# YT (Yield Token)

## Introducing YT (Yield Token)

YT represents an asset that entitles the holder to the yield generated by an underlying yield-bearing asset (YBA) from now until a specific expiry date. In other words, each YT holder has the right to claim all the yield produced by one ST during this period. For example, holding one YT-mSOL-2412 means you own all the yield generated by 1 SOL staked on Marinade from today until December 28, 2024.

## YT Characteristics: A Time-Decaying Asset

YT is a time-decaying asset, meaning its value decreases as it gets closer to its expiration date. As the term shortens, the value of YT gradually trends towards zero. This happens because the YT consistently pays out yield to its holder, reducing the remaining future yield over time.

Since YT generates yield while it decays over time, if the yield received during the holding period exceeds the cost paid by the YT holder by the time it expires, the holder makes a profit. Conversely, if the yield received is less than the cost paid, the holder incurs a loss.

$$
\begin{split}
   PnL\_{holding\ period} &=YT\_{latest} + Cumulative\ Received\ Yield - YT\_{cost}  \\
      &=YT\_{latest} + Cumulative\ Received\ Yield - (YT\_{amortized} + YT\_{unamortized} ) \\
&=(Cumulative\ Received\ Yield - YT\_{amortized}) + (YT\_{latest} - YT\_{unamortized}) \\
&=Realized\ Net\ Yield\ + Market\ Value\ Change
\end{split}
$$

When holding a YT, your profit comes from two parts:

1\. Realized Net Yield: The difference between the yield received and the decrease in the YT’s value due to time decay (**time-amortized value**).

2\. Market Value Change: The difference between the current market value of YT and the holding YT’s **unamortized value**, which is calculated based on the purchasing implied yield and the new time to maturity.<br>

## **Implied Yield: The Key to YT Pricing**

The core variable in valuing YT is the implied yield, which reflects the expected return when holding the corresponding [PT](https://docs.rate-x.io/ratex/ratex-protocol/basic-concepts-of-yield-trading/pt-principal-token) until maturity. Since YT + PT = ST, selling the future yield of an ST (which is YT) leaves you with the PT. By holding the PT until it matures, you ultimately receive the ST. Thus, the selling price of the YT equates to the anticipated yield one would gain from holding the PT to maturity.

$$
ST=PT\times (1+Implied\ Yield)^{T}
$$

$$
PT = \frac{ST}{(1+Implied\ Yield)^T}
$$

$$
Price\_{YT} =ST-PT= ST-  \frac{ST}{(1 + Implied\ Yield)^T}=ST\times (1-\frac{1}{(1+Implied\ Yield)^T})
$$

If time to maturity is fixed, the price ratio of YT to ST can be represented as a univariate function of the implied yield. This relationship underscores how the YT/ST price ratio is directly influenced by the implied yield, serving as the sole determinant.

<figure><img src="https://4093451055-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fa2Rm35xpqcW5HfYXEdpV%2Fuploads%2FDiNJ0GWKyJxxdgXe2zEg%2Fimage.png?alt=media&#x26;token=36529566-532d-4c11-b179-c68d3ec7c49b" alt=""><figcaption></figcaption></figure>

<figure><img src="https://4093451055-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2Fa2Rm35xpqcW5HfYXEdpV%2Fuploads%2FI3flKsEXsnJHkbyRpXwL%2Fimage.png?alt=media&#x26;token=879a4be3-ffe2-4a0d-9a51-8401b3c3e505" alt=""><figcaption></figcaption></figure>

When you trade YT, you're essentially betting on **the future implied yield**.&#x20;


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