Introduction
A short sale creates two connected but distinct records. The seller receives cash when shares are sold, and also takes on an obligation to return an equivalent number of shares. Keeping those records separate is essential: the cash received does not make the share obligation disappear.
This tutorial uses a simplified accounting model to represent that position and track partial repurchases. It focuses on the cash ledger and the number of shares still owed—not on the position’s expiration payoff or investment return.
The Two Ledgers
The cash ledger records proceeds received from short sales and amounts paid to repurchase shares. The share ledger records the number of shares owed. A repurchase reduces both the cash balance and the outstanding share obligation, but the reductions are measured differently: cash changes by the repurchase price, while the share obligation changes by the number of shares bought.
Unless stated otherwise, assume a hypothetical short-sale account with no transaction costs, taxes, interest on cash, dividends, borrow fees, collateral changes, or margin requirements. Treat all listed prices as the transaction prices per share. In an actual account, proceeds may be restricted or subject to collateral arrangements; the simplified cash ledger here does not imply that the seller can freely withdraw them.
| Event | Cash ledger change | Short-share ledger change |
|---|---|---|
| Sell \(q\) shares short at \(S\) | Increase by \(qS\) | Decrease by \(q\) shares; record \(-q\) |
| Buy \(r\) shares to return | Decrease by the repurchase cost | Increase by \(r\) shares toward zero |
A useful sign convention is to record shares owed as a positive count, \(Q\), when calculating the remaining obligation. The corresponding signed stock position is \(-Q\). For example, owing 70 shares means \(Q=70\) and a signed position of \(-70\) shares. These are two descriptions of the same short position, not two separate obligations.
Opening and Updating a Position
If \(q\) shares are sold short at price \(S_0\), initial proceeds are \(qS_0\). If \(r\) shares are later bought at price \(B\) to return them, the cash ledger falls by \(rB\), and the remaining obligation falls by \(r\) shares. Thus, for one opening sale and one repurchase, the ledger balances are:
Here \(C\) is the cash balance after the transactions and \(Q\) is the remaining number of shares owed. A positive \(C\) does not mean the position is fully closed: the share obligation is zero only when \(Q=0\). If \(Q>0\), shares are still owed, even if the cash balance is large.
Why the Short Position Has a Negative Share Sign
The signed-share convention follows directly from the obligation. A long position of \(q\) shares represents ownership of \(q\) shares, so its signed quantity is \(+q\). A short position represents an obligation to deliver \(q\) shares rather than ownership of them, so its signed quantity is \(-q\).
At the opening of a short sale, the cash receipt and the share obligation are recorded separately. At the sale price \(S_0\), the cash amount is \(qS_0\); the market value associated with the negative share quantity is \(-qS_0\). Their sum is zero before costs or other cash flows:
This identity explains why the initial cash receipt alone is not a complete description of the transaction. The seller has received cash, but the matching obligation to return shares remains. This is an accounting representation at the opening price, not a statement that future prices or other cash flows cannot change the position’s value.
Multiply its share count by its transaction price to find the cash proceeds. Add the shares to the amount owed.
Multiply the repurchased share count by its transaction price. Subtract that cost from cash and subtract those shares from the amount owed.
The cash balance is measured in dollars; the remaining obligation is measured in shares. Confirm each has the correct unit and sign.
Worked Examples
Worked Example: Partial Repurchase From One Short Sale
A hypothetical investor sells 160 shares short at $42.50 per share. Later, the investor buys 60 shares at $39.00 per share to return them. Find the cash balance and the number of shares still owed. Ignore all fees and other cash flows.
Method. Keep a cash ledger and a share ledger. The common mistake to avoid is calculating the repurchase cost incorrectly or reducing the cash balance by the number of shares rather than by the dollar cost.
Step 1: Opening proceeds. The short sale produces \(160\times \$42.50=\$6,800.00\). The initial obligation is 160 shares.
Step 2: Repurchase cost. Buying 60 shares at $39.00 costs \(60\times \$39.00=\$2,340.00\).
Step 3: Update cash. The remaining cash balance is \(\$6,800.00-\$2,340.00=\$4,460.00\).
Step 4: Update shares owed. The remaining obligation is \(160-60=100\) shares.
Check. The repurchase cost is $2,340.00, not an amount based on the number 60 alone. The cash calculation is in dollars, and the remaining obligation is in shares. The result is a cash balance of $4,460.00 and 100 shares owed.
Worked Example: Short Sales at Two Prices
A hypothetical investor first sells 45 shares short at $72 per share, then sells another 55 shares short at $68 per share. The investor later buys 30 shares at $70 per share to return them. Find the cash balance after the repurchase and the remaining number of shares owed. Ignore fees and other cash flows.
