# How To Measure Investment Volatility: Capital Asset Pricing Model & Beta

by on 2011-06-280

We often hear about stocks being volatile and risky. But what does it really mean? Let’s take a look at how it’s all measured.

“Volatile” is what you’d probably describe someone with a short fuse or a volcano waiting to erupt, but it’s also a financial term that helps us describe stocks. Understanding volatility and how to measure it can be frustrating to someone without a degree in finance. But never fear! Here, we’ll break down the terms and look at an actual example to help us grasp this deep, yet important topic.

Simply put, volatility means variation or changes in price over time. Financial instruments are said to be extremely volatile if prices fluctuate wildly in a short period of time. The greater the volatility, the higher the risk involved.

“Risk measures” is the term used to describe the historical predictors of investment risk and volatility. There are actually five principal risk measures: Alpha, Beta, R-Squared, Standard Deviation, and Sharpe Ratio. Fancy terms, if you ask me, but these risk measures exist in order to allow us to compare how well different investments perform and whether they’re a fit for our investment needs. You may find that you’re really just cut out to stick with conservative savings accounts and large company stocks and you wouldn’t be able to sleep at night if you went for an all out Latin American fund, for example. So how do you make such a decision? While you can determine this via your gut instinct, you can actually turn to some technical ways to do it, but to understand those ways, you may want to wrap your mind around a little math. Now before you turn away because there’s a formula ahead, I’d encourage you to give it a chance. It’s actually quite interesting (especially if you’re new to the numbers behind the subject of risk). Here’s where the fun begins.

## Measuring Investment Volatility and Risk With The CAPM Formula

There’s this thing called the Capital Asset Pricing Model (CAPM), which is just a fancy name for a concept that mathematically illustrates the relationship between an asset’s expected return and risk. CAPM is a model that attempts to price or value an individual security or portfolio. This is represented by the formula:

E = F + β (M – F)

Where:

• E is the Expected Return of the Capital Asset (whether it be your Gold fund, your Large Cap stock or your Emerging Markets ETF, etc)
• F is the Risk Free Rate (money held in a “safe” account such as Savings that yields a steady interest rate)
• β is the Beta Figure (the market risk)
• M is the Expected Market Return

The CAPM boils down to saying that an investment’s expected return should make up for the risk that it presents. According to the CAPM, investors should be compensated for their physical investment (money) plus the risk involved. If the actual return of an asset does not match or exceed the required expected return, then it’s probably not a wise investment.

## What Is Beta?

Let’s learn more about Beta, since this figure is key to the Capital Asset Pricing Model. Beta (β) is an asset’s market risk. The general market is said to have a Beta of 1.0. An individual stock’s beta is measured in comparison to this baseline of 1.0. You can find a stock’s Beta by searching for its ticket symbol or name on Reuters.com. Apple stock’s Beta, for example, is 1.35. Therefore, Apple is 0.35 times more volatile than the general market. A stock that has a Beta of 3.0 would be three times as volatile as the market.

### CAPM Example: Apple

Apple is one of the most talked-about technology companies now, so I’ll use Apple (or AAPL) as our example for calculating CAPM.

Recall the formula for CAPM: E = F + β (M – F)

Let’s use the following figures for our example:

1. F = 3%
Let’s say for example, that 3% is the rate of return on an interest bearing account. Of course, this value varies according to the interest rate environment, but we set it at 3% for the purposes of this illustration.
2. β = 1.35
According to Reuters, Apple’s Beta is 1.35, making it 0.35 times more volatile than the general market.
3. M = 9.4%
From 1900 to 2010, the average total return per year of the Dow Jones Industrial Average was approximately 9.4%.

So the equation looks like this:

E = (3%) + 1.35 (9.4% – 3%)
E = 11.64%

The CAPM of 11.64% tells us that Apple would need to earn 11.64% per year for it to be worth the risk of being selected as an investment.

Obviously, if I use a savings vehicle with a higher rate of return or if I expect the market to return better than average results, the CAPM or expected return of the asset will change accordingly. Nonetheless, CAPM is a good method for determining whether or not an investment is worth pursuing.

## How to Use the Capital Asset Pricing Model

You can see that CAPM isn’t hard to calculate once you understand what the figures mean. But how useful is Capital Asset Pricing when you’re deciding how to build a portfolio?

As an investor, I may choose to invest in a portfolio of less risky assets if I decide that the CAPM percentage meets my personal comfort level. Perhaps I’m only comfortable investing in stocks that have a CAPM of less than 15%, which would be a generally less risky decision and a vote for relative stability.

On the other hand, I could decide to invest in a riskier portfolio and invest a smaller portion of my wealth in cash (such as certificate of deposits or money-market accounts). The ratio of risky assets to risk-free assets here isn’t equal, but I can achieve an aggressive return if I pursue one of two approaches:

1. I invest all my wealth in a risky portfolio and let it grow over time.
2. I invest a percentage of my wealth in a risky portfolio and the remainder in cash (stable) vehicles, letting the risky portfolio grow aggressively over time.

From a personal point of view, option 2 is more attractive. The risk-free investments (cash-stable vehicles such as savings and CDs) are not correlated to the risky assets of the portfolio, so even if my risky stocks sink one quarter, my core savings will be untouched. Most likely, the risky stocks will rebound if I’m patient and let them grow slowly.

In essence, a higher return portfolio of risky stocks PLUS a reserve of cash-stable vehicles can be an efficient plan that will yield both returns and security. Just make sure you don’t end up with a passive aggressive portfolio like this one.