• Scroll to view all countries

Please Choose Your Country

Welcome. This website is intended solely for the use of institutional investors, consultants and other professionally recognized financial intermediaries in specific countries. Intech Investment Management LLC (“Intech”), is an investment adviser registered with the United States Securities & Exchange Commission. Intech is not permitted to offer products and services in all countries. It is the responsibility of prospective investors to inform themselves of and to observe all applicable laws and regulations of any relevant jurisdictions, including the legal requirements and tax consequences within the countries of their citizenship, residence, domicile and place of business with respect to the acquisition, holding or disposal of shares or securities, and any foreign exchange restrictions that may be relevant thereto. The products and services referred to in this website are not offered to any person or entity in any jurisdiction where the advertisement, offer or sale of such products and services is restricted or prohibited by law or regulation or where we would be subject to any registration or licensing requirement not currently held by Intech or our affiliates. If Intech does not offer a website for your country, please visit www.janushenderson.com.

Australia Wholesale Client Confirmation

Not your country? Please choose your country here.

This Website is intended solely for the use of wholesale clients in Australia and their professional consultants and investment advisers and is not for general public distribution.

This material on this website is not intended for distribution to, nor should it be relied upon by, retail clients. If you are a retail or individual investor, then please leave this Website.

Intech is permitted to provide certain financial services to wholesale clients in Australia pursuant to an exemption from the need to hold an Australian financial services licence under the Australian Corporations Act 2001. Intech is regulated by the Securities Exchange Commission of the U.S. under U.S. laws, which differ from Australian laws.

The words ‘Intech,’ ‘we,’ ‘us’ or ‘our’ used herein refer to Intech Investment Management LLC (“Intech”), an investment adviser registered with the United States Securities & Exchange Commission, and ‘you’ or ‘yourself’ may refer to an individual, Independent Financial Advisor, consultant, company, or other entity visiting this website. This website is issued by Intech Investment Management LLC (“Intech”).

Unless stated otherwise, information on this web site is provided by the issuer of the applicable financial product.

Information contained on this Website is published solely for general informative purposes and should not be relied upon as financial product advice. This content has been prepared without taking into account the objectives, financial situation or needs of any person. Before making an investment decision you should consider the appropriateness of the information on this website having regard to these matters and where relevant read any disclosure document relating to a financial product. You should also consider obtaining independent advice before making any investment decisions.

This website is intended only for wholesale clients (as defined by section 761G of the Corporations Act 2001) in Australia and their professional consultants and investment advisers who are who are knowledgeable and experienced in the financial services market and in investment products of this nature.

Should you proceed to access this Website, you will be representing and warranting that you are a “wholesale client” as defined by section 761G of the Corporations Act 2001. The information is not authorized for use in a jurisdiction where distribution is not authorized and is not intended for distribution to retail clients.

In continuing to access or use Intech’s Website at intechinvestments.com (“Website”), you agree to be bound by the Terms of Use applicable to your use of this Website and any information obtained from it. If you do not agree to these Terms of Use, please do not use this Website or download or read content from it.

The information contained on this web site is believed to be accurate and current at the time of compilation and is provided in good faith. Intech does not accept any responsibility arising in any way (including negligence) for errors in or omissions from information contained on this web site or for any loss or damage (whether direct, indirect or otherwise) suffered by the recipient of the information contained on this web site, or any other person. Intech does not accept any legal responsibility for material published on third party linked sites.

What follows is not an offer or invitation to acquire an investment to, and should therefore not be relied upon by, any person anywhere other than Australia or any person in any jurisdiction where such an offer or invitation would be unlawful. Persons in respect of whom such prohibitions apply must not access this Website.

If you choose to access this Website from locations outside of Australia, you do so at your own initiative and risk, and are responsible for compliance with all applicable laws. Otherwise, please return to intechinvestments.com and choose the appropriate jurisdiction, where you will find investment products and services that are available to you.

This Website is reserved exclusively for non-U.S. persons and should not be accessed by any person in the United States. A “U.S. Person” is defined by U.S. laws and regulations in force from time to time. If you are resident in the U.S., or as a corporation or other entity are organised under U.S. law or administered by or operated for the benefit of a legal or natural U.S. person, you should take professional advice to determine whether you are a U.S. Person and you should not access this Website until you are sure that you are not a “U.S. Person”.

