Modern portfolio theory by Markowitz says basically that for increased levels of risk you should demand higher levels of expected return. We can combine instruments together to help maximize our expected return and minimize our risk. This we all know as diversification. Theoretically, there is a set of portfolios that are all "efficient" because they have maximized their expected return given a certain level of risk.
This is regarded as absolute truth, and provides us the ability to discuss Beta and the Capital Asset Pricing Model which are excellent ways of viewing the market; however, I found that personally when I built a portfolio of stocks I didn't know how to truly measure the risk I was taking, nor could I maximize my return based on that risk. Quite frankly, most investors have NO idea how to use any of that theory. All they really can gather is that they need to diversify.
One of these assumptions we have to make is that picking stocks is not an exact science. Many studies have shown, the average portfolio builder will do just as well throwing darts at a board of ticker symbols than diving in and doing their, "Jim Cramer Homework." So, it doesn't take long before we can make the not so horrible assumption that stock pickers will pick stocks that make money 50% of the time. Our average Joe now has a list of 10 stocks he wants to purchase. He does not know this now but 5 will go up in value, and 5 will go down. He now has the difficult decision to make of how many shares to buy of each of the 10 stocks.
The first and somewhat obvious method is to buy 100 shares of each stock. He will then have 1000 shares of stock and his stocks will be evenly distributed. But the mildly involved already know that if stock number 1 costs $5 per share and stock number 2 costs $100 per share, he has not equally distributed his money. Interestingly, the first method is very similar to how the Dow Jones Industrial Average works. Next we realize that we need to take the total amount we want to invest and divide into 10 equal pieces, then use those pieces to invest in each stock. So if we have $10,000 to invest, we then need to buy 200 shares of stock 1 and 10 shares of stock 2, so we then have $1,000 invested in both. We continue that for each of the 10 stocks. This is how most other market averages like the S&P 500 work.
Before I present my method, I would like to make a quick note for description purposes. We all have had portfolios and have tried to use the second method above to invest. We may then find ourselves in a situation where we check our stock portfolio's total value on a day to day basis. This is not the healthiest method of staying sane but it is human nature. After a few weeks we'll notice that while we have invested equally in all the stocks, a few of the stocks have a tendency to catch our eye the most. They move a great deal and their movement is large enough as to have a large degree of effect on our portfolio. We might wonder whey some of the other stocks, seem to move nowhere at all, and never have an effect on the bottom line. Inevitably we'll focus all of our mental effort on the volatile stocks and forget completely about the low volatility ones because, our brains have already figured out that we are not diversified at all. We have over invested in volatility and under invested in low volatility.
The third method which I propose is to use some measure of volatility to change the amount we invest in each stock, with the underlying goal of creating a volatility neutral portfolio. If we invest more in those stocks that seem to never move, and less in the ones that move a great deal, then there must exist some combination where a "good day" in one stock is equivalent to a "good day" in any other with respect to its effect on our portfolio.
Naysayers may point out that we have made a new assumption. This new assumption is that volatility remains constant. This is not true, but volatility often begets more volatility and vice versa. One can imagine a stock that moves a great deal one day, out of nowhere, due to some amazing piece of news. Investors and traders will then try and buy or sell that stock the next day depending on their own views about the big movement. This buying and selling will create more movement which will of course bring more buying and selling. Vice versa if stock does not move, most investors will assume that it is not going to move the next day and their money will be better spent elsewhere. This is a self-fulfilling prophecy and soon no one will want to do anything with the stock and its volatility will stay low. This being said over time volatility does change for reasons like the one above and when that happens the portfolio should be readjusted to reflect the new volatilities.
One can use just about anything to measure volatility, but for the average investor historical values of daily high, low, and close are pretty easy to come by. If we take the average change from day to day we'll get a rudimentary level of volatility. For example if a stocks closing price goes from $10.10 to $10.25 and then to $10.15, the absolute value of the changes were $0.15 and $0.10, giving us an average daily volatility of $0.125. I like to include the high and low to know something about how much the stock is moving during the day. If high(1), low(1) and high(2), low(2) are the highs and lows for day 1 and 2 respectively I then use the equation d = MAX(ABS(high(2) – high(1), ABS(low(2)-low(1)). If you're handy with excel you can get a spreadsheet from Yahoo finance of historical stock prices and then quickly come up with the value d as it changes each day. We then take an average of d over time, for example 25 days is a month in stock market terms. We can assign this value v1 to stock number 1 and continue this process for each of our 10 stocks.
We now have a set of numbers which represent the volatilities for each of the 10 stocks we are going to buy.
(v1, v2, … v10)
Since we are trying to make weights that value the stock with least volatility highest, and the highest least we need to reorder the volatilities. If we find the maximum of them and divide by each individual volatility we will get a new reordered set with order we are looking for.
(vmax/v1, vmax/v2, … vmax/v10)
Now that we have an index we can then use these values to come up with the percentage of the total portfolio each stock must be to be volatility neutral. The sum of these volatilities can be called the volatility of the portfolio but it really a nonsensical number. That is used in the calculation of the percentage. We take each of the reordered weights and divide by the sum to come up with a percentage to invest in each. Now simply multiply your percentage by the total amount to be invested and this will give you how much money you should invest in each stock. At the end of this you will find a neat relationship between the volatilities and percentages. If one stock is twice as volatile as another stock for example it moves $4.00 per day and the other moves $2.00 per day, you will invest twice as much money in the $2.00 volatility stock as you do the $4.00.
Sometimes our eyes can get a little blurry when looking at equations but essentially this will create a portfolio that, given certain assumptions, will for some period of time into the future create a portfolio of stocks that are volatility neutral. One can imagine our Average Joe investor who has picked 5 stocks that will go up and 5 that will go down. If 1 of the stocks that will go down has been moving a great deal up to this point and he does not invest using this method, there is a likely hood that even though he should break even with 5 up and 5 down, because he invested equally in this stock, he might lose money as the performance of this stock will dominate his portfolio performance. One can even imagine if average Joe picked so well 9 stocks went up and 1 went down and that 1 was so volatile as to destroy almost 10% of his money. If we weight things appropriately and believe that volatilities persist, then in both scenarios he should fair better with a volatility neutral portfolio organization.
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