# 5 – M4 L1A 05 Demean Part 1 V3

So, you just learned how to demean a factor so that the values add up to zero. But why do we do this, the short answer is that, later on, we’re going to test the factor as if each value associated with each stock also determined, the stock weight in a theoretical portfolio. We want to make this theoretical portfolio dollar neutral, that is, the dollar amount of all long positions equals the dollar amount of all short positions. We want to do this to test the predictive power of the factor while excluding the influence of the overall market. So, why is a dollar neutral portfolio less influenced by overall market movement? Well, market movement refers to the general direction of most stocks in a country or region. If a portfolio was long only, it would likely move in the same direction as the market. If a portfolio was short only, it would likely move in the opposite direction of the market. A long short portfolio means we can take long and short positions. A dollar neutral portfolio is a special case of a long-short portfolio. Is the case where the value of the longs equals the values of the shorts. If a portfolio were halfway along and have short, then the market movement would have a minimal effect on the movement of this dollar neutral portfolio. So, a dollar neutral portfolio is set up to approximately be market neutral. Note that, an assumption we’re making is that on average the Beta of each stock to the market is one. Remember that, Beta in the capital asset pricing model refers to how much a stock moves when the market moves. In general, the average Beta of stocks may not be exactly one, but when a portfolio contains thousands of stocks it’s a reasonable assumption. So, a dollar neutral portfolio may move a bit with the market but it would ideally be close to market neutral. Let’s now switch from talking about portfolio positions in dollar amounts to talking about portfolio positions in terms of weights. Let’s review the meaning of portfolio weights and introduce the concept of the notional. The notional or trade book value is the gross dollar amount associated with a portfolio. The amount of money we’d allocate towards a stock equals its portfolio weight times the portfolio’s gross notional value. If a portfolio notional is 100 million and the stock is given a weight of 0.01, we multiply the weight of 0.01 times 100 million which is 1 million. This would be the amount of money we’d allocate toward the stock. For a long or short portfolio, we can also use the weight times the notional to see the dollar value placed on that stocks position, whether it’s a long position or short position. For example, assuming a notional of 100 million, let’s say we have a stock with a weight of 0.01 this translates to a position of $1 million. Likewise, another stock with a weight of negative 0.01 then has a position of negative$1 million. Notice in this example, assuming that there are only two stocks in the portfolio, these positions add up to zero. When all the positions add up to zero, the portfolio is dollar neutral. Remember, the goal of having a dollar neutral portfolio is to make the portfolio market neutral or at least close to market neutral.