WE BELIEVE THAT THE INFORMATION THAT MAY BE VIEWED ON THIS WEBSITE IS ACCURATE AS AT THE DATE OF PUBLICATION, BUT WE DO NOT GUARANTEE THE ACCURACY OR CURRENTNESS OF THE DATA AND WE DISCLAIM ALL REPRESENTATIONS AND WARRANTIES OF ANY KIND, WHETHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION, WARRANTIES OF MERCHANTABILITY, FITNESS FOR PARTICULAR PURPOSES, TITLE AND NON-INFRINGEMENT. FURTHERMORE, THE INFORMATION MAY BE AMENDED BY US AT ANY TIME WITHOUT NOTICE. BY PROCEEDING YOU AGREE TO THE EXCLUSION BY US, SO FAR AS THIS IS PERMITTED UNDER APPLICABLE LAW, OF ANY LIABILITY FOR ANY DIRECT, INDIRECT, PUNITVE, CONSEQUENTIAL, INCIDENTAL, SPECIAL OR OTHER DAMAGES, INCLUDING WITHOUT LIMITATION, LOSS OF PROFITS, REVENUE OR DATA ARISING OUT OF OR RELATING TO YOUR USE OF AND OUR PROVISION OF THIS WEBSITE AND CONTENT REGARDLESS OF THE FORM OF ACTION, WHETHER BASED ON CONTRACT, TORT (NEGLIGENCE), WARRANTY, STATUTE OR OTHERWISE, AND REGARDLESS OF WHETHER WE HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. IF YOU ARE DISSATISFIED WITH ANY PORTION OF THIS WEBSITE, OR OF THIS IMPORTANT INFORMATION, YOUR SOLE AND EXCLUSIVE REMEDY IS TO DISCONTINUE USE OF THIS WEBSITE.

If you are unsure about the meaning of any information provided on this Website, then please consult your financial or other professional adviser. We do not offer investment advice.

Cookies: This Website uses cookies to remember your preferences and to help us to improve this Website through the use of web analytics. By continuing without changing your cookie settings we will assume that you are happy to receive cookies for these two purposes. For full details on how to manage our cookies and how we use them, please see our Cookie Policy as well as the Cookies section within our Privacy Policy.


Decline - I am not a wholesale client

A couple of weeks ago, I received an email from an old friend with the subject: Sound Familiar? It contained a link to an article in Financial Advisor Magazine where the author describes “the free lunch in investing” by quoting a 1992 article in the Financial Analysts Journal written by David Booth and Eugene Fama...

“The portfolio compound return is greater than the weighted average of the compound returns on the assets in the portfolio.”

This sounds familiar all right!

This idea is central to Intech’s investment philosophy; our founder actually published this observation as a mathematical theorem in 1982 – ten years before the Booth and Fama FAJ article appeared! But, as Booth and Fama point out, it’s not exactly a free lunch. It requires some statistics, and some discipline. While our investment team uses some intense math, most investors can grasp the basic mathematical concepts by digging just a little deeper into the concept of return.


Formula graphic_1

Fernholz, R., & Shay, B. (1982). Stochastic Portfolio Theory and Stock Market Equilibrium. The Journal of Finance, 37(2), 615–624. https://doi.org/10.1111/j.1540-6261.1982.tb03584.x.


How Can the Sum be Greater Than the Parts?

At first glance, the whole idea may seem a bit strange. How can a portfolio’s return be greater than the weighted-average return of the stocks it holds? As you may know, Markowitz (1952) formalized the concept that a portfolio’s return over a single period is simply the weighted-average return of the stocks in a portfolio; that was, however, only true for the arithmetic return. The same does not apply for a portfolio’s compound (or geometric) return.

To understand the difference between arithmetic and compound returns for a portfolio, it’s important to review and define return calculations more generally. While this may seem like a trivial exercise, its answer has repercussions on risk and portfolio management.

The classic definition of the (arithmetic) return on an investment is simply the difference between the final value and the initial value, divided by the initial value (also written as: return = final value / initial value – 1). This formula is fine for a single-period, but most investors have long-term time horizons and are interested in a multi-period, compound return that combines the n annual returns of r1, r2, . . . , rn . The common methods for calculating compound returns – arithmetic, geometric, and logarithmic – all have different characteristics.

Arithmetic Average Returns

These returns are the sum of all the annual returns, divided by the number of years (where n = number of years, and r = each year’s return):

formula1

Arithmetic returns are widely used in Modern Portfolio Theory (MPT). The calculation, however, has an upward bias as an estimator of expected long-term growth to an extent that can easily reach absurd proportions. For example, consider a +100% return in year one followed by a -50% return the following year. Here, the arithmetic average return over the two-year period is 25%, but in reality, such an investment would have zero growth over the two years.

Geometric Average Returns

These returns are the n-th root of the product of the annual returns, where n is the number of years.

formula 2

This is the most commonly used method by investment professionals. It helps to avoid some of the absurd results demonstrated in the example of arithmetic average returns given above, and this gives the calculation some scientific gloss. Unfortunately, the geometric return is awkward to work with, and it too has an upward bias as an estimator of expected growth over the long term.

