The Utility of Probability

We intuitively understand probability, but its application is incredibly complex. For the record, probability is defined as the likelihood of an event occurring, expressed in % terms. Textbook explanations talk of rolling a dice and predicting the chance of getting a 6. These are benign experiments with results of little consequence. But when probability is applied to real events, interesting, if slightly unnerving, possibilities emerge.

Let’s take power cuts as an example. In most Indian metros, we are used to 24-hour power, but there is always a probability of grid failures that will cause a blackout. I don’t think even power equipment manufacturers provide 100% uptime guarantee, although the probability of failure is extremely low. So if we didn’t have any grid failures in the last five years, the probability of such failure increases with each additional day. Yet, the way we look at it, if something hasn’t failed in the last five years, it probably won’t in the future.

This paradox is explained to an extent by the framing of the situation. Underlying every probability data is the assumption of a very large number of observations. We think five years is large enough, when apparently it is not, as is seen from the recent crisis. If property prices are rising over the last few years, it is probably time for a correction, but we believe otherwise. However, we do grasp probability pretty well in other areas. For example, when a batsman hits a century, we expect that he will soon get out. We know scores above 150 are very rare. (Why so many batsmen get out between 100 and 150 is another question altogether.) In a game of cricket, with a definite start and end, we can easily imagine possibilities and compute probabilities. But in life, defining a start and end period is easier said than done.

We shouldn’t feel too sorry for the theory itself is weirdly structured. It says, for example, that the probability of getting heads or tails when tossing a “fair coin” is 50% when the experiment is repeated a large number of times. So if I take a random coin, what’s the probability of heads? This dilemma is beautifully captured in one of my favorite Jay Leno punch lines, “George Bush’s popularity rating hit a low of 25%, which means, now only one in four people support his presidency. So when the President is having dinner with his wife and two daughters, he is the only one that thinks he is doing a good job.” The second statement logically flows from the first one, but one can immediately see the fallacy. So if autism affects 1 in 10 children, we know there is no way to rule out our kid by gathering a group of 10 children. The statistic is chilling, but it has no practical utility, which leads us to believe that our child is not the “1”, resulting in complacency and complications.

So what to do with probability data? One could argue that we should strive to minimize the probability of adverse events (or failures). For example, the probability of traffic snarls can be minimized through electronic monitoring of traffic patterns and adjusting the timing of signals or diverting traffic through alternate routes. This will work, and brilliantly so, but here’s the problem. Once these things work on a consistent basis, we assume that they will never fail. So when they do fail for whatever reason, we are caught unawares. And my uneducated opinion is that as we keep minimizing the probability of failure, the magnitude of failure goes on increasing. If the traffic signals were coordinated and centrally controlled, a break down will result in unmanageable chaos. And with every day such a system works brilliantly, the probability of failure, infinitesimal as it may be, keeps mounting. But a high probability doesn’t mean the event will occur:)

Value of a Stock – Part I

For a financial layman, like I was a year ago, the price of a stock is a mystery. Why does Microsoft trade at $25 whereas Google trades at $450? And why do analysts mean when they say Google is cheap at $450? Isn't MS dirt cheap at $25 then?

That's the first rule. The price by itself doesn't tell you anything. What you need to know is the price of a stock relative to its value – another term relentlessly abused by the financial press and analysts. Let me try and debunk this mystery.

Buying a stock is an investment so you expect some returns. Think of a bank term deposit. Let's say, you put in $1000 for a year, the bank pays you some interest. The interest is your return from the deposit. Of course, the big difference between the two is that the returns of a stock are not well-defined. Let's dig deeper.

If you hold a stock, your return can either be capital gains or dividends. Capital gains are simply the profits you make when you sell the stock at a price higher than what you paid to purchase it. For example, if you buy MS at $25 and sell at $40, your capital gains are $15. Dividends are cash payments made to you by the company at regular intervals, usually annually or quarterly. For example, MS recently announced a quarterly dividend of $0.13 per share.

Now that we know the types of returns, the big question is, how do you know if a stock will deliver any returns? And are those returns good enough? Let me answer the second question first. Your stock has to at least beat the 5% APR offered by your bank, if not, what's the point? Might as well invest your money in bank deposits and sleep in peace. But, are you happy if the stock returns exactly 5%? No, because you are taking on an appreciably higher risk by investing in the market. When you take that kind of a risk, you expect to get rewarded. So the return from a stock has to be definitely higher than your bank rate. But, how much higher?

