Natural Leverage

Synthetics create leverage on the $NUMA token

Natural leverage refers to the leverage that is inherently part of holding the $NUMA token, 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 leveraged-long position against rETH. This occurs because of volatility in the value of outstanding synthetics. As the total value of oustanding synthetics increases, the leverage on the $NUMA token increases; the opposite is true when the value of outstanding synthetics decreases. This means that when the price of rETH increases, 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 on these price swings—furthering the efficiency 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 is a leveraged-long on 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 ❄️⚪️.

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