# Assessing a Portfolio’s Diversification

#### Table of Contents

Higher levels of diversification allow you to take less risk to help achieve your desired level of return. At Betterment, we have carefully constructed our recommended portfolio strategy to achieve optimal diversification; it’s one of the core principles of our investment philosophy. We also allow investors to use our customization feature, Flexible Portfolios, to meet their individual needs. To help investors maintain diversification while adjusting their portfolios’ individual asset classes, we give real-time feedback about the level of portfolio diversification as they construct a Flexible Portfolio.

## Why does diversification matter?

It’s worth taking a moment to review why diversification matters.

An objective of almost any portfolio is to seek growth with as little volatility as possible. Most assets will have price swings along the way; however, not all asset prices change at the same time or in the same way. In other words, price volatility is unavoidable, but if we choose the right set of investments, we may be able to lower the overall volatility of the portfolio. This is possible when the prices of individual parts of the portfolio move in different directions. As illustrated below, the less that prices move in tandem, the smoother the returns of the overall portfolio are expected to be. The value across time of the two-asset portfolio is likely to be somewhat smoother while any drawdown in value is less severe. You can see more research on diversification here.

#### Illustration of Diversification

*Figure 1. **T**he less that prices move in tandem, the smoother the returns of the overall portfolio are expected to be. *

A simple example below shows that as you add to a portfolio uncorrelated assets—i.e., assets whose prices move independently of one another—the overall portfolio becomes less volatile, even when each asset has the same individual level of volatility.

#### Volatility of a portfolio with *N* uncorrelated assets, all with 12% assumed volatility

**Figure 2.** This figure is hypothetical in nature and simply shows six portfolios of imaginary uncorrelated asset classes with an assumed volatility of 12%. The example demonstrates the mathematical reality that a portfolio of assets that do not perfectly correlate is less volatile than any single asset in the portfolio.

## Understand the Efficient Frontier

Mathematically, as long as assets not perfectly correlated, we can combine them into a portfolio to lower the overall volatility. Below, you can see the result of various portfolios that combine global stock and bond assets. Because of diversification, we can see that the combinations of assets are expected to perform better than the individual assets themselves.

#### Efficient Frontier for the Betterment Portfolio Strategy

**Figure 3.** This figure illustrates hypothetical annual expected excess returns—i.e. returns that exceed the risk free rate—projected for portfolios of the Betterment Portfolio Strategy. The calculation uses our asset class return assumptions found here using the Capital Asset Pricing Model. The blue points represents the Betterment Portfolio Strategy across the entire risk spectrum. The grey points represent other portfolio combinations using the fund components of the Betterment Portfolio Strategy. At each level of risk, the set of Betterment-recommended portfolios have higher hypothetical expected excess returns.

*These returns do not include a Betterment management fee or fees charged by issuers of particular securities. These returns include reinvestment of dividends and are in excess of the risk free rate. This calculation is hypothetical in nature, does not represent actual returns attained, and does not take into account any future economic or market conditions. The impact of trading, and other income is not considered. Actual results may differ significantly from the values shown.*

You can also see that there is a boundary at which we can no longer create a portfolio that has a higher expected return, given its level of risk (points no longer go higher or further to the left). The set of portfolios that comprise the outer boundary is called the efficient frontier. The efficient frontier is the set of hypothetical optimal portfolios that seek to provide the best possible risk-adjusted return, which is an input in determining the specific portfolio that Betterment recommends to a customer.

Ideally, investors want to invest in portfolios on or very close to the efficient frontier. When a portfolio moves further from the efficient frontier, it may be taking additional risk that you are not being fully compensated for.

Risk and returns are fundamentally linked. When you take more risk in your portfolio, you should aim for expected compensation via a higher return; it doesn’t make financial sense to take on more risk for less or the same returns. Investors should avoid portfolios that take unnecessary and uncompensated risk. The efficient frontier acts as a kind of north star, illustrating the best returns an investor could expect for a given level or risk.

## How We Measure Diversification

When investors use Betterment Flexible Portfolios, we measure the amount of uncompensated risk they are taking in their portfolio. In other words, we measure how far the portfolio is straying from the efficient frontier.

Using our portfolio optimization process, we have worked to make sure any recommended portfolio in the Betterment Portfolio Strategy is optimally diversified and sits on or very close to the efficient frontier. Because our recommended portfolios are optimally diversified, these serve as the starting point for any comparison. This is also why we recommend that investors choose the Betterment Portfolio Strategy.

To measure diversification in a Flexible Portfolio, we calculate the expected return and volatility of the customized portfolio and compare it to an appropriate comparison portfolio in the Betterment Portfolio Strategy. Put simply, a Flexible Portfolio is well diversified if it has the same risk-adjusted return as the comparison Betterment portfolio. So, we define our diversification rating as the difference between the volatility of the Flexible Portfolio and the rescaled volatility of a comparison portfolio in the Betterment Portfolio Strategy.

This process has two steps. First, we identify the portfolio in the Betterment Portfolio Strategy that has the closest expected return to use as our comparison portfolio. For example, if a Flexible Portfolio has an expected excess return of 5%, then we compare it to the 76% stocks, 24% bonds allocation of the Betterment Portfolio Strategy.

Then, we assess how much additional risk the Flexible Portfolio may be taking on by scaling the Betterment-recommended portfolio to have the exact same expected return as the Flexible Portfolio. Now that we have two portfolios with comparable expected annual returns, we evaluate how much additional risk (expected volatility) a custom portfolio may be taking. That extra risk is the result of under-diversification—either from not holding enough assets or holding too much of one asset or a number of similar assets.

Shown graphically, you can see that a portfolio consisting of 80% US stocks and 20% US bonds is expected to achieve the same annual return as the Betterment 63% stock portfolio, but has almost 10% more risk.

#### Uncompensated Risk from Poor Diversification

**Figure 4.** See Figure 3 for more information on the analysis behind this chart. Here we visualize the uncompensated risk—same hypothetical expected excess return but different expected volatility.

## Offering Feedback in Flexible Portfolios

As we see above, diversification (or lack thereof) can be measured by the amount of uncompensated risk a portfolio is taking when compared to an optimal Betterment portfolio.

When an investor is adjusting a portfolio using Flexible Portfolios, we provide real-time feedback on the amount of uncompensated risk. If a portfolio’s uncompensated risk is too high, we will highlight it and recommend increasing diversification across assets.

There are a number of reasons investors may want to adjust the holdings in their portfolios. Our feedback on the diversification helps these investors make changes while highlighting the potential impact to the future performance of their investments.

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