Logarithmic Average Returns

These returns are the sum of the logarithms of the annual returns (plus one), divided by the number of years.

formula3

Unlike both arithmetic and geometric returns, logarithmic returns are the only calculation that is unbiased as an estimator of expected long-term growth. What’s more, logarithmic average returns are the most conservative estimator of expected long-term growth:

Arithmetic Geometric Logarithmic

Comparing Compound Returns

Consequently, for single-period returns, arithmetic returns are sufficient, but to examine accurately a portfolio’s compound return, we recommend using stocks’ logarithmic returns. They’re an unbiased estimation of expected compound returns and they produce the most reliable results.

Relating Single-Period and Compound Stock Returns

The stock attribute that drives the difference between single-period and compound returns is volatility. As a stock’s volatility increases, the negative impact on long-term compounding also increases, resulting in a lower compound return. The log-return of a stock is approximately equal to its average arithmetic return minus half its variance. Many refer to the latter term as “volatility drag.”

formula_4

Relating Stock Returns to Portfolio Returns

When applying the above relationship to a combination of stocks in a portfolio, the stocks’ portfolio contributions become interesting because of their potential diversification effects. The contribution of a stock to a portfolio’s compound return can be greater than its own compound return, because the contribution of a stock to the portfolio’s variance is less than its own variance.

The incremental portfolio return contribution of a stock increases to the extent that diversification reduces overall portfolio risk. Therefore, the compound return of a portfolio is not simply the weighted-average compound return of its constituents – it’s potentially greater!

 

Formula graphic 2

Portfolio Compound Return: This is the expected long-term performance of a portfolio using continuously compounded log-returns. Stock Effects: This is the contribution of stocks’ compound returns to portfolio compound returns. They’re typically the focus of traditional stock pickers and often thought to drive portfolio compound returns. Diversification Effects: This is the contribution to a portfolio’s compound return attributed to diversification. It measures the extent to which the volatility of the portfolio is less than that of its constituent stocks.

Fernholz and Shay (1982) described the amount by which a portfolio’s compound return exceeds the contribution of compound returns from the underlying stocks as “an excess growth rate.” It is a critical component to a portfolio’s compound return and measures the extent to which the volatility of the portfolio is less than that of its constituent stocks. That is to say, it represents diversification.

In other words, you can uncover alpha by optimizing portfolio diversification: combining volatile, uncorrelated stocks, thereby improving a portfolio’s diversification, you can increase this source of alpha.

Harnessing Volatility

Intech has sought to capitalize on these diversification effects for over 30 years. While most active managers focus on the stock effects by trying to forecast stock returns, we focus on diversification effects, due to the interactions between stocks.

Harnessing stock price volatility to optimize diversification is important for both growth and risk control. By systematically replenishing diversification, we attempt to preserve portfolio efficiency and capture a trading profit – a rebalancing premium.

This is a vastly different paradigm of investing and it offers a framework that can help explain many so-called “anomalies.” For instance, in our paper, Diversification, Volatility, and Surprising Alpha, which was recognized among the Best Factor Investing Papers by Savvy Investor, we offered a factor-free explanation as to why many simple, systematic investment strategies beat cap-weighted indexes. You can dig deeper here:

Diversification, Volatility, and Surprising Alpha How do naïve and systematic portfolios outperform a cap-weighted benchmark over the long term? Download to Learn More

Fernholz, E. R. (2002). Stochastic Portfolio Theory, Volume 48 of Applications of Mathematics (New York). Springer-Verlag, New York. Stochastic Modelling and Applied Probability.
Fernholz, R. and B. Shay (1982). Stochastic portfolio theory and stock market equilibrium. Journal of Finance 37 (2), 615–624.
Markowitz, H. (1952). Portfolio selection. Journal of Finance 7 (1), 77–91.
The views presented are for general informational purposes only and are not intended as investment advice, as an offer or solicitation of an offer to sell or buy, or as an endorsement, recommendation, or sponsorship of any company, security, advisory service, or fund nor do they purport to address the financial objectives or specific investment needs of any individual reader, investor, or organization. This information should not be used as the sole basis for investment decisions. All content is presented by the date(s) published or indicated only, and may be superseded by subsequent market events or other reasons. Although the information contained herein has been obtained from sources believed to be reliable, its accuracy and completeness cannot be guaranteed. Past performance is no guarantee of future results. Investing involves risk, including possible loss of principal and fluctuation of value.

Related Posts

Top Blog Posts - 2022 Year in Review

Low Volatility? Exactly What Kind of Volatility Are We Talking About?

Finding Limits to Asset Class Diversification? Take Another Look at Your Equities.

2025 Intech ©. All rights reserved.

Privacy Policy | California Privacy Notice | Terms of Use | Cookie Policy