Does Bankruptcy Risk Increase Value? Puzzles and Diversification

We usually compare the market price of different companies thinking we are comparing their fundamental values. Following this practice, financial analysts believe that diversification destroys value since the price of diversified firms (“conglomerates”) is 11% lower than the price of similar portfolios of focused firms.

In our paper, price is equal to fundamental value for each listed company. However, we show that price differences do not reflect value differences across firm types because of their unequal bankruptcy probability. Even after considering firm characteristics, including bankruptcy probability, price comparisons do not reflect value comparisons due to a survivorship bias: default has killed more firms among riskier than among safer ones. To get an unbiased value comparison, we would need to know the current price of all the firms that defaulted. This is impossible because markets price surviving firms, only.

While this last observation is obvious, its implications are subtle and relevant. Since the market price of firm x equals its value conditional on its survival, the price of firm x exceeds the value of all firms of type x that have existed. Thus, there is a price/value wedge, which increases in the bankruptcy probability of type x firms. Safer listed firms have a lower price/value wedge than riskier listed firms since more of the former survived (and will survive) to downturns while more of the latter disappeared (and will disappear) in downturns.

According to our reasoning, the discount of diversified conglomerates paradoxically reflects their higher ability to survive to economic downturns.  We investigate this hypothesis by analyzing separately firms with very high default probability (that should display a high price-value wedge) and firms with low default probabilities (that should have a small price-value wedge). Consistent with our conjecture, the conglomerate discount reaches 13.3% for the former while it is just 5.6% for the latter.

All price comparisons of companies with different survival skills suffer from a survivorship bias. Our insight should thus explain other “pricing puzzles” that remain puzzles until we realize that stock prices equal the value of surviving firms, only.