Making better investment decisions by thinking probabilistically

In my last article, I screened for turnaround stocks, those that had high Value and Momentum Ranks. Several of the screen results were subject to takeover offers. This may mean that cheap stocks where trading momentum has turned positive are attractive to acquirers. However, we need a much larger sample size than three to say that for definite since it is also possible that the takeover is the source of the positive change in price momentum. It may be an outcome rather than a cause. For example, TI Fluid Systems (LON:TIFS) had a decent StockRank prior to receiving an offer, but Momentum was its lowest component. Whether it is cause or effect, investors in turnaround stocks need to be prepared for the odd takeover offer.

When faced with an investment opportunity, investors typically use investment ratios to help assess its suitability. For example, Quality investors may look at long-term returns on capital or equity, Value investors may use P/E ratios, and Momentum investors may examine recent price changes. Most investors will look at all of these factors and many more. The Stockopedia StockRanks take many of these metrics and combine them to give a single measure, which may also be helpful. Investors should be wary of oversimplification, but when applied consistently, these metrics can give investors a significant advantage in their pursuit of beating the market.

However, once a company has received a takeover offer, either a firm offer or a possible one, the previously wide field of potential long-term outcomes typically narrows to a much smaller subset of short-term outcomes. The usual metrics are no longer particularly useful for identifying whether an investor should continue to hold such a stock. At this point, a different skill set is required to analyse the investment case. When I looked at National World (LON:NWOR) as one of the turnarounds, I said:

This makes it a special situation, and investors need to take a probabilistic approach to the various outcomes rather than pure valuation metrics.

In this article, I will describe how that approach may be undertaken.

Scenario planning

The key first step is to list all the potential outcomes. Prior to the subsequent news of an improved but "final possible offer" from Media Concierge, here was what I thought the possible outcomes were. (See the original article for a summary of how the company ended up in this situation.)

The idea is to consider the widest possible list of outcomes. Even then, this is tricky to do. Where I list bids at higher prices from Media Concierge, this is intended to reflect a possible range of outcomes rather than multiple increasing bids. As it happened, I was too optimistic with this range, and while an increased possible bid arrived, it had only been upped to 23p and declared final, i.e., the bidder would only consider increasing it further if another bidder arrived.

Valuing each scenario

The second step is to put a value to each scenario. With firm bids, this is relatively straightforward. However, for scenarios where the bid fails, investors need to guess the likely market outcome. One way would be to take the undisturbed share price. However, after a bid fails, the price rarely drops all the way back down to where it was before, as some investors will take the sign that there is bid interest, which means others see the company as undervalued even if a price couldn't be agreed.

In this case, things are complicated further by the various management and shareholder personalities. I have tried to estimate the outcomes here, but this is far from exact:

Adjusting for the share component of potential offers

There are two further factors that investors may want to consider. The first is any discount they may wish to apply to bids that will be in shares. With bids that have a large share competent, often the price of the acquirer drops, making the bid worth less. Take Volex (LON:VLX) , for example. Despite their cash and shares bid for TT electronics (LON:TTG) being rejected, the shares have dropped 16% as the market fears that they will come back with a higher bid:

In the National World (LON:NWOR) example, I am assuming that the only sensible bidder would be Reach (LON:RCH), and if they did bid, there would be a large share component, and their shares would drop around 10% in response.

The time value of money

The second factor to consider is that even if a firm bid is made tomorrow, it will be some time before that money is received. In some cases, the wait may only be a few months. However, where regulatory approval is required, or there are other factors delaying completion, the wait can be extensive. For example, International Distribution Services (LON:IDS) has agreed to a 370p bid consisting of 360p per share in cash, a final dividend for FY2024, and a special dividend conditional upon completion. However, the shares trade below this level given that the deadline has been delayed until March 2025, close to a year after the price was agreed. Having money tied up waiting for completion has a real cost in terms of interest that could be earned on the cash or alternative investments that could be made. Personally, I vary the discount I apply for the time value of the money depending on my view of the other opportunities available. At the moment, there are so many undervalued small cap companies that I estimate that a six-month wait for the cash is probably worth 10% to me. More conservative investors may want to use the interest they could get in a bank until the estimated time to completion. Scenarios where the bid fails and the share price drops in the near term obviously don't require this discount. Overall, multiplying these together (or, more precisely, the estimated value, one minus the discount, and one minus the time factor) gives what is known as the Net Present Value (NPV) of each possible scenario:

Assigning probabilities

The final part of the process is to assign a probability to each scenario. There is a considerable amount of personal judgment involved. If investors have experience with similar scenarios or, even better, data on how things have played out in the past, they can use these to guide them in assigning these probabilities. Otherwise, investors simply have to make their best guess. This may sound haphazard, but the reality is that much of investing involves estimating an unknown future, and we do this implicitly with much of our investment analysis. In this case, we are just being explicit about it. One thing that is certain is that the probabilities should add up to 100%. Here were my probability estimates at the time:

Using this to make better decisions

The final outcome is to calculate what is known as a Risked NPV by taking the sum product of the NPV values and the probability of these happening across all scenarios. This is what I get based on the above:

This was my best guess of the most likely short-term outcome, weighted across all possibilities I was able to conceive. This led me to sell some, but not all, of my shares when the price approached a level where the discount to my short-term Risked NPV valuation didn't provide enough upside for me. That a subsequent possible bid was increased to 23p and the price rose doesn't make this the wrong decision. I acted based on my guess at the probabilities involved. Investors who were able to more accurately estimate those probabilities may well have made better short-term decisions than me, but this is always the case with financial markets.

Adapting to change

When new news arrives, the key is to update the possible scenarios and the probabilities. In this case, a number of my more optimistic bid scenarios disappear, but my estimate of the probability that the 23p bid succeeds increases:

Again, these outcomes and probabilities are my best guess. Many sensible investors will no doubt disagree about both. Indeed, I urge investors to do their own scenario planning and calculate their own Risked NPV for this and similar scenarios. Often, the value is as much in the process as the outcome.

Further thoughts

Even though this probabilistic approach is particularly useful for takeover offers and similar situations where there is a limited number of short-term outcomes, it can also be a string in investors' bows for other investing challenges. As investors, we tend to be too certain about things. We say things like "This company will beat expectations" or "This company will warn and drop 30%". If investors want to scare themselves, keep a diary of the things believed to be almost certain to happen and track how few of them really do! This is a common trait. In his study of expert judgement, Philip Tetlock found that most people made poor predictions about the future. The expert forecasters in his research only did slightly better than chance and usually worse than simply extrapolating current trends.

A particular type of person, however, made significantly better predictions than others: Tetlock called them superforecasters and wrote a book about them of the same name. Rather than focusing on narrow expertise in one area, as most experts do, superforecasters were able to gather evidence from a variety of sources and assess its likelihood. They worked well in teams, reviewed their own accuracy, were willing to admit error and could adapt their opinion. The superforecasters tended to have a probabilistic approach. They didn't just predict an event will happen. Instead, they estimated how likely the event was, listed the other potential outcomes, and estimated how likely you believed they were, too. Perhaps we should all make an effort to think more probabilistically in investing, and life.

[Disclosure: Mark holds shares in National World (LON:NWOR) ]