What Correlation Coefficients Mean for Your Portfolio

It’s a professional liability. We have no choice. There’s no alternative.

Some nasty vocab is the vernacular of finance, and we have to use it even if it’s as unpleasant as another Adam Sandler movie.

When we do use it, we have to be careful not to sound like all the money morons out there. You know, the ones with mouths that work and brains that don’t.

But fear not. There are two big differences between Financia Luchadores and the talking heads.

First, we’re not morons.

Second, we actually know what words mean. And we can profit handsomely from our knowledge, spinning la lingua franca talk into dollars.

On deck for discussion: Correlation coefficient and diversification.

We scuff up our FL chalkboard with these two terms at once because they’re more intimately related than second cousins at a Kentucky cookout.

And we do so because, in the popular literature on investing, there seem to be very few resources that make correlation coefficients approachable and useful. Either the math gets in the way, or there’s no linkage between the “what” and the “what to do,” or there’s an overly-quantitative approach to using correlation coefficients that tries to make them do more than they’re supposed to.

In this post, we’ll:

  • Define what correlation coefficients are, and what they mean.
  • Describe how they can be used and what their true value to investors is.
  • Identify their role in portfolio allocation decisions and rebalancing habits.

Gotta Keep ‘Em Correlated

It ain’t causative. It don’t mean things gon’ be that way forever. It just a durn statistic.

True, true and true. So why do we care about correlation coefficient? To help us build a solid and balanced financial portfolio, good sir.

Correlation coefficient provides a “normalized” way to understand the covariance of two variables. It helps us understand the association of movement in value between two assets over some period of time.

If one has gone up, did the other go up or down, or stay the same? And if the second asset’s value did move, by how much?

The correlation coefficient number gives us insight into this relationship in a simple indexed value, based on an averaging of historical data that covers a period long enough to encompass various economic environments.

The Correlation Matrix

Here’s how the indexing works:

  • A coefficient of -1 means that, every time there has been an upward movement in Asset A, there was a downward movement in value of Asset B. They’re perfectly negatively correlated.
  • A coefficient between -1 and 0 means that Assets A and B are negatively correlated, so their movements tend to be in opposite directions. But the association is weaker than perfect.
  • A value of 0 means Assets A and B are completely uncorrelated. One’s movement told us nothing in reference to the other’s.
  • A value of 1 means a perfect positive correlation, with values between 0 and 1 indicating a weaker positive correlation.
Correlation Coefficients Summary & Examples
Correlation Coefficients Summary & Examples

Correlation coefficients are relative. Not second-cousin relative. More like the two-trains-passing-on-the-tracks relative.

There always has to be a baseline against which something’s movement is assessed. Which is why assets are paired in the examples column of the table above.

Assets don’t have a correlation coefficient. Instead, they have unique correlation coefficients for each comparator.

That’s why we tend to see correlation values shown for an array of asset types in what’s known as a “correlation matrix.”

For your viewing pleasure, here’s one from LendingRobot.

LendingRobot Correlation Matrix
LendingRobot Correlation Matrix

Note: Abbreviations used in the above table are as follows: VTI (Vanguard Total Stock Market ETF); VPACX (Vanguard Pacific Stock Market Index ETF); VEURX (Vanguard European Stock ETF); VBR (Vanguard Small Cap Value ETF); VNQ (Vanguard REIT ETF); AGG (iShares Barclays Aggregate Bond Fund ETF); TIP (iShares TIPS Bond ETF); VWEHX (Vanguard High Yield Corporate Fund ETF); and Mktpl Lending (Lending Club, Prosper and Funding Circle loans).

Use the Force

That’s all great, you say, but it’s about as useful as a box of hair. What do we do with it?

First, calculating correlation coefficients is not something you need to worry about doing on your own. The computations are straightforward enough, as long as you don’t mind a bit of Greek. But there are plenty of resources out there, like LendingRobot and many others, that have done the data work for you. All you need to know is understand what the numbers tell you, and what to do with them.

Which is really just one thing.

Including assets of low correlation in our portfolio means we can drive up returns relative to risk.

We can make more money, given a level of total risk. Or, given an amount of total desired return, we can endure less volatility. More for less. Twofer Tuesday. That kind of thing. Mmmm…tasty.

That’s the central tenet of Modern Portfolio Theory. Which is pretty cool and Nobel-worthy, but also kinda math-y for our purposes to derive formally here.

