# 8 – M4 L1A 08 Rescale Part 2 V3

At first glance, leverage looks awesome because if we take enough short positions, we could technically have enough cash to pay for all of our long positions. But does this mean that more leverage is always better? Unfortunately, the answer is no. If the stock price went down 10 percent, then our leveraged position would go down 20 percent, which is greater than the loss we’d incur without leverage. So, as the saying goes, there’s no such thing as a free lunch. Which means that the benefits of leverage come at a cost. Using leverage can increase our potential gain but can also increase our potential losses. A useful measure of the amount of leverage in a portfolio is the leverage ratio. In terms of dollars, if we added up the magnitudes of the long and short positions, and divided that sum by the notional, this would be the leverage ratio. For example, if a portfolio had a notional or initial capital of $1 million and had$1 million in long positions, the leverage ratio would be one. If the portfolio had the same notional of 1 million but borrowed cash to go long two million positions, its leverage ratio would be two million divided by one million or two. If the portfolio had long positions totaling $1 million and short positions also totaling$1 million, then the leverage ratio would also be two million divided by one million, which is two. If the longs were two million and the shorts were two million, then the leverage ratio would be four. So, I hope you noticed that the more positions we take and absolute magnitude relative to the initial capital, the higher the leverage ratio. For theoretical portfolio, that’s used for analyzing a factor, we assume a $1 notional. We add up the sum of the absolute values of the weights, then divide by the$1 notional to calculate the leverage ratio. Dividing by one doesn’t change the sum. So, we can skip the division. For example, if we had three stocks in the portfolio with weights of negative 0.5, positive 0.3, and positive 0.2, the sum of their absolute values is one. So, the leverage ratio is also one. If on the other hand, the portfolio had weights of negative one, positive 0.6, and positive 0.4, then the sum of their absolute values is two. So, the leverage ratio is also two. Let’s revisit our goal, which was to rescale portfolio weights, so that we have a leverage ratio of one. To do this, we can sum up the absolute values of the weights and divide each of our original weights by this sum. By doing this division, we are re-scaling the factor values so that the sum of their magnitudes equals one.