Moving From Target Returns to Expected Returns

Investing is really just a probabilistic endeavour not unlike gambling. Lets think about that for a moment. Like gambling, investing has a set of expected outcomes and like gambling, the only certainty is that there is no certainty. However, despite this lack of certainty we need to act.

For precise prediction, we rarely have the required information and by adding more information we do not necessarily obtain more accurate results. To counter this we need to look at decision making as a set of probabilistic outcomes. By calculating a probability distribution we can arrive at an expected value which takes into account probable chances of loss. In other words the chance of an adverse result. In total this will enable us to calculate an expected return rather than a target return. This is no different from producing a decision tree of probabilistic outcomes.

By expressing opinions in expected value terms we are admitting that there may be a chance of a negative result. By reviewing all of the scenarios (good, bad and neutral, etc) we can start to think of the payoffs and the probabilities of those payoffs. It removes the risk of focusing too much on particular scenarios (often the positive ones). In behavioural finance this is known as "anchoring"- if we start to think of the target return for of a certain stock we start to look for evidence that will support that target whilst dismissing contrary information.

By considering multiple scenarios, we are enabled psychologically to consider all the available information. This allows us to enter into the investment position with the idea that there may be an unfavourable result. In other words, we can be wrong without a fear of failure.

So what does all of this mean? Lets take a look at an example.

Stock exceeds earnings target. 25% probability. Stock rises by 3%
Stock meets earnings target. 50% probability. Stock rises by 1%
Stock misses earnings target. 25% probability. Stock falls by 4%

(0.25 x 3% + 0.50 x 1% + 0.25 x -4%) = 0.25%

We can see here that our expected return is not really all that favourable, even though the probability is clearly in favour of a positive result. Lets look at an even more illustrative example.

Stock exceeds earnings target. 25% probability. Stock rises by 3%
Stock meets earnings target. 65% probability. Stock rises by 0.5%
Stock misses earnings target. 10% probability. Stock falls by 10%

(0.15 x 3% + 0.65 x 0.5% + 0.20 x -10%) = -1.225%

This is clearly a bullish outlook but the expected return is negative. So what should we do? Short sell?

Now lets look at a typical stock which is facing some problems. Each piece of bad information gives us a small reduction in the price but any positive information has a big impact (upwards) on the price. Lets look at an example:

Stock exceeds earnings target. 25% probability. Stock rises by 15%
Stock meets earnings target. 50% probability. Stock rises by 0.5%
Stock misses earnings target. 25% probability. Stock falls by 2%

(0.25 x 15% + 0.35 x -0.5% + 0.50 x -2%) = 2.575%

Again, the odds are not in favour of a positive outcome but the expected value is positive. Look past the frequency of success and start thinking about the expected value. It's not the frequency of being correct that matters; it's the magnitude of being correct that matters. These are simple examples just used to illustrate a point but remember that through investing, we are dealing in a probabilistic endeavour so it needs to be asked "are target returns really that relevant"?