The intuition does just fine for us chatty Luchadores. Correlation coefficient can be thought of as a compass helping us move toward an appropriately diversified and balanced portfolio.

In investing, risk is quantified by the spread or dispersion of outcomes. A wider dispersion implies higher risk, while a narrower valley of outcomes implies lower risk. We think of all this as volatility: the expansion and contraction of our nut size as time unfolds and we Luchadores stay millionaires in early retirement.

Your holdings could be worth $1 million or -$3 million tomorrow: High risk.

Your holdings could be worth $350,000 or $325,000 tomorrow: Low(er) risk.

Strategery

And how do we make our dispersion of outcomes lower? By incorporating into our portfolio assets that are relatively uncorrelated – that is, those with low correlation coefficients…like P2P loans and U.S. stocks.

To see the effect in action, compare a one-asset portfolio with a two-asset portfolio. Both are worth $100,000 to start.

  • The single-asset portfolio is comprised solely of Asset A. Asset A’s expected annual return is 2%, and its dispersion of outcomes for each year ranges from -3% to 7%, all this based on historical performance.

So, at the end of the year, we’d expect to have a portfolio worth $102,000. But it could be worth as little as $97,000 or as much as $107,000. Our dispersion gives a $10,000 bracket surrounding our $102,000 “central” expected outcome.

  • Here’s the two-asset portfolio. It’s 50% Asset A, and 50% Asset B, which are uncorrelated (i.e., they exhibit a correlation coefficient of zero).

Asset B is cash held in a high-yield online savings account, giving a return of 1% annually. Its dispersion of outcomes leaves nothing to chance: No matter what, you’re gonna get 1%, even if Adam Sandler is elected prime minister of the universe.

So, $50,000 goes into Asset A, with an expected end-of-year value of $51,000, and worst-case and best-case outcomes of $48,500 and $53,500, respectively.

The other $50,000 goes into Asset B, giving an expected end-of-year value of $50,500.

The best-case overall outcome for the two-asset portfolio: $53,500 + $50,500 = $104,000.

The worst-case overall outcome: $48,500 + $50,500 = $99,000.

Expected overall outcome: $51,000 + $50,500 = $101,500. That bracket around the expected value: $5,000.

Forceps, Please

So let’s autopsy. The expected outcome from the two-asset holdings is $500 less (i.e., about 25% less, since $1,500 is 75% of $2,000).

But with the two-asset portfolio, we significantly mitigate risk. Rather than face a possible $3,000 loss, we won’t (likely) do worse than a $1,000 loss. That is, our anticipable losses are cut by 66%. The bracket surrounding our expected outcome is reduced by half.

The disparity works in our favor here. We give up only 25% in expected returns in exchange for a reduction in potential losses by 66% and a reduction in overall variation around the expected result of 50%.

That’s the power of diversifying.

Not diversifying is like saying, well, you’ll save weight by removing your car’s seatbelts, airbags, doors, fenders and headlights, so you’ll probably get to your destination faster and maybe use less gas… but, in the event you ram a stray Kia, your chances of immediate death are about as good as indigestion after eating a dozen food truck tacos. Chicken or carne asada?

The tradeoff – slightly lower total expected returns in exchange for much lower risk – can be thought of as a beneficial exchange. You give a relatively small amount of expected profit in return for a lot of security against loss. Or, alternatively, you could add a little bit of risk in exchange for a large amount of expected profit.

That’s what diversification is all about. It’s why we care about correlation coefficients and why it’s a good idea to have uncorrelated assets in your overall portfolio.

So what to do about all this.

Profit, naturally. Here’s how:

  • Build a well-diversified portfolio comprised of several low-correlation assets.

More on this rich topic in other posts. But the basic logic for doing so is this: You don’t know what the future economic environment will be, so you can’t be perfectly allocated for it. Instead, you have to allocate to take advantage of, and protect yourself from, whatever future unfolds.

If all investors heeded this fundamental truth, all investors would be much, much better off.

We can use history and statistics to help be as well-positioned as can be, but we’re still taking on the risk of an unknown future no matter what. Which means we need low-correlation variety in the portfolio – equities, from domestic, international, developed and developing markets; real estate, including REITs; P2P loans and select fixed income; as well as some cash.

The FL-Approved general financial portfolio allocation structure will be the topic of much discussion in future posts, elaborated in accordance with these principles.

  • Construct that portfolio to take advantage of long-run trends.

