How does an investor’s need to budget for risk relate to shopping for apples at the local grocery store? As it turns out, quite a bit.

Introductory microeconomics courses spend a lot of time discussing consumer choice: How do individuals choose what to buy in light of budget constraints? Given a certain budget, considering market prices, and in light of consumer preferences, what’s the best bundle of goods and services to buy? It’s a standard “utility maximization” problem.

If you progress into advanced courses, you learn that economists are probably the only ones who take their utility curves shopping with them and bother doing that type of optimization. However, you also learn that, while individuals might not actually act like the hyper-rational agent of Economics 101 books, groups of individuals tend to behave as though they are engaging in this type of calculation—even if each individual makes decisions based on habit or heuristics (rules of thumb).

You also learn that it’s hard to account for tastes: different people have different preferences over the attributes of goods and services. To take apples and oranges as an example, people have different preferences between crunchy and squishy, sweet and sour, and any other dimensions you can imagine. This gives rise to a medley of preferences that must be accounted for.

Just like shopping, investing is about making choices:

  • With a grocery basket, shoppers try to pick the best bundle they can afford
  • With investing, people want to pick the best allocation they can afford—but investing involves a lot more uncertainty

Judging a piece of fruit’s quality before buying it is significantly easier than gauging the quality of an investment before allocating towards it. Given the mix of skill and luck that goes into determining investment outcomes, investors might be best served by focusing on what they can control: the process they use to make decisions.

We cannot control outcomes, but we can control our processes. Understanding the parallels—and differences—between shopping and investing can help improve an investment process, even when we cannot control the outcomes.

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I see a compelling analogy between the choices a consumer makes in investing household income in grocery items with the choices an investor makes in budgeting for risk. As with consumer choice, the actual decisions of investors might be driven more by rules-of-thumb than by calculations. However, in the investing world, many portfolio managers do engage at least partially in this type of calculation, mixing art and science. The inputs to portfolio construction involve expectations around risks and returns and there’s uncertainty around those estimates. (In fact, you can even find uncertainty around the uncertainty!) And just as different people have different preferences over a grocery item’s range of attributes, they also have preferences over an investment’s range of attributes, including:

  • Income versus price gain potential
  • Environmental, social, and governance features of one company versus another
  • And, one of the most frequently considered dimensions of investing: People’s preferences between risk and return

Risk can mean different things to different people, from uncertainty around investment outcomes, to variability in returns during one’s journey toward a given outcome. An investor can measure risk in different ways, and feel the presence of risk in different ways.

To make this concept more concrete, I used the excess returns of the FTSE Global All Cap Index for equities and the Bloomberg Barclays Global Aggregate Index for fixed income, whose longest available common time period is February 2003 through February 2018. To highlight some of the issues around measuring risks and returns—and the importance of one’s holding period (how long an investor intends to hold an investment)—I calculated some descriptive statistics for the two indexes in the table below.*

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So how does budgeting for risk come into play? Just to illustrate the concept, I will pretend as though the annualized standard deviation of monthly returns of the indexes in above table is the “right” measure of risk.

An investor might set a particular risk budget: an amount of volatility he or she is willing to tolerate. Given a particular budget, how should he or she spend that budget? This is a portfolio allocation question. The standard way to solve this problem is to map out all the allocations that maximize the average expected return for a given level of risk. In the jargon of investments, this creates what’s called an “efficient frontier” of portfolios.

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By adding a low risk security, such as a one-month Treasury bill, to the mix of possible investments, an investor may do even better than what’s found on the efficient frontier. Suddenly, the investor can invest along the “capital allocation line”—or the combination of the optimal risky portfolio with the low risk security shown in the figure below.

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The power of the capital allocation line is that an investor can decide his or her risk tolerance and find the portfolio allocations with the best chance of hitting that target. I should use the past-tense, as this exercise is backward-looking: it tells us the historical standard deviation and historical returns. Portfolio managers develop expectations of risk and return to spend their risk budgets.

Investors may also have preferences for:

  • How total return is generated from income or price changes
  • Around the stability of the income component and price component, as discussed in my previous blog post.

With competing priorities: a risk budget and a yield target, the investor’s choice becomes more complicated, as there may be trade-offs between the priorities. But this framework can help an investor think through what those trade-offs might be.

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With this highly stylized hypothetical example, there isn’t much of a gain in income for additional risk around the total return. Therefore, perhaps the most powerful way to manage the trade-offs of budgeting for risk—while targeting income—is to expand the investment opportunity set. Instead of this simplified example of two risky assets, an investor with a risk budget and an income target might want to consider more of a “go anywhere” type of approach. A “go anywhere” approach is not the same as a “Wild West” approach to investing. As I’ve written before, it simply means casting a global net for opportunities, and rethinking some subconscious perceptions around investing outside one’s home country.

While difficult to put in practice in a quantitative way, the analogy between consumer choice and investor choice can at least provide a conceptual framework for thinking through the tough problem of investing for income in a risk-managed way.

 

Standard deviation is the square root of the sum of squared deviations from the mean. It is often used as a measure of volatility, variability, or risk.

* The average return was calculated as twelve times the arithmetic average of the monthly returns for the time period indicated. The annualized standard deviation average is the square root of 12 times the standard deviation of monthly returns.

 

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