# 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 *P _{1}=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: P_{2}=P_{1}*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”: *(P _{1}+P_{2})/2=(P_{1}+P_{1}*g)/2=P_{1}*(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.