- Survivorship bias, cost in statistics and home ownership affordability

Survivorship bias, cost in statistics and home ownership affordability

Written by Wilfred Ling

Friday, 29 April 2011

In many investment index, there is a problem called survivorship bias. There is a tendency for poor performing fund to be closed down or merged with a better performing one. When this happens, the fund ceased to be included in the index. This results in the index performance appearing to be better than it should. An unsavvy investor would think that the index has done well without knowing that poor performing funds have been dropped out.

This can happen to a fund manager trying to market its services. For example, a fund manager may have 20 funds in year 1990. In 2011, 10 of the original funds are no more included in the index because it closed down or merged with others. A potential client who looks at the current performance may think that the fund manager did well for the past years but what he is looking at are the best performing funds. After taking into account of the bad funds that closed down, the fund manager’s skill was just so-so.

Some indices are gross of fees while others are net of fees. Take for example MSCI index has two set of indices namely Gross and Net representing before and after withholding taxes respectively. Again, an unsavvy investior would mistakenly believe that the index has done well if he would to just look at the Gross. What matters is the one that is net of taxes and fees.

The statistics regarding home affordability is subjected to survivorship bias as well. A politician said that home ownership in Singapore is affordable because 80% use average of 25% of the income for housing loan. Some practitioners use 35% as the benchmark. So 25% of debt to service ratio looks very good. But this statistics has survivorship bias because those who cannot afford this amount would give up on their loan and sell their property to redeem their loan. In other words, the ‘poor performer’ would not be included in the statistics. In addition, those who cannot afford the housing loan were never qualified to get a loan in the first place. This means the figure looks better than reality. Another problem is the statistics is ‘gross’ of fees. What do I mean? I have many clients whose debt-to-service ratio is around 25-30% of their income. So the ratio looks good on paper. But because both persons have to work, they forgo having more children than they desire. The opportunity cost of forgoing a bigger family has to be taken into account. If one of them stopped work, they will not be able to afford the housing loan (or their debt-to-service ratio will breach 35% limit recommended by many practitioners). Since the birth-rate in Singapore is so low, it is not only a personal problem but a national crisis. Some couples have chosen to hire a domestic worker to take care of the housework and children while both couples worked. It is not unreasonable that the cost of a domestic worker is $1000 per month (depending whether from Philippines, Indonesia, etc) after taking into account of lodging, insurance, medical, food and the headache in managing an individual transplanted from a different culture usually not by choice but because of poverty. In this case, the actual debt-to-service ratio goes up from 25% to 50%!

Just be careful with statistics is what I am trying to get my point across.

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