You're Losing Long-Term Return by Not Understanding the Role of Risk

Original article posted on "Separating Value From Bias" Substack here: #11: You're Losing Long-Term Return by Not Understanding the Role of Risk

Understanding concepts like volatility and correlation can help us maximize risk-adjusted return

So I wanted to do a whole post about how to think about the effectiveness of stocks and bonds in portfolio construction and I realized I couldn’t really do that justice without first doing a dive into understanding volatility and correlation.

Trying to control for volatility and correlation is one of the primary uses of bonds in a portfolio.

So before I do a deep dive into why you’re probably not thinking about or utilizing bonds properly in your portfolio, I need to start with an exploration of volatility and correlation.

When I talk to clients I usually find they fall into two buckets:

1) Return-only focused client: These are the folks who only see the top-line gross return and not on the foundation under which it is built. So if they’re shown a fund making 12% versus one making an 11% return, they’re immediately drawn to the 12% number without fully weighting the additional risks it poses over the lower 11% return.

2) Risk-averse client: On the polar opposite side of the spectrum of the people I described above, are people who are so scared of the thought of losing money in the short-term that they don’t realize how their fear is actually losing them money via opportunity cost in the long-run. These are the type of people who will put all their money into an investment making 4% with a 0% chance of losing money in the short-term instead of an investment making 10% with a 1% chance of losing money in the long-run (but with a lot of short-term fluctuations).

Both clients come to me essentially trying to get my opinion on what decision to make.

This, of course, is an impossible question to opine on without understanding who they are as people and what their risk-tolerances and understanding of risks are.

The answer has a lot more to do with psychology and what’s right for their value system and perspectives than the math.

As I’ve written about previously, the level of objective risk that might be right for one person might be totally wrong for another given their individual value system.

The sad thing is a lot of the time people aren’t coming to me to ask my genuine opinion on their decisions. For the most part, they’ve already more or less made up their decision as to what they are going to do and want me to validate their decision making process.

They know I’m a math and numbers guy and essentially they want a stamp of approval from the “math” guy to justify a decision they’ve already committed to—regardless of what the actual math says.

This is something I won’t do.

But what I try and get clients to think critically about is thinking of risk and return together—to measure the value of a return in relation to its risk.

In finance this is known as “risk-adjusted” return.

In order to promote this idea of risk-adjusted return, I’m going to talk about two concepts that add risk to a portfolio: volatility and correlation.

Assets that have high volatility and correlation to one another can drastically hurt long-term returns if you’re not thinking about them in the context of your portfolio.

Understanding the effects of volatility on a portfolio

Volatility in the context of portfolio construction refers to how much an asset’s return can deviate from its mean expected return in any given year.

Let’s consider a two asset portfolio.

Asset A has a 10% mean return and Asset B has a 9% mean return.

However, both assets have different volatility around that mean.

In any given year Asset A has either a -10% return or a 30% return. This is a mean return of 10% with a 20% swing in either direction.

Asset B on the other hand either has a 4% return or a 14% return. This is a mean return of 9% with a 5% swing in either direction.

So clearly Asset A has the higher expected return, but Asset B has the least volatility.

Thinking about our two clients mentioned at the start of the article, the “Return-Only Focused Client” would choose Asset A since it has the higher mean return while the “Risk-Averse Client” would choose Asset B because it has the least amount of risk around not getting close to the mean return.

What are the expected long-term returns and risk of each of these two portfolios independently?

Let’s take a look at the table below:

Table 1: Understanding the Effects of Volatility on Long-Term Returns

The most shocking thing you should take away from the table above is that the long-term expected growth rate of each asset, i.e. the Compound Annual Growth Rate (CAGR) shown in Column F, is not equal to the mean rate (Shown in Column D).

For example, Asset A has an expected mean return of 10% (which is just the average of the -10% return and the 30% return) but has a CAGR of 8.17%.

This is calculated by multiplying the two returns together and then taking the square root (since there are two years we’re comparing) as shown below:

Step 1: (1+ -10%) (1+30%)= (0.9)(1.3)=1.17

Step 2: 1.17^(1/2)-1 = 8.17%

Why is the CAGR of 8.17% less than the 10% mean return??

In fact, it is 18% lower (Column F)!

This is because of the volatility involved. Remember that Asset A’s volatility swings 20% in either direction from the mean return of 10% (Column D).? This drastically reduces the long-term CAGR.

Note that if we look at Asset B, the CAGR (Column E) is 8.89% which is only 0.11% lower than the mean return.

This is only a loss of 1% compared to the mean return of 5%. The reason why Asset B’s long-term return doesn’t decrease nearly as much as Asset A’s, is because of the drastically lower volatility.

Asset A only has a swing of 5% in either direction which is 4 times less than the 20% volatility swing we saw in Asset B.

The point here being is that just focusing on the mean return of an asset without accounting for the volatility of that asset, hurts you in the long-run.

