Natural Leverage

Synthetics create leverage on the $NUMA token

Natural leverage refers to the leverage that is inherently part of holding the $NUMA token instead of ETH. This leverage is derived from the $NUMA pricing formula and is perpetual and naturally occurring, so long as nuMoney is minted. This natural leverage is also non-liquidatable, which is distinct from opening an explicitly leveraged position, such as opening a 10x long or short.

By holding the $NUMA token, users are exposed to a naturally leveraged-long position on the performance of ETH versus the aggregate value of issued nuMoney. As the proportion of the Vault's total collateral is used to mint nuMoney synthethics, the leverage on the $NUMA token increases. The opposite is true when the proportion of nuMoney is reduced. With natural leverage in the system, whenever the price of ETH increases with respect to the issued nuMoney, the price of $NUMA will increase even more. The opposite is also true when the price of rETH decreases.

This leverage creates more volatility in the $NUMA token, which creates more arbitrage opportunities between the LP and the vault. As such, the protocol capitalizes on this volatility and increases the rETH backing of the $NUMA token every buy and sell—furthering the effect of the collateral snowball.

Here are some examples of how natural leverage operates in the numa protocol—

Let’s say the vault contains $1,000,000 in rETH, and the total synthetics value is $500,000: the price of $NUMA is $1, since there are 500,000 $NUMA in circulation.

If rETH goes up 10% in value and the synthetics value stays at $500,000, the vault would then be worth $1,100,000. And the value of $NUMA would then be $1.20 (+20%), since the price of $NUMA is the vault value minus the synthetics value, divided by the number of $NUMA in circulation.

$1,100,000 (vault value) - $500,000 (synthetics value) = $600,000 ($NUMA backing)

$600,000 ($NUMA backing) / 500,000 ($NUMA tokens) = $1.20 ($NUMA price)

Now, let’s say some people decide to take profit on this move and mint $nuUSD, so the vault value is still $1,100,000, but the synthetics value would increase to $700,000. Now, there would be ~333,333 $NUMA in circulation, since some were burnt to mint $nuUSD. Then, rETH makes another 15% move up, while the synthetics value is flat again. In this case, the vault would then be worth $1,265,000, and the price of $NUMA would increase to ~$1.70 (+41%). In the two moves up, rETH increased a total of 27%, while the natural leverage of the $NUMA token provided a ~70% increase in price.

$1,265,000 (vault value) - $700,000 (synthetics value) = $565,000 ($NUMA backing)

$565,000 ($NUMA backing) / 333,333 ($NUMA tokens) = ~$1.70 ($NUMA price)

What about if rETH goes down? Let’s start with the $1.70 $NUMA price, $1,265,000 vault value, and $700,000 synthetics value again. If the price of rETH drops 10%, then the vault value would drop to $1,138,500, while the synthetics remain at $700,000: the price of $NUMA would then be ~$1.31 (-23%). The drop in $NUMA was greater than the drop in rETH, since the $NUMA token has leveraged exposure to rETH. However, unlike explicitly leveraging, the long position of the $NUMA token can’t get liquidated, such that $NUMA can be held indefinitely as a proxy for an rETH long.

$1,138,000 (vault value) - $700,000 (synthetics value) = $438,500 ($NUMA backing)

$438,500 ($NUMA backing) / 333,333 ($NUMA tokens) = ~$1.31 ($NUMA price)

These examples are not exhaustive and are merely meant to show how the natural leverage works. In reality, there are a lot more factors involved, including explicitly leveraged long and short positions being opened, closed, and liquidated. There will also be constant volatility in the synthetics value as a ratio compared to the vault value. Further, the static value of the LP against the volatility of the $NUMA token should force a lot of arbitrage vault volume, which increases the rETH backing of the $NUMA token ❄️⚪️.