# Portfolio Optimization

Portfolio Optimization

Volatility Plus Expected Return

The Northwest Passage

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Portfolio optimization theory was introduced by Harry Markowitz in the 1960s. Markowitz posited that the ideal combination of financial assets would minimize risk for any level of expected return, and maximize return for any given level of risk. And he specified a way to identify the portfolio mix that would do that: mean-variance optimization.

Many analysts and academics have added and extended the basic Markowitz model over the years, but the basic insight and underlying premise endures; higher returns are good, but higher risk is bad … and finding the optimized combination is mathematically complicated.

But you don’t always need all the complication. There are simpler ways to use the basic Markowitz framework to “sort-of almost” optimize—you can by-pass much of the math by taking the “Northwest Passage.”

Volatility, a measure of risk, is central to the Markowitz framework. There are other risks (not captured in volatility measures) but by and large, a stock’s volatility gives a pretty good picture of how risky it is. A stock that often jumps up or down 1% or 2% in a day is far more volatile, and more risky, than a stock that typically fluctuates by, say, ½ of 1%.

The predominant measure of volatility is the “standard deviation” of returns, expressed as an annual rate.

You can look up a stock’s standard deviation on any number of websites. The values given at various on-line sources can differ a little, depending on how recent the update, what time period is covered, and other computational specifics, but most stocks will map out at about the same volatility no matter which source you use.

The second dimension of the Markowitz model is “expected return.”

This is harder to estimate, and there are many ways to do it. Wall Street analysts spend entire careers estimating expected returns, and one approach would be to use Wall Street analyses.

A different and simple approach is to use a stock’s average return on equity (ROE) over several years (or over a whole economic cycle). A more complex approach would be to apply the capital asset pricing model (CAPM), which uses a stock’s beta and risk-free (Treasury) interest rates to estimate what future return a security “deserves.”

Yet another simple measure of expected return is the “earnings yield.”

That’s the inverse of the price-earnings ratio (P/E). If a stock has a P/E ratio of 10, it has an earnings yield (E/P) of 1/10 =.10, or 10%; if it has a P/E of 8, its earnings yield is 1/8 =.125, or 12.5%.

Basically, the earnings yield expresses what would be expected for a long-term return if the market always values this stock’s earnings as it does today.

(From that E/P starting point, you can also tweak your expected returns depending on your outlook. Were this year‘s earnings abnormally high? … then maybe you bump the E/P down a bit. Is future growth going to increase notably? … then maybe you bump the E/P up a bit.)

In the Cabot ETF Investing System, I focus on the nine key market sectors of the S&P 500 index. Let’s use those nine sectors to search for a Northwest Passage among them.*

Here is a table showing the nine sector ETFs (plus SPY, the S&P 500 tracking ETF), along with current volatility (standard deviation), P/E ratio and earnings yield:

The final column shows each sector’s correlation with the overall SPY. We’ll get back to that below.

Here is a scatter plot of the 10 entries (nine sectors plus SPY). Each entry is located horizontally according to its volatility (standard deviation) and vertically according to its expected return (E/P – Earnings Yield).

Notice that the general scatter runs from lower left to upper right. That shows the market’s basic risk-return tradeoff. We can easily get higher expected returns by simply cranking up the risk. As we shift toward the right, the average expected return rises.

With optimization, we try to beat that rule (to the extent possible) by maximizing expected return without necessarily (or unduly) increasing risk.

Stated the other way around, we want to minimize risk for any level of expected return.

That means, for example, if we were making a single sector choice between Consumer Staples (XLP) and Consumer Discretionary (XLY), we’d always prefer XLP. These two Consumer sectors are offering the same expected return (same height on the scatter), but XLP is notably less volatile (more to the left).

In a vertical example, if we compare Financials (XLF) and Technology (XLK), we’d always prefer XLF, because they’re both offering similar risk, but XLF has higher expected return.

(Note: “Always prefer” does not mean forever. “Always” only means as long as the risk-return relationships remain as they are here.)

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More generally, we prefer stocks toward the upper left—the Northwest corner—and we avoid stocks toward the lower right.

That means we prefer Health Care (XLV) over Utilities (XLU) and we prefer XLU over XLY. We prefer XLF—and maybe Energy (XLE)—over XLK. We prefer SPY (the whole S&P index) over Industrials (XLI), XLB and XLK.

In fact, we could draw an upper boundary diagonally from XLV to XLF, and say we only want sectors at or near that Northwest boundary.

Any combination of XLV and XLF would be somewhere on that line** and we can move along that line (either direction) by varying the mix of XLV and XLF in a two-sector portfolio.

Where we wish to position along that line depends on our risk aversion. To be very conservative, we hold a lot more XLV (sliding to the lower left); to be more aggressive we hold a bit more XLF (climbing toward the upper right).

But just two sectors as investment is narrow base. For more diversification, we can add in some XLU and XLE (and maybe even some SPY), because they are very close to that Northwest boundary line.

These additions would reduce expected return a little, but would usually reduce volatility more.

(Remember, all the earnings yields and volatilities are estimates from the past, not known values for the future. So every point location on the scatter really represents a little cloud of possibility, and we never really know how far the final reality will be from the initial point estimate.)

This search for a Northwest Passage is not true optimization. What it misses is the relationships (correlations) among the candidate stocks (sectors). Among the 10 candidates (nine sectors plus SPY), there are 45 individual correlation pairs.

There are computer programs to sort through all that and offer a truly optimized mix of all 10. But that solution will include a mix of both long and short positions (not suitable for all), and often some trivial positions that are often not worth implementing. And given the uncertainties inherent in the future, it’s often just as effective to just head for the Northwest Passage.

*Although I’ve used the nine-sector S&P ETFs to illustrate the mean-variance optimization framework, this framework is not in fact the model underlying the Cabot ETF Investing System, which is a combination of economic and market timing models with different logic and theory and experience behind it.

**A combination portfolio of XLV and XLF (or of ANY two securities) does not in fact fall on the straight line between them. Instead, the line “bows” a little toward the left of the straight line. (Expected return will be a weighted average, but the volatility will be less than a weighted average.) The amount of “bowing” depends on the correlation between the pair. Correlations have grown quite high in recent times. Seven of the nine sector correlations are greater than .90, and only one is (barely) below .80. High correlations with the 500 index reflect high correlations among the individual sector pairs. High correlation reduces the pairwise bowing considerably, and straight lines are not unreasonable.

Get more details on the Cabot ETF Investing System here.

Your guide to ETF investing,

Robin Carpenter

Editor, *Cabot ETF Investing System*

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