# Improving on the Altman Z-Score, part 2: The Ohlson O-Score

In this series of posts we’re exploring some of the alternatives to the 45 year old Altman Z-Score for successfully predicting bankruptcies. So far we’ve looked at the 2010 CHS model which is generally regarded as the best all-round replacement. Today we’re going to take a look at the 1980 Ohlson O-score, followed by the 1974 Merton ‘Distance-to-Default’ (DD) method in the third and final instalment. The O-score is still heavily referenced in academic literature and has its place in the arsenal of analysts around the world. All together it sounded like it was worth taking a closer look at.

**Ohlson O-score**

Similar to the Z-score, the O-score can be described as a statistical bankruptcy indicator generated from a set of balance sheet ratios. Where it differs from Altman’s original is in **its application of a much larger sample of corporate successes and failures** to inform the model. The wider pool of just over 2000 companies gives it a more robust sample for basing the scaling factors applied to its nine variables with the aim of increasing its accuracy. The difference in this sample size is especially apparent when compared to Altman’s original whose statistical technique of pair matching limited him to just 66 companies (it’s amazing it’s still as successful as it is!). Subsequent studies have generally found the O-score to be a better forecaster of bankruptcy than the Z-score, however neither has been able to regularly beat Merton’s DD or the CHS model since their discoveries.

## How It Works

To begin with, let’s take a look at each of the variables and think about why they’ve been included.

**Adjusted Size:**Ohlson measures a company’s size as its total assets adjusted for inflation. Smaller companies are deemed to be more at risk of failure.- AS = log(Total assets/GNP price-level index)
- Where GNP price-level index = (Nominal GNP/Real GNP)*100

**Leverage Measure:**Designed to capture the indebtedness of a company, the more leveraged the more at risk the company is to shocks.- LM = Total liabilities/Total assets

**Working Capital Measure:**Even if a company is endowed with assets and profitability, it must have sufficient liquidity to service short-term debt and upcoming operational expenses to avoid going bust.- WCM = Working capital/Total Assets

**Inverse Current Ratio:**This is another measure of a company’s liquidity.- ICR = Current liabilities/Current assets

**Discontinuity Correction for Leverage Measure:**Dummy variable equalling one if total liabilities exceeds total assets, zero otherwise. Negative book value in a corporation is a very special case and hence Ohlson felt the extreme leverage position needed to be corrected through this additional variable.

**Return on Assets:**An indicator of how profitable a company is, assumed to be negative for a close to default company.- ROA = Net income/Total Assets

**Funds to Debt Ratio:**A measure of a company’s ability to finance its debt using its operational income alone, a conservative ratio because it does not include other sources of cash. If the ratio of funds from operations to short-term debt is less than one the company may have an immediate problem.- FTDR = Funds from operations/Total liabilities
- Where Funds from operations = pretax income + depreciation

**Discontinuity Correction for Return on Assets:**Dummy variable equalling one if income was negative for the last two years, zero otherwise.

**Change in Net Income:**Designed to take into account any potential progressive losses over the two most recent periods in a company’s history.- CINI = (Net income(t) - Net income(t-1)) / (Net income(t) + Net income(t-1))

## Why these variables?

Ohlson’s true explanation for choosing these variables is actually rather candid and surprising; he says his main driver was simplicity and that there was no attempt to select predictors on the basis of rigorous theory. The first six were chosen just because he perceived them to be the ones most frequently mentioned in previous literature. At least he’s honest about it!

Having calculated our variables, we would then need to enter them into the logit model he provides to find the O-score. The model is based on the data of industrial firms between the years 1970-1976 that had been trading on the exchange for at least three years. It gave him a sample of just over 2000 firms of which 135 had failed. Shown below is an example of the formula for ‘Model 1’ of the O-score, the model used to predict failure within 12 months.

- O-score = -1.32 – 0.407*AS + 6.03*LM – 1.43*WCM + 0.757*ICR – 2.37*ROA – 1.83*FTDR + 0.285*DCLM – 1.72*DCRA – 0.521*CINI
- Probability of Failure = P = exp(O-score)/1+exp(O-score)

The O-score is transformed into a probability using a logistic transformation whereby P>0.5 indicates an at risk company and P<0.5 a safe one.

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## How well does it work?

At this point we would ideally like to see the results for each decile of probability in predicting changes in sample portfolio values, similar to how we reviewed the CHS model. Unfortunately the data required for this isn’t presented by Ohlson however a study in 2007 from Marquette university asserts a rather spectacular success rate of 96% in both the 1 and 2 year prediction time frames. Unfortunately the team do not go into a lot of depth on their analysis so instead we can look at a paper from Virginia Tech in 2010 which helpfully compared the models of Altman, Ohlson, Merton’s DD and the CHS model at predicting businesses' cost of debt.

The decision to use companies cost of debt rather than absolute numbers of bankruptcies is that the cost of a firms debt is a very good measure of its distress risk and potential for bankruptcy. It is also much easier to calibrate and validate such a study across different models. The team find that the accounting based measures of Altman and Ohlson are in fact only very weakly related to distress risk measured in this way and in fact do no better than a naïve measure of bankruptcy risk, the leverage ratio. They are also found to react poorly to periods of shock in the market and be very specific to particular industries. This is a stark contrast to the 96% sucess rate previously so what's going on?

It would appear that there is a wide array of methods available for assessing the accuracy of a bankruptcy model, direct statisitcis, credit spreads, different timeframes and market conditions. Having conducted a review of as many comparative studies between the four main models that I could find, it seems that no-one has a definitive answer to which indicator is best for which situation. A study in 2008 for example found that the Z-score outperformed Merton’s DD method; however that goes completely against what the CHS model team and the Virginia Tech paper found subsequently. It seems like as with so many financial analysis tools, the results are there to be interpreted rather than followed religiously and that a combination of indicators is probably the most sensible way forward. With this in mind we’ll discuss one last bankruptcy model in the next blog, the fourth and final most popular bankruptcy predictor, Merton’s DD.

N.B There have been a few attempts at creating an adjusted Z-score and O-score since their inception, mainly aimed at taking into account changes in the way modern businesses are managed such as the increased spending on R&D. Unfortunately studies into their effectiveness generally find them to produce similar if not worse performing models.

**From the Source**

- You can read the original document here (with login).
- And the Virginia Tech paper here.
- Marquette University here.

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