Cognitive Bias (1)

Wikipedia defines cognitive bias as a 'distortion in the way humans perceive reality'. Let's see if you have a bias in the way you evaluate investment opportunity described below. This was an investment scheme presented to my father.

A wealth management firm has an investment scheme for retirees. The firm says they have investment experts who analyze the markets using proprietary tools and have a great track record. The firm claims that its returns in previous three years have been at least 15%. According to the scheme, the firm will invest your money in different investments. Depending on the blended returns from the investments, the investment firm gets certain commissions according to a three tiered schedule:

Blended return (r)	Commission	Returns to investor
Less than or equal to 10%	0	r
Between 10% and 20%	20% over 10% (=0.2 X (r – 0.1))	10% + 0.8 X (r – 0.1)
Over 20%	2% plus 40% over 20% (= 0.02 + 0.4 X (r – 0.2))	18% + 0.6 X (r – 0.2)

The firm says that the incentives are very clearly if they don't give the investor a return of at least 10% the firm gets nothing. Therefore, the firm will really make sure that the investor gets a great return.

What do you think of this investment opportunity? Click here to see my take.

Let me first state my assumption before I tell you that I would never invest in something like this. I believe that markets are by and large efficient. Unless an investor (in this case the firm) has insider information about an investment, the investor cannot do better than investing randomly. This is the guiding principle of most of the finance professors at the Chicago GSB.

If the above holds true, the firm cannot really pick investments. Let us say that they have 10 investment options. Let us say the investment firm manages investments for 10 retirees. Since the firm has no ability to pick investments, it will invest randomly. Retiree 1's funds go into Investment 1; retiree 2's funds go into Investment 2 and so on.

Let us assume that the general market (think of this as the S&P 500 index) grew at 8% that year and the return on the individual investments look as follows:

Investment 1	-8%
Investment 2	-4%
Investment 3	0%
Investment 4	4%
Investment 5	8%
Investment 6	8%
Investment 7	12%
Investment 8	16%
Investment 9	20%
Investment 10	24%

On average, the investments gave a return of 8%. Four investments did worse than the general market and four did better. Two matched the market performance. Let us see how our retirees did. Keep in mind that in this market, if any investment gets you less than 8%, you are worse off then investing in the broad index.

Investment	Investment return	Firm commission	Retiree return	Retiree
Investment 1	-8%		-8%	Retiree 1
Investment 2	-4%		-4%	Retiree 2
Investment 3	0%		0%	Retiree 3
Investment 4	4%		4%	Retiree 4
Investment 5	8%		8%	Retiree 5
Investment 6	8%		8%	Retiree 6
Investment 7	12%	0%	12%	Retiree 7
Investment 8	16%	1%	15%	Retiree 8
Investment 9	20%	2%	18%	Retiree 9
Investment 10	24%	4%	20%	Retiree 10
Average	8%	2%	7%

On average, the retirees did worse than the market. The investment which looked good upfront turned out to be a bad one. The problem was that the incentives that seemed well aligned were actually not well aligned. For the incentives to be well aligned, the firm should have offered a minimum guaranteed return. The way the scheme was structured, the firm never lost any money.

This is an example of a Confirmation Bias. At first glance, we only try to see how the scheme might work to our advantage. We don't try to imagine how it might work against us. The second effect here is the Base Rate Fallacy. We don't consider that in fact no one can pick stocks or other investments without having insider information. Since this firm does not have insider information, their probability of picking good investments is 0. We still think that since the firm's incentives appear aligned, they must be confident of their ability to pick good investments. Since they appear confident, they must be able to pick good investments.

To read more about such biases, go to the list of cognitive biases on Wikipedia. It is one of the most comprehensive lists on the topic that I have seen. I strongly recommend it to anyone who has any interest in the topic.