What size popcorn should I buy?

The perils of relative valuation

Natasha for her 30th birthday was treating her friends at a fancy restaurant. She decided to start off her meal with dessert and so she picked out a chocolate mousse and an orange tart. The mousse was delicious but she could not enjoy the tart cause the mousse was sweeter than the tart and so she could barely taste it.

That same day a magician was entertaining the restaurant crowd and he eventually showed up at Natasha's table. He entertained the group of friends with a few card tricks before informing Natasha that he had a gift for her. He checked his pocket and brought out a beautiful silver watch. Natasha was speechless not because of the kind gesture but because the magician had removed her own watch and was merely returning it. So how was the magician able to remove Natasha's watch without her realizing it?

Turns out that when the magician touched her wrist to remove her watch he also applied even greater pressure on her shoulder.  The reason Natasha could not enjoy the tart is the same reason why Natasha could not feel the magician's hand on her wrist.

Biologically, we tend to perceive things in a relative fashion, and hence while the tart was sweet it was not as sweet as the mousse. Similarly, while there was pressure on her wrist, there was even greater pressure on her shoulder.

What I suppose becomes the important question here is how does our biological inclination towards perceiving things in a relative manner impact our decision-making?

Let's go back to Natasha who has now gone for a movie. She buys a large caramel popcorn to munch on while enjoying the film.  How did she decide which popcorn size she wanted to pick?

Let’s break down the choices.

• The small costs Rs 150 and has 150 pieces of popcorn in it. That gives it a price to popcorn ratio of 1.

• The medium costs Rs 200 and has 200 pieces of popcorn in it. That gives it a price to popcorn ratio of 1 too.

• The large costs Rs 250 and has 300 pieces of popcorn in it. That gives it a ratio of 0.83.

If you were to buy the small or medium popcorn, you would be paying 1 Rupee for one piece. If you bought the large you only paid 0.83 for a piece. The large is clearly the best popcorn for the price, right? (cheapest bet)

While that is true, you might counter that by saying that you would have bought the small one cause you did not have the appetite for the large, and being influenced by that 0.83 ratio may have made you spend more? So is small the best deal?

No matter what size you bought, you just spent Rs 150 or more on popcorn that costs less than Rs 50 in the store.

This right here is the biggest problem with relative comparisons.

In figuring out the best deal, we forget that the market itself may be overpriced. In the financial markets comparing the price of a company relative to its earnings, creates the same issue.

Of course, one company is cheaper than the other company but does that really make that company cheap? I suppose the question becomes are you comparing the best popcorn deals in the theatre or are you just buying popcorn packets from the store?

What makes it worse is that we can compare different popcorn sizes in theatres. In the financial markets, it’s hard to find easily comparable firms. You may just end up comparing popcorn to samosa or burgers.

To minimize bad relative comparison, we need to break down ratios by their key drivers and then make sure that the key drivers are comparable. For instance here is a breakdown of the PE ratio, using the one-factor dividend discount model.

As you can see from this simple model, the PE ratio is largely determined by the dividend payout ratio, the growth rate, and the discount rate. The dividend payout can be further broken down as a function of growth and roe. Eventually, the key drivers of the PE ratio will be –

• Return on Equity – Higher the ROE, higher the PE ratio. (A higher ROE will imply a higher payout ratio too)

• Growth – Higher growth should ideally lead to a higher PE.

• Cost of Equity – Higher the risk(discount rate) lower the PE.

While this is a simple breakdown it helps as now a firm with a higher PE  would be explainable because it also has a higher ROE or a higher growth rate. 

While this does not remove the underlying problem which is the fact that the whole market may be overpriced or underpriced it does reduce the chances of you comparing popcorns to samosas and coming to faulty conclusions.

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