Even though Asset A’s expected mean return in the short-term is 10%, in the long-run it is only 8.17%. This is 0.72% lower than Asset B’s long-return even though Asset B’s mean return in the short-term was 1% lower than Asset A’s.

Risk matters.

We need to be able to measure return relative to risk.

The table below does that by taking the return and dividing it by the risk or the volatility.

Table 2: Comparing Return Relative to Risk

Column E in the table above measures the return relative to the underlying risk or volatility.

We can see that Asset A offers an expected mean return that is 50% of the underlying risk while Asset B offers an expected mean return that is 180% of the underlying risk.

In other words, even though Asset A has the higher expected mean return, Asset B is giving us the biggest bang for the buck in terms of return relative to risk.

In finance, we use concepts like the Sharpe Ratio to understand how the expected return of an asset compares to its underlying volatility.

The formula for the Sharpe ratio is more complicated than the ones I’ve used in this example, but I wanted to illustrate to the reader the overall concept—instead of getting bogged down with the formulas.

Understanding correlation

Correlation is a way of understanding how well two returns move in coordination with one another.

If two assets move in the same direction, that’s called positive correlation.

If they move in opposite directions, that’s called negative correlation.

Let’s take a look at two different assets we are thinking about including in a portfolio.

We’ll call them Asset C and Asset D.

For example, let’s say that every year that Asset C has an increase in a given year and Asset D also has a similar increase in its return.

For example, let’s assume that for every 2 percentage points that Asset C’s return increases in a given year, Asset Ds return goes up by 1 percentage point. Analogously, for every 2 percentage points that Asset C’s return goes down by 2 percentage points, Asset D’s return also goes down by 1 percentage point.

Even though the amount that Asset D’s return goes up or down is lower than Asset C’s, it is 100% correlated to Asset C’s return. In fact, the change in return from year to year of Asset D is actually half the change in return in Asset C.

Table 3: Two Assets with 100% Positive Correlation

For example, in the table above we can see that when Asset C’s return increases by 8 percentage points from 12% to 20% from Year 2 to Year 3, Asset D’s return only increases by 4 percentage points from 5% to 9%.

Analogously, when Asset C’s return goes down by 4 percentage points from 20% to 16% from Year 3 to Year 4, Asset D’s return goes down by only 2 percentage points from 9% to 7%.

So these two assets have a 100% positive correlation.

Negative correlation means that two assets move in opposite directions.

Let’s assume that for every 2 percentage points that Asset C’s return increases in a given year, Asset D’s return goes down by 1 percentage point. Analogously, for every 2 percentage points that Asset C’s return goes down by 2 percentage points, Asset D’s return also goes up by 1 percentage point.

Table 4: Two Assets with 100% Negative Correlation

For example, in the table above we can see that when Asset C’s return increases by 8 percentage points from 12% to 20% from Year 2 to Year 3, Asset D’s return decreases by 4 percentage points from 3% to -1%.

Analogously, when Asset C’s return goes down by 4 percentage points from 20% to 16% from Year 3 to Year 4, Asset D’s return goes up by 2 percentage points from -1% to 1%.

So now these two assets have a 100% negative correlation.

If I’m aiming to construct a portfolio of two assets, should I get two assets that have a positive correlation with one another, or that have a negative correlation with one another?

We’ll take a look at this in the next section.

Positive Correlation Increases Volatility of a Portfolio

Let’s explore the effects of positive and negative correlation. Let’s go back to our original portfolio of Asset and A and B that we looked at the beginning of this post.

Asset A has a 10% mean return and Asset B has a 9% mean return.

However, both assets have different volatility around that mean.

In any given year Asset A has either a -10% return or a 30% return. This is a mean return of 10% with a 20% swing in either direction.

Asset B on the other hand either has a 4% return or a 14% return. This is a mean return of 9% with a 5% swing in either direction.

As we discussed previously, even though Asset A has a higher mean return, the higher volatility of Asset A means that the long-term return (CAGR) of Asset A is actually lower than Asset B.

But what if we were to create a portfolio that contained both Asset A and Asset B?

Would we be able to reduce the volatility by doing so?

Let’s try that by assuming we keep a 50/50 mix of Asset A and Asset B in the portfolio at all times (by rebalancing the portfolio at the end of the year).

How does that effect the portfolio?

Let’s look at both portfolios assuming that both Assets have their “high” return in the first year and their “low” return in the second year.

In other words, these two assets are 100% positively correlated.

Table 5: Two Asset Portfolio with Positive Correlation

As we can see from the above table, there is not much value in doing a 50/50 mix of Asset A and B in a portfolio. The resulting mix has a lower mean return/risk (Column E) and lower CAGR (Column F) than just using Asset B alone. As such, the client should just invest in Asset B instead of using a 50/50 portfolio of Asset A and Asset B.

But what if these assets were negatively correlated?

In other words, assume that every year that Asset A had its “high” return that Asset B had its “low” return.

What would the effect of the portfolio look like under those conditions?

We can see the answer to that in the table below.

