# Portfolio Volatility Analysis

Volatility Analysis

A Volatility-Balanced Portfolio

How Much Risk Are You Comfortable With?

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Each month, the Cabot ETF Investing System identifies several Favored market sectors. “Favored” means these sectors are likely to do well under current economic conditions, and “several” usually means two, three or four of the nine S&P component sectors with liquid ETFs.

These Favored sectors are selected using a sector selection model that compares economic conditions today to economic conditions in the past—in order to select sectors that will outperform under similar conditions. When our market-timing indicator is positive, we invest in these sectors.

My subscribers often ask about how to allocate funds among the Favored sectors; what portfolio weights to use. My general answer is to put roughly equal dollar amounts in each. That’s because the selection model doesn’t distinguish degrees of favorability (e.g. “Somewhat Favored” or “Highly Favored.”) So with no indication of preference among them, buying equal dollar amounts seems as good a bet as any.

But equal dollars isn’t really the same as equal weighting. Some sectors are more volatile than others, so even if two sectors have very similar prospects, if their volatilities differ they’ll likely advance (or decline) in different amounts. Equal dollar amounts in two sectors can end up making quite different portfolio contributions. (Of course, you’ll always get somewhat different contributions just by chance, but we’re talking systemic differences here.) But if you know the volatilities, you can adjust the dollar amounts to balance the portfolio effects.

Volatility can be measured in various ways. The two most common volatility measures are called “beta” and “sigma.”

Beta is a market-relative measure, and is expressed as a multiple of S&P 500 fluctuations. So a beta of 1.25 means fluctuations are typically 25% greater than the S&P, and a beta of .90 means fluctuations are 10% smaller than the S&P.

Sigma is an absolute measure, expressed in terms of annualized percent change. The specific statistical measure is “standard deviation” which is calculated with a lot of squares and square roots and ratios in the formula. But we don’t have to worry about that. The thing to know about standard deviation (sigma) is that it expresses a range of probability; it’s the range of returns (up or down) that a stock is likely to stay within about 2/3 of the time. So if you hold a stock with a 15% sigma, that means over the course of a full year, 2/3 of the time that stock (or ETF) will add an extra 15% better than expected, or 15% worse. That sounds complicated because of the probability factor, but it helps to convey the magnitude of the potential gain or loss.

(With volatility, you’re mostly concerned about potential loss. So here’s an easy rule-of-thumb for assessing risk with beta and sigma; multiply beta times 10 and subtract sigma, and you can expect to experience at least that degree of loss about once every six years.)

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Ok, but what about sector weighting? If equal dollar amounts don’t make equal contributions to returns, how could we plan equal contributions? Let’s consider an actual example. Here is a table of current volatilities for the nine S&P components and the S&P tracker overall (SPY):

The two most volatile sectors are Energy and Basic Materials, which are more than twice as volatile as Utilities (23% sigma versus 10% sigma). That’s a huge difference. If XLB, XLE and XLU were our Favored sectors in a given cycle, and were bought in equal dollar amounts, the gains or losses in the first two would probably swamp the portfolio effect from Utilities.

To equalize expected portfolio effects, we can adjust the allocations to give equal weight to the probable outcomes.

Here’s how. First, add up the three relevant sigmas (23.12 + 23.31 + 10.10 = 56.53 in the example). Then divide this sum by each of the three individual sigmas. This gives 2.45, 2.43 and 3.70. Finally, normalize these three values so they sum to 100%, by dividing each value by their sum.

LB 2.45/8.58 = 28%

XLE 2.43/8.58 = 28%

XLU 3.70/8.58 = 43%

This volatility-balanced portfolio will make the three sectors have approximately equal contributions to the portfolio cycle. But notice that this process will always reduce overall volatility, because you’ll tend to load-up on lower-volatility sectors and lighten-up on the higher-volatility. So equalizing impacts reduces volatility, and—usually—expected return.

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Alternative strategies are also possible. What if we forego diversification and forget about volatility balancing, and just always buy the single most volatile Favored sector (weight = 100%)? We’d have bigger gains and losses (maybe very scary!), but the larger gains should win out over time.

And where does “Godot” come in? In Samuel Beckett’s famous play, Vladimir and Estragon contemplate life, death, boredom and the meaning of existence as they wait (and wait, and wait) for the mysterious Godot who may have the answers.

Volatility analysis doesn’t take us quite so deep as all that, but does leave us with these existential questions for investors: How much risk do I really want? How much risk can I really stand? How can I manage to get to that balance?

Godot can’t help with those issues (and Godot never quite arrives); we can only peer inside ourselves…and make a plan.

So should you equalize by offsetting volatilities with differential order sizes? That depends on your risk profile. My advice is not to equalize exactly (it never plays out exactly anyway), but to take account of the volatility differences to tilt a little (up or down) toward a risk level you’re comfortable with.

Your guide to ETF investing,

Robin Carpenter

Editor, *Cabot ETF Investing System*

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