the market expects. At maturity, PT always pays its fixed principal and YT collects whatever yield was actually generated. All the difference lands on YT.

Suppose the market priced 10 YT at 3.33 (a 50% expectation). Compare buying YT with simply putting the same 3.33 PAXG into PAXGy:

Actual yield over the year	10 YT collect	Result for the YT buyer	3.33 PAXG held as PAXGy become	Result for the PAXGy holder
0%	0	−3.33 (−100%)	3.33	0%
20%	2.00	−1.33 (−40%)	4.00	+20%
50% (as expected)	5.00	+1.67 (+50%)	5.00	+50%
80%	8.00	+4.67 (+140%)	6.00	+80%

• If the yield matches the expectation, buying YT earns the same as holding PAXGy.
• YT pays off only if the yield turns out higher than the market expected, and it loses, even when gold still yields something, if the yield is lower.
• With 3.33 PAXG, a YT buyer gets the yield of 10 PAXGy: YT works as leverage on gold yield, in both directions.

The seller of those YT, meanwhile, has fixed their result: 3.33 received today plus 10 PAXG from PT at maturity, whatever happens to the yield.

Step 8 — How YT holders actually collect the yield

The vault does it automatically with simple accounting:

1. PAXGy grows on its own. Its value in PAXG rises as yield accrues. After six months, the 10 PAXGy in the vault are worth about 12.25 PAXG.
2. The vault splits the value. 10 PAXG are reserved for PT holders; everything above that belongs to YT holders.
3. The vault remembers when each holder got their YT. It keeps a running index that rises with PAXGy’s value. Each holder’s accrued yield is YT balance × (index now − index when they received the YT).
4. When YT changes hands, the account is settled. The seller is credited the yield accrued up to that moment and can claim it at any time. The buyer starts accruing from zero.

Nobody distributes yield by hand. Holders see their accrued yield in the app and claim it whenever they want. At maturity, PT redeems for its principal and YT holders have collected all the yield, shared according to who held the tokens and for how long.

Step 9 — Maturity is a fixed date

Every PT and YT belongs to a maturity with a fixed calendar date, the same for everyone. A 1Y market opened on 28 Sep 2026 issues tokens that mature on 28 Sep 2027, regardless of when anyone buys them.

Buying later means buying less time. Three months after opening, only nine months of yield are left, so YT trades for less. At 2.80%, the YT on 1,000 PAXGy is worth about 27.2 PAXG at opening and about 20.9 PAXG with nine months left, if rates have not moved. If rates have moved, the price reflects the new expectation: about 29.9 at 4% or 7.5 at 1% for the same nine months.

See Maturities for how new maturities are opened.

Step 10 — Gold price is not gold yield

YT carries only the yield. It never carries the gold price.

PT redeems in PAXG, so if the price of gold rises, the 10 PAXG the PT holder receives are worth more. That gain stays with the principal. If gold’s price falls, that loss stays with the principal too. YT holders are exposed to gold rates, not to the gold price.

All values on this page are examples, rounded, and not quotes or forecasts.