# Measuring Investment Risk – Standard Deviation

Now, we’re getting into some statistics, which is not my strong point.  I understand the basics, but not much more than that.

Standard deviation (σ) is a measure of how volatile something it.  It’s a measure of how far a value can be from the expected value (the mean μ).  The easiest method to calculate the average is to take a list of historical prices (adjusted close prices) and calculate the average return from that.

## Daily Returns

First is to create a list of daily returns from the prices, and take the average of all the values in that array (N).  The first value in the array is 1, because there is no change.  You can download free adjusted close prices from Yahoo Finance (they’re adjusted for dividends and splits).

$latex \mu = \frac{\sum_{t =1}^{N}\left(\frac{P_{t}}{P_{t-1}}\right) -1}{N}$

Once the average is calculated, you can calculate the standard deviation.  The easiest method of calculating standard deviation is to use Excel or other programming language to do it, but you can do it manually as well.

$latex \sigma = \sqrt{\sum_{i=1}^{N}(x_{i} – \mu)^2}$

The standard deviation is currently one of the best measures of risk for an investment.  And you can calculate the standard deviation of a portfolio as well, just start with the daily returns of the portfolio instead of a specific investment.

## Intuition about Values

The higher the standard deviation, the more the investment varies from the average return, and the more risk an investor would take on.

In general, the larger the average return, the larger the standard deviation should be, because no one wants to take larger risk for lower return.

Disclaimer: I’m writing these posts as a way to solidify my understanding of class materials, they may not be completely correct – and I welcome any corrections.

## 2 thoughts on “Measuring Investment Risk – Standard Deviation”

1. Done by Forty

The math formulas, they make my brain hurt. 🙂

Thanks for this post though. I, like you, have only a basic understanding of standard deviation but have generally thought of it as just being how volatile the ride is. Like you said, more volatility ought to be paired with greater returns, in theory.

1. Mom Post author

During undergraduate, I worked for the university’s math department, and it was great being able to ask the math professors to explain things to me. I took a few of the upper level math classes (like number theory, differential equations and linear algebra) because the professor was cool and thought I had enough math background to understand the material – and it was useful in computer science classes. But I haven’t used a lot of it in many, many years….