Cognitive bias: Unit dependence and naive diversification

Naive diversification and unit dependence

Let’s make a simple case study so you will easily understand the unit dependence bias and naive diversification.

You are given $20,000 by a relative. You can invest this amount in IBM and Apple stocks (stock price: $91.72 for IBM and $15.21 for Apple).

You can invest in two portfolio M or S. Which one do you choose?

Unfortunately, the first portfolios are not available anymore. You are now offered instead to invest in one of the two portfolios below. Which one do you choose?


MBA students have been confronted to this choice and most of them did not have the same preference in the first and in the second case, even though the portfolios are strictly identical. Only the way to present the information (in dollars or in number of shares) has changed.

Two biases are involved in this decision-making.

  1. Unit dependence bias: Unit dependence bias makes us solve a problem differently according to the units used to present it. Unit dependence bias is a specific case of the framing effect, to be influenced by the way a problem is presented.
  2. Naive diversification bias: Diversification bias is a kind of heuristic, an intuitive tool to solve rapidly complex problems. This heuristic has been first observed in marketing by Simonson, a psychologist. He showed that when people have to make simultaneous choices (for example, to choose in one shot the portfolio with the best asset allocation), they tend to diversify more of their allocation than when making sequential choices.

Consequences on the financial markets

Studies in behavioral finance have shown that many investors tend to make a “naive diversification” of their investments, like in the example above.

It means that if they can invest in 5 funds, they will invest 1/5 of their total investable amount in one of these 5 funds, with little regard to whether the options are a stock fund, a bond fund, or a mixed fund (Benartzi & Thaler, 2001). This bias can lead to suboptimal investments.

For further information about the unit dependence bias:

Biases in allocation under risk and uncertainty: Partition dependence, unit dependence, and procedure dependence Thomas Langer , Fox 2005