There are a large number of statistical measures available for looking at a mutual fund, ETF, stock or a combination of these in the total portfolio.

For an individual investor, what are the important measures and what do they mean? Over the next two days I will highlight the measures I think are critical to understanding and managing your investing portfolio.

Today, I’ll start with the best measurement of risk in any investment – its volatility. Then I’ll move on to Beta, which is often incorrectly thought of as a measurement of risk. Beta is actually a measure of how any investment will move in relation to a benchmark.

### Volatility: The Standard Measure of Risk

The first measure that it makes sense to look at when evaluating any possible investment is volatility. Simply stated, volatility measures the variability in the price of an asset over time. Volatility is commonly calculated as annualized volatility, and if you do not see a specific period attached to a volatility number, assume that you are looking at annualized volatility.

Volatility tells you a great deal about an investment. First, volatility provides an estimate of how much value your investment can lose over a period of time. This is crucial. As a rule of thumb, you can estimate the level of losses that you might experience in a very bad year by calculating twice the volatility.

For example:

The annualized volatility of the S&P 500 over the last five years is around 17% according to Morningstar. Knowing this, we would estimate that we would have a -34% return in a very bad year. In the worst year in recent history, 2008, the S&P 500 did lose just about that much, approximately 37%.

Another example:

The annualized volatility for the iShares Emerging Markets ETF (EEM) over the past five years is 27%, so the estimated loss in a very bad year would be -54%. EEM returned -49% in 2008.

The historical volatility depends on the period of history you select. Three-to-five years is generally long enough to be fairly stable and short enough to be representative of current markets. While this is only a rule of thumb, it is a good way to develop an intuition for what the volatility number means.

**Historical Volatility**

Volatility is often referred to as the standard measure of risk. You can find historical volatility data in a range of places. Morningstar, for example, provides historical volatility for stocks, funds and ETFs:

Here, for example, you can see the historical volatility for Google’s stock.

Here is historical data for the volatility of the Vanguard S&P 500 Fund. The Volatility is labeled as Standard Deviation in this table, the statistical process used for calculating volatility. It is not uncommon to see volatility expressed as the Standard Deviation of returns.

Here is the historical volatility for the iShares Gold ETF, GLD.

### Beta: Understanding How Your Investments Will Move in Relation to the Market, and Measuring Performance

Beta measures how much an investment (stock, fund, ETF or total portfolio) tends to move in response to a benchmark. The most common benchmark used for Beta is the S&P500. There is a long and interesting history as to why the S&P500 makes sense as the default benchmark and why Beta is an important variable. The interested reader will find a great summary in Burton Malkiel’s *A Random Walk Down Wall Street*. If a mutual fund has a Beta of 1.1 (this may also be written as 110%), then the fund will tend to gain 1.1% when the S&P 500 gains 1% and lose 1.1% when the S&P500 loses 1%.

Beta greater than 1.0 can be thought of as a ‘lever’ that allows you to increase your exposure to market risk. The Beta for an S&P 500 fund is, of course, exactly equal to 1. An asset with a Beta of 0 tends to move entirely independently of the S&P 500.

**Not a Measure of Risk**

Beta is often referred to as a measure of risk (high Beta being high risk and vice versa), but they are not the same thing. While high Beta investments do tend to be high risk, low Beta investments are not necessarily low risk.

The iShares Gold ETF (GLD) has a trailing three-year Beta of 0.07, so by the numbers one might thing that it is low risk.

No.

GLD has an historical risk level (volatility) very close to that of the S&P 500. Gold bullion has a low historical Beta but is also not a low risk asset.

A similar example holds for long-term government bonds. The iShares 20+ Year Treasury Bond Fund (TLT) actually has a slightly negative Beta with respect to the S&P500, but this is not a low risk fund (TLT lost almost 22% in 2009).

It is particularly dangerous to use Beta as a measure of risk for individual stocks. France Telecom (FTE), for example, has a Beta of 0.7 (well below that of an S&P500 index fund) but this stock has substantially higher volatility than the S&P 500.

**Beta**

Beta can also be very revealing in terms of understanding how markets work. The Beta for the iShares MSCI Emerging Markets Index Fund (EEM) — a broad portfolio of emerging market stocks — is 1.36%. This means that EEM tends to amplify movements in the S&P 500 (EEM will tend to go up 1.36% when the S&P 500 goes up 1%, and vice versa). The Beta for the iShares MSCI Brazil Index Fund (EWZ) is 1.50. The fact that a number of emerging markets have Betas greater than 1 means that emerging market holdings tend to amplify swings in domestic markets.

Beta is a very useful measure in understanding how a stock, fund, or portfolio will respond to moves in the S&P 500. Beta greater than 1 means that a stock, fund, or portfolio will tend to amplify a move in the S&P 500. Beta less than 1 means that a stock, fund, or portfolio tends not to be as responsive to a move in the S&P 500. Knowing the Beta of your portfolio tells you how sensitive your portfolio is to a decline in the S&P500. Back in early 2008, I wrote an article explaining that a low-Beta portfolio would provide protection against the effects of rising volatility.

**Beta Sheds Light on Mutual Fund Performance**

One of the reasons that Beta is so important is that it helps investors determine whether a fund’s past performance is due to skill on the part of the fund manager or simply due to a manager ‘amplifying’ the S&P 500 — in other words, obtaining their market-beating returns in a rising market by taking more market risk.

A mutual fund with a Beta of 1.2 should generate a return of 12% when the market rises 10% — with no skill required. This fund is also likely to drop 12% if the market drops by 10%. Why? Because the fund is simply amplifying the moves in the S&P 500. * Investors should be very wary of fund managers who charge big fees for simply creating a portfolio with a higher level of Beta.*

Tomorrow, I’ll review six more measures any investor should make themself familiar with.

(photo: Heavy Weight Geek)

SC_investorhow can one calcuate the volatility of a multi-holdings portfolio. I would assume that you could do a weighted average based on the volatility of the holdings benchmarks. Is there a website that will assist in this calculation?

Geoff ConsidinePost authorYou cannot just do a weighted average of volatilities of individual holdings to get volatility for the total portfolio. The reason is the correlations between holdings. The aggregate volatility of a portfolio is determined by the volatilities of the individual holdings and the correlations between the individual holdings.

Your question also seems to span two issues. You can calculate the historical volatility based on total portfolio returns. If you have a portfolio that has a meaningful history, you can calculate directly from the portfolio returns. If you are talking about testing a hypothetical portfolio, you must create the historical volatility for that portfolio from the components and calculate the volatility from that backtested history.

Nanette ByrnesOn the Bogleheads board there’s been an interesting discussion of the post (http://www.bogleheads.org/forum/viewtopic.php?p=1013523#1013523) in which one reader raises the question of whether these figures used by Calpers and others are real rates of return. I didn’t find it clearly stated in their papers, so reached out to Keith Brainard, the research director at NASRA. Brainard explained that for public funds the investment returns being discussed are made up of two elements: an inflation component and a real rate of return. “Really, the more important figure is the real rate of return,” he notes.

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MariusOne can calculate volatility, beta and other statistical metrics of a multi-holdings portfolio on InvestSpy.com. It’s free of charge.