What Makes Standard Deviation Important?

This week our discussion will revolve around the importance of standard deviation. In my opinion, standard deviation is important because it helps explain the significance of the area around the mean. It adds color to the scenario. If I put an apple on the table, and call it the mean, the standard deviation will tell me if it’s a Granny Smith, McIntosh, a Red Delicious, or a Gala apple.

This week I wanted to highlight how I use standard deviation in my workplace as the primary data-point. I will share with you one way I use standard deviation to help me in my investment decision-making process.

Position Size

One primary use of standard deviation in my profession is to determine an appropriate position size for an investment that I want to make. Let’s assume for a moment that we are managing our portfolio with a total value of $1,000,000. And I determine beforehand that the most I am willing to lose on a trade is $10,000 or 1% of the total portfolio. Thus, I will implement a stop-loss feature on these trades. Let’s also assume that I want to purchase two stocks – Verizon (VZ) and Netflix (NFLX). How much should I invest in each?

I would first determine the mean and standard deviation of the historical price for each security. As a rule of thumb, I typically use a historical time period that is about half of my average holding period because mean and standard deviation are lagging indicators in this case. So, if my average holding period is 6 to 9 months, I will use a historical time period of 3 to 4.5 months for my calculations.

In the figure below I calculated the 3-month standard deviation for both securities. I entered the portfolio value and the amount that I’d be willing to lose. I will use a stop-loss feature for these securities but both have different volatility traits, so I can not use a fixed amount to invest. This may lead to getting “stopped-out” of the position too early or may lead to a position size that is too small for the portfolio.

The tables below show that VZ has a standard deviation of $2.50 and NFLX has a standard deviation of $51.42. By itself these numbers as a static metric do little to explain the stock volatility so we could scale it by the average stock price over the same period to determine volatility. The average stock price for VZ was $56.78 and the average price for NFLX was $394.65.

So, if we look at the coefficient of variation (SD/mean) we will see that VZ is (2.50/51.42) 4.86% and the coefficient of variation for NFLX is (51.42/394.65) 13.0%. Obviously NFLX is much more volatile than VZ.

I want to put a stop loss feature on these trades with enough downside breathing room so that I’m not stopped-out too quickly. I use the -1-standard deviation as my stop-loss price. So, with VZ trading at $54.54, my stop loss goes to $52.04. With NFLX trading at $561.98, my stop-loss will be at $510.56.

To determine my appropriate position, I can take the amount I’m willing to lose on the trade and divide that by the difference between the stock price and the stop loss price. In the VZ case it would be 10,000/ (54.54-52.04) = 4000. I would buy 4000 shares or $218,000 worth. In the case of NFLX, 10,000/ (561.98-510.56) = 195. I would buy 195 shares or $109,000 worth.

Using the standard deviation will help me with my profit-taking decision-making process as well. As another rule, I like to try to keep my win to loss ratio near 3-to-1. Following this rule means, in aggregate I only have to be right 30% to 35% of the time and still make money. So, if I calculate the +3-standard deviation for the securities I purchase and use that as a potential exit point, I will have better results overall. In other words, if I’m stopped-out of my positions 66% of the time but 1-in-3 positions reaches the +3-standard deviation, I should be okay. I only have to be right 25% of the time to break even.

Joseph S. Kalinowski, CFA