**By Blake Curtis of Wilshire Advisors.**

A common catchphrase used to explain the importance of diversification is “Don’t put all your eggs in one basket.” This analogy of spreading risk is intuitive: One basket might break, one might be stolen, and one might end up in cold storage with a lost key. The eggs and baskets do well to illustrate the power of diversification to reduce risk but may not fully do the term justice.

By focusing only on distributing risk, this fails to capture most investors’ primary interest: seeking returns. In November 2020, Wilshire published a research piece “‘Ti– i– i– ime … is on My Side:’ Taking Full Advantage of the Institutional Investment Horizon,” where market beta and rebalancing were identified as two of the essential elements of portfolio construction. The following example highlights those topics and will seek to uncover where the “free lunch” of diversification originates — hopefully without breaking too many eggs along the way.

To begin, imagine an asset whose long-term holding period return is zero — meaning that a dollar invested in this asset will still be worth a dollar at some indefinite point in the future. (Inflation will be ignored throughout this article for the sake of a clearer discussion.) The second characteristic of this asset is variance. In other words, the value of the asset at any point in time may drift higher or lower, before eventually returning to the original investment amount.

Here is an example of an asset with varying valuation day to day but a long-run return that converges back to $100:

While the value of the investment will change, by definition its worth will converge back to the initial amount invested given enough time. The first question to ask: Is this asset attractive?

Most would recognize that taking risk without a reward is irrational — especially if there is a more efficient way to earn that return. For example, if it is possible to preserve the value of an investment in a savings account with zero risk, that choice minimizes risk while preserving value and is therefore more rational. While this is true narrowly speaking of this one imaginary asset, the next step is to consider diversifying risk into another basket (aka asset) in an attempt to improve the overall investment outcome.

Instead of only one imaginary asset, the opportunity set is now expanded to an arsenal of five uncorrelated investments that are rebalanced regularly as a diversified portfolio of assets. Continuing the hypothetical scenario, assume all five assets individually have the same characteristics as the first one mentioned. They each would preserve the value of the original investment during long periods of time as a stand-alone asset but would also experience variance along the way. Each asset will receive one-fifth of the investment capital to produce the following portfolio:

Admittedly, this portfolio feels like it is headed nowhere fast. However, the variance concept introduced earlier has now been specifically defined as a 30% standard deviation of return – in the real world, that would be a relatively high-risk asset. The reason that this is important is that the 0% assumed return is referring to the compounded annualized growth rate, often shortened to “CAGR.” In other words, this return accounts for the fact that the current period’s return is impacted by the previous period’s return — and will either start the next period higher or lower depending on the current period’s return. In layman’s terms, many investors would breathe a sigh of relief at having maintained their original investment value after having experienced 30% volatility.

Hidden by (or really, implied by) our risk and return assumptions is that, due to compounding, the arithmetic return of each asset equals 4.1%. As great as this new information is, it is not yet actionable, since arithmetic returns are not actually earned by investors. The realized return for holding each of these assets will be impacted by volatility, so the only way to get anywhere close to earning the arithmetic return is by removing some of the volatility. Hmm, if only there were a way to reduce the risk of a portfolio …

This is where correlation and rebalancing move front and center. If each of these assets were perfectly correlated, combining them into a portfolio in an attempt to reduce risk would be futile. The way to reduce the volatility of assets is by combining them with other uncorrelated (or lesser correlated) assets to reduce their aggregate risk. This concept can be compared to noise-canceling earphones. Sure, it is possible to dampen the volume of the outside world with insulation, but it turns out that adding more noise actually reduces the perceived volume if the additional noise is out-of-phase. Adding more insulation is like adding cash to a portfolio — it dampens the total “noise” of the portfolio but doesn’t change the characteristics of the sound; whereas adding uncorrelated assets is like introducing noise-canceling signals that interfere with the outside volume — making it sound quieter as the sound waves cancel each other.

The second critical component is rebalancing. The value of uncorrelated assets in a portfolio is highly dependent on their exposure, or sensitivity, to drivers of return. Rebalancing allows a portfolio to maintain an optimal mix of each asset to deliver its targeted impact on returns. If a portfolio is not rebalanced, returns will cause the weights of assets to drift and potentially reduce the diversifying power of the assets.

The more frequently rebalancing occurs, the more time the portfolio will spend with an optimal balance of assets (though transaction costs should be a consideration in determining rebalancing). Now, armed with uncorrelated assets and a rebalancing plan, it is time to cancel out some portfolio noise.

Skipping over some portfolio math, a portfolio with five equally weighted assets that are uncorrelated, where each has a risk of 30%, will result in a portfolio risk of 13.42%. Calculating the portfolio return, it is known that each asset has an arithmetic return of 4.1%, so the portfolio also has an arithmetic return of 4.1% (the portfolio’s arithmetic return is just the weighted average of the assets’ arithmetic returns). The geometric return, however, is where diversification begins to do its magic. The portfolio has less than half the risk of investing in any of the individual assets. But recall that volatility also impacts the CAGR. Using this "new and improved” portfolio risk level, the CAGR of a portfolio with an arithmetic average return of 4.1% and a volatility of 13.42% comes to…

3.22%^{1}.

In other words, combining five regularly rebalanced, volatile and uncorrelated assets that each have a CAGR of 0% annually results in a portfolio that is able to compound a positive return of 3.22% annually. Probably the key word in this statement is “rebalanced,” as a buy-and-hold portfolio would have a geometric return of the dreaded 0% in the long run.

This example underscores the other side of diversification that the egg basket analogy fails to capture. As great as risk reduction is, it’s important not to overlook the very positive impact it can have on improving returns as well. While the above example may seem completely abstract with no real-world corollaries, there are assets with similar relative characteristics in the investing world. Within the commodities basket, the individual precious metal, industrial metal, energy, and agricultural contracts are an often-overlooked asset class full of volatile instruments with low CAGRs. Here, there are more than five uncorrelated assets with similarly high levels of volatility available to investors.

In a world that can demand so much and give away so little, it behooves us to reach out and grab what others won’t bother to pick up. Let diversification pay for your lunch — perhaps an egg-salad sandwich.

**Footnotes:**

^{1} Performance noted represents hypothetical performance and does not include fees, expenses, and transaction costs. Hypothetical performance uses various assumptions and is reported with the benefit of hindsight, and does not reflect the impact that certain economic and market factors might have had on the decision-making process, nor can they accurately account for the ability of an investor to withstand losses. Investors should not assume that the results of the hypothetical returns will be the same for any actual account managed.

All posts are the opinion of the contributing author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CAIA Association or the author’s employer.

**About the Author:**

**Blake Curtis** joined Wilshire in 2017. He provides consulting services and client support, including portfolio and manager analysis, to public and corporate pension plans, foundations and endowments, and defined contribution plans. He received a Bachelor of Science degree in finance from California State University, Northridge.