For a moment, let's set our stock aside and take the stock market as a whole (or simply the "market'). The market is represented by indexes such as Dow Jones, NASDAQ and S&P 500 – there are many more, but these are the popular ones. These indexes are comprised of multiple stocks from various industries. So you will have stocks from FMCG, tech, telecom, infrastructure etc. Some of these cos will be good, some bad, some growing and some declining. Let's say you want to invest your money in the "market" - in other words, think that you are buying 1 stock of the S&P 500 index. What should be your return? There are ways to derive this, but the simplest way is to look at the returns delivered by S&P 500 in the past. Take the year-end values of S&P 500 over the past 30 years, find out the annual return (annual growth, to put it crudely). Now, determine the difference between the S&P return and your bank rate. This delta is called the Market Risk Premium, which is the additional return you are expecting because you took the additional risk of investing in the stock market rather than the safer term deposit.

But remember that the stock market has many companies so the negative effects of some stocks are offset by the positive effects of others. For every Sun that fails, there is an Apple or a Google that delivers stellar performance. So the risk of investing in the "market" is different from that of buying a specific stock. Some stocks are safer than the market and others are riskier. For example, P&G has been making hair and body care products since forever. And unless we dramatically change our ways of personal hygiene, it is fair to assume that P&G will continue to sell its products. So, it is a safer bet. Contrast it with Google, which is threatening MS and Apple today, but could just as easily be threatened by Facebook or MySpace. Therefore, Google is riskier than the market.

To determine the relative risk of a stock versus the market, analysts use a term called Beta. Without getting into the details, it is a factor to arrive at the risk premium for your stock, which is a product of your stock's beta and the Market Risk Premium. (By the way, the Beta of the market is 1.) Beta for cos such as Google will be >1, and that of Unilever etc is <1. Now add this to your bank rate to find out the return you must get from the stock. Let's take an example.

Say, annual returns of S&P over last 30 years is 8%

Beta of Google is 1.17

Your bank deposit rate is 5% (Technically, this should be the rate on US treasury bonds, but this is a fair approximation.)

Therefore, Market Risk Premium (MRP) = 8% - 5% = 3%

Risk premium for Google = Beta * MRP = 1.17 * 3% = 3.51%

So expected return for Google = 5% + 3.51% = 8.51%

In other words, Google is an attractive stock, if and only if, it offers returns above 8.51%. The next part will discuss how to determine this.

To be continued…

More Than You Know

Just started Taleb's Fooled by Randomness. As it happens, this is the third consecutive book I am reading which talks about the role luck, randomness etc – I am using these terms to loosely mean uncertainty – plays in our lives. The previous two are Michael J. Mauboussin's More Than You Know and Malcolm Gladwell's Outliers. I will quickly summarize my takeaways from the first one.

The point is stunningly simple. That the market has several players, and the same bit of information is interpreted differently by different players. Naturally, a pre-condition is that the market players be heterogeneous and for the most part they are. When heterogeneity is maintained, the market on average correctly reflects the underlying state of the economy. One particular story (a true one, I believe) is used to convincingly illustrate this phenomenon. At a village contest, people were asked to guess the weight of an ox. The average value of the guesses turned out to be correct answer, although none of the individual guesses was anywhere close. The so-called experts represent only some players in the market, and at best, their predictions may only be close to the actual. When heterogeneity is compromised, however, players fall prey to group-thinking, and we end up with unsustainable booms followed by the unavoidable busts. The practical consequence is that one is better off investing in index funds rather than mutual funds.

Anyone invested in the market would know that "overvalued" and "undervalued" are two terms that every analysts throws in at will in his analysis. The value of a stock is the discounted value of its future cash flows (profits loosely), and the price is what it currently fetches in the market. Now, if the price of a stock is higher than its value, it is overvalued. The typical analyst recommends selling overvalued stocks and buying undervalued ones because sooner than later price adjusts to reflect value. The point made in the book is that it is not enough for you to find a great stock that is undervalued. The premise is that price will adjust to reflect value (in this case, price will go up). Meaning, there are just enough people out there thinking the same way as you are so that the demand for the stock pushes its price upward. If everything thinks the way you do, the stock would skyrocket immediately. And if no one agrees with you, well, the stock might stay undervalued forever.

So the trick is not just to find stocks that are undervalued, but also predict whether the market will agree with your assessment. It is probably for this reason that analysts love to appear on TV shows and rattle out their predictions. If enough people watching the show fall for it, well, you've got yourself a self-fulfilling prophecy. (The last point is my extrapolation).

The book covers such wide range of topics that I don't even remember all the things discussed. It definitely was worth my time, and hopefully I will get around to reading it again.

Tailpiece: Pune Mirror found my post worthy to be included on their website..

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