Making Gains in Bear Markets: Leveraged Shorts
Shorting is a great mechanism to obtain gains when markets turn sour. DeFi allows for the addition of leveraging into short crypto positions. Let’s see how this is done.
Consider an initial position of $S ($=USDC) dollars. We wish to take a short position on some crypto asset called X. For example X=ETH. For this, we borrow against our USDC with leverage equal to: L. This means we borrow D=(L-1)*S in the amount of asset X. Our total initial position (equity) is hence equal to P1=L*S. We’d like to enter a liquidity pool (LP) in the tokens: X-USDC. Since the LP is balanced (50:50) we must sell a portion of our X token (to USDC) prior to entering the pool. Calculating this amount is simple: we have (L-1)*S in the asset X. We need to reduce this to L*S/2. So we must sell the difference: (L-1)*S-L*S/2 = S(L/2-1) worth of X into USDC.
Let’s put some numbers to the variables to make things clear. Say S=$10,000 and X=ETH trading at $2,000 per X. We want to borrow at leverage L=3. This means we borrow (L-1)*S=(3-1)10,000 = $20,000 worth of X which would amount to: 10ETH. Our total initial position is: $10,000+10ETH = $30,000. This is unbalanced. We need $15,000 (USDC) plus $15,000 (worth of ETH) to enter the ETH-USDC LP. We have more ETH than we need, hence we need to immediately sell $5,000 worth of E (i.e. 2.5ETH). Now we have: $15,000+7.5ETH and can enter the LP.
Question: How does our equity change when the borrowed asset price fluctuates?
Fortunately there is a simple formula that answers this question: P2=P1*g, where g = (1+d)1/2 is the LP-gain and d is the % change in the borrowed asset.
Coming back to our example… Say the price of ETH drops by 1% (from $2,000 to $1,800). Our position would then be valued at (approximately): $30,000*0.998 = $29,850, i.e. we’re down $150.
This however is not the end of the story… We need to account for: i) yield faming gains, and ii) borrowing interest loss.
i) Yield faming gains: These gains arise from trading fees we receive as incentive for participating in the LP. Let’s say the price fluctuation of X happens during a T day interval and during this time the we accrue an effective APR of a%. The starting point on which the yield farm APR is accrued is not simply our initial total position since our position fluctuates during the T days. So as an approximation we can take the mid-point (average) between our initial and final position values as the starting point for the APR accrual. We will call this our “average position”: (P1+P2)/2=(P1+P1*g)/2=P1*(1+g)/2=L*S*(1+g)/2. So our gain from yield faming is: 0.5*L*S*(1+(1+d)1/2)*(exp(a*T/365)-1).
ii) Borrowing interest loss: A similar calculation follows for our debt. We borrowed D=(L-1)*S. The loss factor is now g = 1+d since the debt is calculated outside of the LP. Assuming a borrowing interest of d%, the debt after T days is: 0.5*(L-1)*S*(2+d)*(exp(b*T/365)-1).
The effective total second position (equity or E) after taking yield farming and borrowing interest into account is then:
E = L*S*(1+d)1/2+0.5*L*S*(1+(1+d)1/2)*(exp(a*T/365)-1)-(L-1)*S*(1+d)+0.5*(L-1)*S*(2+d)*(exp(b*T/365)-1)
To gain insight into this complicated formula we plotted the equity versus d below for nominal values of S=10,000, L=3, T=30, a=40%, b=20%.
Notice how we gain even when the borrowed asset loses value. This makes sense given that we have effectively taken a leveraged short position on the asset.
If you want to learn more about short leverage farming and how you can put it to use in a bear market schedule your free consultation with our experts today.