# Want to Rebalance Your Short Positions? Here’s How.

By Wayne Weddington, Contributing Editor,* Library for Smart Investors,* November 1, 2017

Short-selling is an extremely important tool in the investor's toolkit. And it is a critical component of market liquidity. A 'buy-only' market gets bloated and is subject to volatile dislocations, a deleterious boom-bust cycle. The upswings feel great until they turn and bite.

The security short-sale answers the question: what would you do if you expected a stock or the Market to decline? The answer is that the investor would short the stock or the Market, which is the practice of selling securities (borrowed from the broker, but not owned by the investor) with the hope to purchase it back at a lower price. It is the inverse of the well-regarded (and quite profitable) principle to buy-low and sell-high. Short selling is the aspirational trade to sell 'high' and buy 'low' which can also be quite profitable. (Note: it is slightly more volatile trade because markets basically trade and trend up. Short sell cover opportunities generally occur over shorter time periods than market expansions.)

In the current lexicon of do-it-yourselfers in the market, it would not be unlikely that the average investor would have a short or two in his portfolio. She may even have several names, or he may have a goal for a dollar-equal short versus long. You know who you are so no need to explain all of the varieties here.

But what is less appreciated are the peculiarities to maintain a profitable short position. Many investors engage a rebalance strategy that results in lesser profitability by inadvertently trading an imbalance in the desired short market exposure. The maintenance of a short portfolio is not intuitive. Trading intuition in a short position rebalance results in the oft-derided investment strategy to buy-high and sell-low, a strategy I would not recommend at all. It is a proven loser.

This author is going to get a little wonky in the balance of this article, but before that let us discuss the core mistake with a simple example. Suppose you wanted to maintain a portfolio that was long AAPL $10,000 and short IBM $10,000 over the past year. Every quarter you would rebalance so that each position was equal to the other. To re-balance the long AAPL position is intuitive. If, for example, the market value increases to $12,000 next quarter, you would sell $2,000 to restore it to $10,000. If the position declined to $9,000, you would purchase $1,000. It is obvious because the Net Asset Value of the position is embedded in the long position. But it is not as simple for the short.

If for example the IBM market value increased to $12,000 next quarter, the temptation would be to buy $2,000 to restore the absolute market value from $12,000 to $10,000, taking a loss. But the opposite holds true. Just as with the long position, you would sell $2,000 to restore the net asset value ($10,000 cash 'benefit' minus $2,000 unrealized loss) to $10,000. If the position declined to $9,000, you would purchase $1,000 and take a profit.

It preserves the time-honored and liquidity-honored principle to buy 'low' and sell 'high.'

## The Wonky Follows:

Below is one simple scheme for initiating and maintaining the short side of your investment portfolio.

The goal is to achieve a dollar rebalance scheme to reconcile the difference between the current market value of the Long and Short Positions of a portfolio and the target capital exposure to be allocated to each position. Normally, these schemes consider only the open market value of the positions prior to re-balance, that is p*n where p is current price and n is current position. We propose something slightly different.

The market value of the positions is only a fraction of the picture. Instead, we should use the total cost of the position (“C”) plus the actual value of the profit/loss on the position (“PL”). Together they present a value representing the total capital allocation (“CA”) and it correctly determines the true value of capital allocated for both Long and Short Positions. While this method is indistinguishable from the traditional methodologies on the Long side (since 'CA' and the market value are equal), it manifests a counter-intuitive notion of capital allocated for the Short Positions: it values the resultant cash that redounds to your account by selling the borrowed securities of the short and adds that cash position to the current profit/loss on the position.

Below is the formula representation of this rebalance approach. Variable 'n' represents the “signed” number of shares in the position, which is minus for short and positive for long. Index 'i' denotes the current transaction of adding or covering some shares on the position.

In the above, the first line shows the capital in the position as equal to total cost plus profit/loss, 'PL.' The total cost is the product of the [total number of shares currently held, ] times the [average cost of open shares, ].

At each new transaction step, the total number of shares is equal to the previous total number of shares plus the share added or covered in the current step. Note that shares are represented by a signed number. Thus, total shares number for shorts is a negative number and shares covered in the current step would be expressed as a positive number.

The average cost of open shares is computed from step to step. When shares get added, the cost of this step gets averaged in as per the above formula.

When shares get partially covered, the remaining position retains the previous average cost.

The profit/loss is computed as the difference between the current market value and the total cost of the position. Of course the sign of shares shall be considered. Thus, for a short position if the current price decreases the profit/loss becomes more positive.

Finally, the formula for 'CA' is obtained by substitution of the above terms in the first formula.

Suppose now that we have a goal value of 'CA0 ' to be the “new” total capital position for any security, and ask ourselves what would be the next (rebalancing) step to achieve that goal. It is clear from the above formula that if the current 'CA' exceeds the goal we need to reduce it by reducing the absolute value of the total shares, which is by covering some 'x' shares. And alternatively, to increase 'CA' we add some 'x' shares to the position. Let us find 'x' for both Long and Short positions:

The first formula (*) obtains the rebalance transaction for Long positions, and the second formula (**) obtains rebalance transaction for Short positions.