Table 6: Two Asset Portfolio with Negative Correlation

In the table above we see that in Year 1 when Asset A has its “low” return of -10% that Asset B has its “high return” of 14%. Then in Year 2 when Asset A has its “high” return of 30%, Asset B has its “low” return of 4%.

In other words, in the table above Asset A and Asset B are 100% negatively correlated.

By looking at the 50/50 Mix of Asset A and Asset B in the negative correlation table versus the previous positive correlation table, two things should immediately strike us:

1) The volatility of the 50/50 Mix

2) The CAGR of the 50/50 Mix

Note that the mean expected return of the 50/50 Mix of Asset A and Asset B is still 9.5%. In other words, in both the positive and negative correlated portfolios have the same mean return.

However, let’s now compare the volatility of the two portfolios. The negatively correlated portfolio above has only an 8% volatility compared to the 13% volatility of the positively correlated portfolio. This lower volatility of the negatively correlated portfolio creates a CAGR of 9.24% as opposed to the 8.78% CAGR of the positively correlated portfolio.

Therefore, the CAGR of the 50/50 mix of the 100% negatively correlated portfolio is greater than either of the two assets individually!

And this is the value of utilizing assets that are negatively correlated. The fact that the assets are negatively correlated means that a portfolio using both assets has lower volatility than a portfolio that just consists of one of the assets.

And this reduced volatility, leads to a greater long-term CAGR than either of the two assets could provide individually.

Not everything is what it seems

Obviously one of the key takeaways I want people to walk away from this post with is the importance of controlling for volatility in selecting assets in a portfolio by considering elements like correlation between assets.

But in the greater context of “Separating Value From Bias”, I wanted to show you how not everything is what is seems to be.

Let’s go back and take a look at the two types of clients I mentioned at the top of this article, the return-only focused client and the risk-averse client.

The Return-Only Focused Client thinks he or she is getting the highest return by merely picking the asset with the highest mean return (Asset A).

The Risk-Averse Client thinks he or she is protecting his or her assets from losing money by choosing the least risky investment option (Asset B).

On the surface, both of those statements seem true.

But as we saw in this post, the reality is quite different.

By not controlling for volatility, the Return-Only Focused Client actually hurts his or her long-term returns since the higher volatility of Asset A degrades the CAGR of the asset over-time.

If the Return-Only Focused Client was truly concerned with returns, he should choose Asset B which has a lower mean return and lower volatility since that will lead to larger long-term returns (CAGR).

On the other hand, the Risk-Averse Client thinks he or she is being “safe” by choosing the least risky investment option. But the reality is they often settle for lower long-term returns because they are unwilling to take any risk in the short-term.? Choosing to make a guaranteed 4% over the long-run isn’t mathematically better than a 10% long-term return that has large ups and downs in the short-term.

You just have to be willing to psychologically withstand seeing your portfolio values go up and down dramatically in the short-term—and that’s not for everyone.

The truth of the matter is that if the Risk-Averse Client really wanted to minimize risk, then he or she would find two assets with the highest return and the exact same volatility that were 100% negatively correlated.

That way whenever one asset had a high return, the other asset would have a low return and the opposing returns would remove all the risk.

They would get the highest return with no risk!

To illustrate this, let’s consider another two asset portfolio, both of which are risky assets individually, but as I’ll show in a second, completely eliminate risk when included together.

The first Asset will be Asset A which we are already familiar with.

In any given year Asset A has either a -10% return or a 30% return. This is a mean return of 10% with a 20% swing in either direction.

Asset F also has either a -10% return or a 30% return. But it is 100% negatively correlated with Asset A. So whenever Asset A has a -10% return, Asset B has a 30% return. And vice versa.

We can see the effect of a 50/50 portfolio of Asset A and Asset F below.

Table 7: Two Asset Portfolio with the Same Return and Volatility, but Negatively Correlated

What should strike you almost immediately from the table above is that both Asset A and Asset F are very volatile individually. But when we combine them in a 50/50 portfolio, the end result is a guaranteed 10% CAGR with no risk because the direction of the volatility of each of these assets offset each other.

In other words, in order to get the highest risk-adjusted return, one has to get the riskiest assets that complement each other and use them together.

Doing so both maximizes the return of the portfolio AND minimizes risk.

This is counterintuitive to the risk-averse client who thinks he or she just has to invest in safe assets to minimize risk.

Obviously it’s nearly impossible to find two assets that are 100% negatively correlated and offset each other’s volatility identically, so this example is not realistic.

But the overall idea of the importance of reducing correlation between assets—and ideally finding assets that are negatively correlated—for the purpose of reducing portfolio volatility and volatility drag still stands.

But what I want to highlight to readers is this: The emotional bias and preconceived notions you have towards return and risk may prevent you from actually accomplishing what you say your goals are—regardless of whether that goal is to maximize return or minimize risk.

In order to abide by your professed values, you have to be both willing to learn and challenge the way you look at and engage with your pre-existing beliefs.