In our daily lives, we perpetually make choices between options with uncertain outcomes. For example, do we stick with the familiar lunch option or do we try the new rancho deluxe double cheeseburger with aji sauce? While personal taste might be the dominant criterion when making lunch choices, consider the choice between paying down debt (a mortgage, for example) or investing for retirement. Here we look for a rational choice that will maximize our financial well-being.

Most analyses will strip out the impact of taxes and fees and reduce it to a choice between two options with different expected returns. The decision then seems obvious: choose the option with the higher expected return. But what is an “expected return” and is it how we make financial decisions?

### We can illustrate by example^{1}:

A. You are offered $100 if a coin toss comes up heads, or nothing if it comes up tails

B. You get $46 for sure.

The expected return is calculated by taking the probability of each event and multiplying it by the reward (or penalty) from each event and summing the results. For example, the expected return from option A is 0.5*$100+0.5*$0 = $50. Since the expected return from Option A is great than $46 then a rational economic agent would choose Option A. *Would you?* We suspect not – and that’s okay. The behavioural psychologist, Richard Thaler differentiated between those who made rational choices based on expected values (Econs) and the rest of us (Humans). So if humans don’t make rational choices, how do we choose?

Having sowed some seeds of doubt about whether expected returns is a decision tool used by humans, we continue with our example of choosing between paying down debt and investing for retirement.

Samir has a debt of $10,000. From his employment income, he has spare cash. Does he use the cash to reduce his debt or invest? We are told that Samir pays 3% on his debt and if he invested in an investment portfolio he can expect a return of 5%. Since the expected return from investment return is greater than his cost of debt, then investing seems the obvious choice.

Not so fast…

Our first step is to recognize that reducing debt is a form of investment. If Samir reduced his debt by paying off $5,000 of his loan then his interest payment would reduce from $300 to $150.

Alternatively, Samir could take his $5,000 and invest it in a Guaranteed Investment Certificate (GIC) and get a return of 3% (a bit of a stretch at current GIC rates, but never mind). He still pays $300 interest on his loan but he receives $150 interest from his GIC so his net cash flow is an outflow of $150.

Either case is risk free and has the same net cash-flows. So Samir’s choice between paying down debt or investing in an investment portfolio is equivalent to choosing between a risk free investment that pays 3% or a risky investment that has an expected return of 5%.

## How risky is risky?

We assume that the loan is only for one year. Samir knows he can make 3% by reducing his debt. We are given additional information about the investment risk: there is a 50% chance that the risky investment has a 14% return and a 50% chance it has -4% return. The expected outcome is 5% (0.5*14%+0.5*-4%).

If Samir was an Econ then he would invest rather than reduce debt because the expected return from investing is higher. But Samir is a human and most humans are risk averse meaning that they feel the pain of losses more than they value gains.

If we wanted to find out how risk averse Samir was we could ask him questions such as:

### What value of X would induce you to accept the following gamble:

A. A 50% chance of losing $1,000

B. A 50% chance of winning X

Most people require X to lie in the range $1,500-$2,500 to accept the gamble, with a higher value reflecting a greater aversion to loss. An Econ would be happy with X having any value greater than $1,000. If Samir had answered $2,000 to the above question we can say that he has an aversion ratio of 2.

Returning to Samir’s options with his $5,000. He knows he has the certain option of gaining 3% or $150 if he reduces his debt. Alternatively, he can pursue the investment option where he has a 50% chance of losing 4% or $200, a net loss of $350 (taking into account he also has to pay $150 of debt interest). Given Samir’s loss aversion he requires a net gain of twice this net loss, i.e. $700. Thus Samir would require a 50% chance of a 17% gain rather than the 14% on offer. Samir’s loss aversion deters him from investing even though the expected return from investing is greater than the return from reducing debt.

While we may be closer to understanding how Samir makes his decisions other factors may be relevant. We learn that Samir earns $50,000 annually and has $50,000 in investments. How might he respond to the following:

### What value of X would induce you to accept the following gamble:

A. A 50% chance of losing $50,000

B. A 50% chance of winning X?

Or

### What value of X would induce you to accept the following gamble:

A. A 50% chance of losing $1 million

B. A 50% chance of winning X?

We can guess that Samir’s loss aversion rises as the impact of the loss becomes potentially ruinous. Loss aversion is thus a function of your wealth, not just your appetite for risk.

Humans are not rational agents when making decisions. The choices investors make may be influenced by their personal aversion to loss that changes depending on their wealth. One of the roles of financial advisors is to understand their client’s actual decision making process, not to impose their own model behaviour. Some decisions, portfolio rebalancing, for example, can be delegated by the client to avoid dissonance between their human tendencies and the optimal economic choice. Other decisions, like the choice between reducing debt and investing cannot be delegated and it may be appropriate to settle for choices that are not economically optimal but are sustainable: better to a happier Human than a wealthier Econ.

^{1} Thinking, Fast and Slow, Daniel Kahneman (2011)

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