Short of developing the entire portfolio strategy, it’s still worth pointing out that stocks always win in the long run. So they’re the foundation of FL-styled portfolios, and an example of how we use statistics and history to do as well as we can given the likeliest future scenarios.

Here are a couple of other easy pointers for now that take advantage of trends and reflect the current investing environment.

Avoid commodities like gold and soybeans or base metals or whatever weird thing your hairy uncle always talks about at the holidays. Yes, they may be uncorrelated with your portfolio’s other holdings. But they tend to perform poorly over the long term. You’re better off with stocks of companies that deal with commodities than interests in commodities themselves. Stocks pay divvies and provide built-in tax benefits but can still expose you to the diversification benefits of commodities.

And, unless you happen to be a professional commodities trader, which you’re probably not, you don’t know what you’re doing in the commodities field and can get skewered pretty fast. If you insist on investing “directly” in commodities because, say, you ate a lot of plant fertilizer as a kid, at least do it via dedicated ETFs.

Also avoid very low rates on government bonds and outmoded investment vehicles like CDs in this investing environment. Who needs these sorts of investments when you have access to high-yield savings accounts for cash? High-yield accounts don’t have the volatility of bonds or the restrictions of CDs, so you’re more liquid and able to capitalize upon opportunities for profit during moments of market lunacy like Brexit. Plus, yields are about the same. Anyone who tries to convince you otherwise on this probably ate a lot of plant fertilizer as a kid.

  • Continually build your intuition behind why assets exhibit certain correlations with other assets.

Why is it that gold and stock returns tend to be inversely correlated? The basic story is that gold is viewed as a haven of safety when there’s economic uncertainty. This drives demand for gold up. The same economic uncertainty makes future anticipated cash flows to shareholders less predictable. This pushes the implied value of stocks downward and depresses demand for shares.

Hence, gold values can rise for the same reasons stock values fall. This intuition applies as well to the relative performance of stocks and bonds.

A strong grounding in the basic economics underlying the numbers means you’ll be more prepared to recognize profitable deviations from norms.

This leads to the next point: When there’s a developed intuition behind the coefficient numbers, it’s easier to start thinking about the presence of mispricing and acting appropriately.

  • Use mispricing as a motivator to rebalance.

Mispricing happens when pricing anomalies arise across asset classes. Yeah, yeah, we’re accustomed to thinking about mispricing in sexy arbitrage and “special situation” conditions like pending acquisitions and mergers. And those can be great if you know what you’re doing.

But milking those sorts of mispricing scenarios involves lots of know-how, and they have a highly constrained timing mechanism: the profit window is relatively discrete and temporary.

With broader mispricing that is seen across large asset classes, the potential for profit is still there, but it manifests differently.

Asset-to-asset pricing deviations from historical correlations tend to happen over longer time horizons. As the saying goes, the market can stay irrational (i.e., mispriced) longer than you can stay solvent.

So it’s not a useful strategy to undertake true arbitraging as you might in special situations.

Instead, the intuition beneath correlation coefficients and mispricing is a powerful motivator to do something even the most disciplined investors find more tiresome than waiting in line at the DMV.

That’s rebalancing.

So sad to sell those strong-performing assets! How painful to buy more of the duds!

Yeah, well, that’s where the long-term profit is. You get great returns buying when everyone else wants to sell. (And vice versa.) Benjamin Graham’s entire career was predicated on this simple notion. Same for Warren Buffet. Are you better than those two hombres?

Now, when allocating initially or rebalancing, correlation coefficients are a good compass. But they’re nothing more than that. Depending entirely on correlation coefficients to make decisions is kind of like driving by only looking at your compass. Without paying attention to what’s going on around you, you’ll probably ruin your airbags.

So the numbers and intuition really are there to help get us over the rebalancing hump. It provides us basis for thinking deeply about the rebalancing decisions we make and justifying – in our minds – that rebalancing really is the right thing.

And there we are. All oiled and shiny with correlation coefficients and what they mean for diversification, portfolio allocation, mean-ass wealth building and our general state of Luchadorianess.

If there weren’t so much money to be made, we’d really have to stop talking like this.

Luchadores, drop me some knowledge on your portfolio allocations and how you stay motivated to rebalance. The Libre household rebalances annually – part of tax loss harvesting, asset reallocation and profit taking all wrapped into one. There’s also occasional “opportunistic rebalancing” that happens when prices get loony. How often do you shuffle the deck?

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