Method. Add the proceeds of the separate sales, then subtract the actual repurchase cost. The common mistake to avoid is using an incorrect total for the opening proceeds or treating the shares sold at the two prices as different kinds of obligations.
Step 1: Proceeds from the first sale. \(45\times \$72=\$3,240.00\).
Step 2: Proceeds from the second sale. \(55\times \$68=\$3,740.00\).
Step 3: Total opening cash. \(\$3,240.00+\$3,740.00=\$6,980.00\). The initial obligation is \(45+55=100\) shares.
Step 4: Repurchase cost. \(30\times \$70=\$2,100.00\). The cash balance becomes \(\$6,980.00-\$2,100.00=\$4,880.00\).
Step 5: Remaining obligation. \(100-30=70\) shares.
Check. The proceeds add to $6,980.00, and the repurchase costs $2,100.00, leaving $4,880.00. The share count falls by 30, from 100 to 70. The result is a cash balance of $4,880.00 and 70 shares owed.
Worked Example: Several Repurchases at Different Prices
A hypothetical investor sells 80 shares short at $31.40 per share and, later, another 50 shares short at $34.20 per share. The investor then buys 60 shares at $32.50 and 25 shares at $36.00 to return them. Find the resulting cash balance and remaining obligation. Assume no fees, interest, or other cash flows.
Method. Total all sale proceeds and all repurchase costs separately, then update the share count. The common mistake to avoid is using one repurchase price for all shares when the purchases occurred at different prices.
Step 1: First sale proceeds. \(80\times \$31.40=\$2,512.00\).
Step 2: Second sale proceeds. \(50\times \$34.20=\$1,710.00\). Total proceeds are \(\$2,512.00+\$1,710.00=\$4,222.00\), and 130 shares are owed.
Step 3: First repurchase cost. \(60\times \$32.50=\$1,950.00\).
Step 4: Second repurchase cost. \(25\times \$36.00=\$900.00\). Total repurchase cost is \(\$1,950.00+\$900.00=\$2,850.00\).
Step 5: Update cash and shares. Cash is \(\$4,222.00-\$2,850.00=\$1,372.00\). The total repurchased is \(60+25=85\) shares, so \(130-85=45\) shares remain owed.
Check. The two sale quantities total 130 shares, and the two repurchase quantities total 85, leaving 45. The dollar ledger uses each transaction’s own price, producing a cash balance of $1,372.00. The position still has an obligation of 45 shares.
Common Mistakes and Exam Traps
- Calling all opening proceeds profit. Proceeds are the cash received at the short sale. They do not, by themselves, account for the obligation to return shares.
- Using the current price to change historical proceeds. The cash originally received is calculated from the sale price at the time of that transaction. A later price does not alter that ledger entry.
- Mixing dollars and shares. Repurchase cost changes cash; repurchased quantity changes shares owed. Keep the units visible in each calculation.
- Assuming a partial repurchase closes the whole position. If the investor sells 100 shares short and buys 30 to return, 70 shares are still owed.
- Applying one price to every transaction. If sales or repurchases occur at different prices, calculate each transaction separately before summing the dollar amounts.
The distinction matters whenever a problem gives several transactions or asks for an intermediate account position. A reliable solution labels the dollar balance and share obligation separately at every step. This tutorial’s simplified model intentionally leaves out items such as dividends, borrow costs, and cash interest; those would require additional cash-flow entries rather than changing the basic distinction between cash and shares owed.
Check Your Understanding
For each hypothetical account, assume no fees, interest, dividends, collateral changes, or other cash flows. Track cash and shares separately.
- An investor sells 90 shares short at $26.40 and later buys 20 shares at $24.75 to return them. Find the cash balance and shares still owed. (Answer: cash balance $1,881.00; 70 shares owed)
- An investor sells 35 shares short at $51.20 and 25 shares at $49.60. The investor then repurchases 18 shares at $50.50. Find the cash balance and shares still owed. (Answer: cash balance $2,123.00; 42 shares owed)
- An investor sells 200 shares short at $18.75, then repurchases 75 shares at $17.20 and 40 shares at $20.10. Find the cash balance and shares still owed. (Answer: cash balance $1,656.00; 85 shares owed)
- An investor sells 60 shares short at $84 and then another 40 shares at $90. The investor buys 25 shares at $88 and later 30 shares at $82 to return them. Find the cash balance and shares still owed. (Answer: cash balance $3,980.00; 45 shares owed)
- An investor sells 125 shares short at $63.20, then buys 40 shares at $58.75 and 50 shares at $66.40 to return them. Find the cash balance and shares still owed. (Answer: cash balance $2,230.00; 35 shares owed)