Game theory attempts to explain our behavior in situations where the success of our choices are impacted by the choices of others. Price wars are the most common example. If Pepsi cuts prices, assuming elastic demand, sales will increase and so will profits. But if Coke follows suit, Pepsi's action will be neutralized such that both Coke and Pepsi end up with lower profits than what they would make if prices werent cut in the first place. So letting prices be is the best course of action for both, which is the conclusion they will eventually reach after the game is played multiple times.
I got thinking if this explains the problem with our traffic rules. When we all follow rules, then it gives those who break them an advantage. Let's say the rule is that we stick to our lanes regardless of traffic. Now, if the traffic is slow, someone can cut across lanes and weave through traffic, assured that everyone is driving in their lane. But once that happens, the rest will naturally feel cheated and start doing it too, and we end up with massive chaos.
I see two ways of addressing the problem. One is to remove the incentive for breaking rules, by imposing hefty and consistent fines, which is impossibly difficult to do in our country. The second is to let people play this "game" enough times until they realize that we are better off following the rules. It doesnt mean every single person has to experience chaos before sanity returns. Once enough people decide to follow rules, a critical mass is reached. You have - tada - a tipping point. You see people following rules, then more people follow rules and so on. The concept of social proof kicks in.
Its not as far-fetched as it sounds. I think it partly explains why Mumbai has better lane discipline and civic sense than other cities - people here have seen traffic chaos so many more times.
I think the unfortunate part is when everyone starts to follow the rules, some of us will be tempted to break them and get an unfair advantage. And when there is no system of fines or penalty, more people will start doing it creating another tipping point and the cycle continues...
Showing posts with label price. Show all posts
Showing posts with label price. Show all posts
Monday, August 24, 2009
Tuesday, July 28, 2009
Value of a stock - Part II
Before we move forward, lets discuss the time value of money. This concept is at the core of financial valuations. It states that a $100 today is worth more than $100 a year from now. Why? You can put your $100 in a bank it will be $105 next year. That's the time value of money. In other words, there is an opportunity cost involved.
Back to our stock now. We've determined the return that we are expecting from the stock. And we have the price of the stock as it trades in the market. We can use the two to determine what should the price one year from now. If price is $10 and expected return is 10%, then price of stock 1 year from now is 10*(1+10%) = 10*1.1 = $11. In other words, if the stock price is $11, one year from now, you can pay $10 to buy it today.
A little digression to understand where a stock's value comes from. A company makes and sells products and earns revenue. Out of this, go expenses such as raw materials, salaries etc. If the company has any debt, it needs to pay interest on that. And what remains is the profit. Of course profits are taxed, so a portion of that goes to the govt. What remains after all these is called Profit After Tax (PAT) or Net Income (NI) is available for distribution among shareholders. In reality, of course, companies "reinvest" PAT, meaning they will use this money to fund further expansion and generate more revenues etc. For simplicity, lets say a company is "mature", meaning there are no opportunities of growth. It will just keep making and selling the exact # of units year after year. As a result, all PAT will be distributed as dividends to shareholders that is you and me:) In reality though PAT doesnt equal CASH - that's accounting for you, which is way out of the scope of this article. But understand that some adjustments are made to PAT to arrive at "Cash Flows (CF)".
Now it all comes together. Once you know the CFs of a company year after year, you can discount them all by the expected return rate to get today's value. But we only have data to calculate last year's CF. How do you know what the company makes in future years? This is where assumptions and projections come in. You look at the economy, industry etc., and predict that revenues, expenses will grow or shrink at a certain rate leaving you with a CF. This is one reason why analysts may have differing opinions about a stock's value - because they have different growth assumptions. Once you buy a share of a company, you own it forever (or until the co shuts down). So you'd have to project CFs out to infinity. To make it mathematically manageable, you project it out 10 years or so, and use a geometric series formula to find the value at the end of 10 years. Now discount all these values to today and you have the value of the firm.
Now, if the firm has taken any debt, that will need to be repaid eventually. So subtract debt from the value of the firm and you have the "equity value" of the firm, which is what shareholders own. Simply, divide the equity value by the number of shares outstanding, and voila! you get value per share.
If this value is less than market price, the stock is overvalued. If it is greater than price, the stock is undervalued.
Back to our stock now. We've determined the return that we are expecting from the stock. And we have the price of the stock as it trades in the market. We can use the two to determine what should the price one year from now. If price is $10 and expected return is 10%, then price of stock 1 year from now is 10*(1+10%) = 10*1.1 = $11. In other words, if the stock price is $11, one year from now, you can pay $10 to buy it today.
A little digression to understand where a stock's value comes from. A company makes and sells products and earns revenue. Out of this, go expenses such as raw materials, salaries etc. If the company has any debt, it needs to pay interest on that. And what remains is the profit. Of course profits are taxed, so a portion of that goes to the govt. What remains after all these is called Profit After Tax (PAT) or Net Income (NI) is available for distribution among shareholders. In reality, of course, companies "reinvest" PAT, meaning they will use this money to fund further expansion and generate more revenues etc. For simplicity, lets say a company is "mature", meaning there are no opportunities of growth. It will just keep making and selling the exact # of units year after year. As a result, all PAT will be distributed as dividends to shareholders that is you and me:) In reality though PAT doesnt equal CASH - that's accounting for you, which is way out of the scope of this article. But understand that some adjustments are made to PAT to arrive at "Cash Flows (CF)".
Now it all comes together. Once you know the CFs of a company year after year, you can discount them all by the expected return rate to get today's value. But we only have data to calculate last year's CF. How do you know what the company makes in future years? This is where assumptions and projections come in. You look at the economy, industry etc., and predict that revenues, expenses will grow or shrink at a certain rate leaving you with a CF. This is one reason why analysts may have differing opinions about a stock's value - because they have different growth assumptions. Once you buy a share of a company, you own it forever (or until the co shuts down). So you'd have to project CFs out to infinity. To make it mathematically manageable, you project it out 10 years or so, and use a geometric series formula to find the value at the end of 10 years. Now discount all these values to today and you have the value of the firm.
Now, if the firm has taken any debt, that will need to be repaid eventually. So subtract debt from the value of the firm and you have the "equity value" of the firm, which is what shareholders own. Simply, divide the equity value by the number of shares outstanding, and voila! you get value per share.
If this value is less than market price, the stock is overvalued. If it is greater than price, the stock is undervalued.
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…
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…
Monday, July 27, 2009
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..
http://www.punemirror.in/index.aspx?page=article§id=4&contentid=200907222009072201490454678e298fc§xslt=
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..
http://www.punemirror.in/index.aspx?page=article§id=4&contentid=200907222009072201490454678e298fc§xslt=
Subscribe to:
Posts (Atom)