What is Gamma?

Measuring how financial planning strategies can improve income during retirement.

Paul Kaplan 22 October, 2014 | 6:00PM

The purpose of financial planning is to help investors reach their financial goals. For a lot of people this means having enough money at the right times to finance various needs or desires, such as a child's education, a special family event like a wedding, or the purchase of a new vehicle.

But by far the largest financial goal is to be able to finance a certain standard of living during one's retirement years. This goal is not only multi-year, but because no one can predict the date of their death on the day their retirement starts, the length of the period is unknown.

While financial goals are almost always stated as amounts of money at specific points in time, much of financial advice focuses on selecting specific investments, such as mutual funds and stocks, and assembling them into portfolios. These activities are often guided by the investor's risk tolerance and other portfolio preferences, such as a predilection for domestic securities, as well as the investor's capacity for taking risk. It is not always clear how the selected portfolio relates to the financial goals that presumably it will help fund.

The focus on security selection and portfolio construction is sometimes expressed as alpha and beta. With respect to managed investment products, such as mutual funds, beta refers to the part of portfolio's expected return that is due to its asset class exposures, while alpha is the expected return of the fund in excess of the expected return on its asset class exposures. Hence, a portfolio construction process with an alpha/beta focus consists of first deciding on an asset allocation (based on risk tolerance, risk capacity and perhaps other factors), then selecting managed products that the advisor believes will provide alpha.

In 2013, David Blanchett (Head of retirement research at Morningstar Investment Management) and I published a research paper titled Alpha, Beta, and Now…Gamma in which we introduced a measure of how much various financial planning strategies can improve income during retirement, and thus on how financial planning impacts the fulfillment of financial goals. We simulated returns on asset classes (stocks, bonds, etc.), formed portfolios and traced how portfolio returns, together with other factors, affect income available for spending during retirement. We call the percentage improvement in income due to financial planning strategies "gamma," the third letter of the Greek alphabet after alpha and beta.

Our main finding is that combining five specific financial strategies could lead to an extra 22.6% in retirement income. This is equivalent to an alpha on the portfolio as a whole of 1.59% per annum. The five strategies that we modelled are:

  • Using a total-wealth framework to determine asset allocation. Total wealth includes human capital, which is the present discounted value of future income. The more human capital a person has, the greater their risk capacity. As time goes by and human capital is diminished, risk capacity falls so that the asset allocation becomes more conservative.

  • Using a dynamic withdrawal strategy as opposed to fixed level of withdrawal from investment accounts. The level of withdrawal depends on financial wealth, which fluctuates with movements in the capital markets, and life expectancy, which falls over time and thus allows for greater withdrawals.

  • Purchasing annuities to generate a higher level of guaranteed income.

  • Making tax-efficient allocation and withdrawal decisions. To take maximum advantage of tax-deferred accounts such as RRSPs and RRIFs, investors should put their most tax-inefficient investments, such as bonds, into their tax-deferred accounts and keep them there as long as possible. This means first withdrawing from taxable accounts during retirement, and only withdrawing from tax-deferred accounts when required to by law or by need.

  • Using an asset allocation technique that takes into account the nature of the investor's liabilities (future spending needs), which for retirees is primarily their sensitivity to inflation.

Since our focus is on income, the main source of risk in our model is the uncertainty of income. So an investor's risk capacity depends on how much income during retirement is guaranteed through sources such as government social insurance programs and annuities purchased prior to retirement. Risk tolerance is a matter of how the investor feels about the uncertainty of income, especially the possibility of income being low.

However, because an investor may need income over many years, it is not enough to model investors' attitudes about the uncertainty of income. We also have to model investor attitudes about income over time. David and I modelled these using two parameters that are standard in economic theory:

  • The subjective discount rate

  • The elasticity of intertemporal substitution

Economic theory postulates that people are impatient when it comes to receiving income (or more precisely, enjoying the goods and services that they buy with income). Hence, a dollar today is worth more to someone than a dollar tomorrow. The subjective discount rate measures the degree of impatience. The higher the subjective discount rate, the higher the expected rate of return on investments that is needed to induce the investor to postpone income.

Economic theory also says that when the market's expected rates of return increase, investors will postpone their consumption because they can get a greater reward by investing their money rather than spending it now. The degree to which they are willing to do this is measurable and is called "elasticity of intertemporal substitution." The higher the value of this parameter, the more the investor will reschedule her consumption into the future when the expected rate of return exceeds her subjective discount rate.

David and I investigated how sensitive our results for gamma are to changes in the three parameters that describe investor preferences: risk tolerance, the subjective discount rate, and the elasticity of intertemporal substitution. One of our findings was that the gamma for investors who have a very low elasticity of intertemporal substitution is much higher than those for whom it is high.

We believe that this finding has important implications for financial planning, particularly with respect to the kind of information that advisors collect from their clients using questionnaires. Specifically, while most financial planning questionnaires are designed to elicit information about an investor's investment horizon and risk tolerance, we are not aware of any that seek to determine an investor's elasticity of intertemporal substitution. We hope that our research inspires incorporation of this aspect of investor preferences into financial planning practices.

Thus, the concept of gamma not only provides some quantification as to the value of financial advice, it also points the way to a more comprehensive view of what it means for financial advisors to know their clients.

About Author

Paul Kaplan

Paul Kaplan  Paul Kaplan is Director of Research for Morningstar Canada.