Sunday, January 3, 2010

The Security Market Line

Let me wish all of you a very happy 2010 to begin with. May you [and me too :)] grow in wisdom this year.


We have heard about the Capital Asset Pricing Model (CAPM). It is a part of Capital Market theory that deals with risk and expected return. It emanates from Harry Markowitz's Portfolio Theory but has been given a formal shape by William Sharpe (1964), John Lintner (1965) and Jan Mossin (1967).

Since this is supposed to be a short post on the Security Market Line (SML), I am not going to go into the derivation of it. It would suffice to say the when the CAPM (which is basically not much more than a linear regression), is represented graphically, it offers us two lines in the risk - return space. One of those lines is called the Capital Market Line (CML) and the other is the SML.

The CML builds on Markowitz's concept of an efficient portfolio but brings in the variable called the risk - free rate of return. Also, the risk is assessed by the standard deviation of the asset's return (total risk). It therefore examines the risk - return relationship of efficient portfolios.

The SML defines Systematic risk as the only relevant risk (since that is the one that must be tolerated and rewarded for by the market) and therefore rather than standard deviation, it uses the Beta of the asset as a measure of risk. The SML examines the risk - return relationship of all assets and portfolios regardless of efficiency.

You might wonder what is an efficient asset or portfolio. To be efficient, an asset or a portfolio has to satisfy either of the following conditions:

  1. It offers you maximum return for a given level of risk 
  2. It asks you to tolerate minimum risk for a given level of return

Since CAPM, in order to give us reliable results, must satisfy the requirements of linear regression, I would suggest using it with the awareness of this fact. You may not want to discard it. Rather, use it wisely.

The SML can be used to:
  1. Classify securities as defensive (Beta < 1) or aggressive (Beta > 1)
  2. Identify undervalued (plotting above the SML) or overvalued (plotting below the SML) securities
  3. Classify groups of securities into either low - risk or high - risk classes.

Your further readings on the subject will reveal vigorous support and criticism of the CAPM and the world has begun to move on with, for example, Fama and French's Three - Factor Model, the discussion of which is beyond the scope of this brief and humble post.

The video below explains each component of the CAPM equation and plots the SML for a simple piece of data:

Monday, December 21, 2009

Return and Risk of a Portfolio

A portfolio is a collection of assets.

It is always better to spread one's investment over a group of assets in order to minimize risk. This is called diversification. How does the risk reduce by doing so? The risk reduces because the loss in one asset can be offset by the gain in another.

It is important to keep in mind that risk reduction will happen if the returns from the assets that comprise the portfolio are not positively correlated. For instance, it does not make sense to have a 2 - asset portfolio, where both assets are of the same category and nature. Then, rather than reducing the risk, we would be doubling it.

Also, the risk of a portfolio responds to the weights of individual assets. Therefore, the amount of money invested in each asset is important in reducing risk. Through portfolio optimization techniques (for example, Markowitz's mean  - variance model), one can decide exactly what proportion of the portfolio should be invested in each asset to arrive at minimum risk.

We should not get carried away by the idea of not keeping all our eggs in one basket. If we have too many baskets, it becomes progressively difficult to monitor each one of them. There is always an optimum number of assets that should form a portfolio. More than that will lead to superfluous diversification, meaning that the cost and effort to track the portfolio will be more than the benefit from it.

The following video demonstrates the computation of return and risk for a portfolio of assets:

Sunday, December 20, 2009

Using Texas Instruments BA II Plus Financial Calculator

Well, I need not write much about how to use the Texas Instruments BAII Plus Financial calculator. I have put together a brief video, which further redirects you to the Texas Instruments BAII Plus atomic learning page and it is quite self explanatory. Have fun with your calculator and make your life easy!!!

Friday, December 18, 2009

Return and Risk of a Single Asset

The concept of Time Value of money says, and it is rational too, that a dollar (or whatever currency is relevant for you) received today is more valuable than receiving it tomorrow. We still find that a lot of people postpone current receipt in favor of a future one. We often commit our funds to one or the other investment. Why do we do that? Well, of course, we are expecting our money to grow with time and for that to happen, the sacrifice of current income that we make today, should provide us some reward in the future. We call this reward, return.

We all know that future is uncertain and though we would like to see everything proceeding as per plan, things do go awry often. The last couple of years are recent testimony to this. It means therefore, that whenever we invest our money in expectation of future returns, there is always a chance that those expectations can be belied. That is what is the risk involved with any investment, that is, the fact that our actual return can differ from our expected return is the risk. If the actual return turns out to be more than expected, we celebrate and if the reverse happens, we can be found moping.

Therefore, just as we can hope to earn a positive return on our investments, we must also be willing to take a chance that they might turn out to be negative.

We can refuse to take that chance and avoid investing. The good part of that is that our money remains safe but dead. Stagnant money is the bad part. If it does not grow, there is only one thing that can happen with it: it goes on losing value. If you have $100 today and you hide them under a mattress, you will find that a year later, their actual worth will be less than a $100.

It follows that our willingness to tolerate a certain degree of risk, translates into a possibility of earning a positive return and the more risk you can bear, the more return you expect to earn. Put differently, if you have to be persuaded to take on some risk, you are going to ask for a suitable return for it. Risk and return go hand in hand.

In this post, I am focusing on how to find out the return and risk if we invest in a single asset (which, of course is not as wise as investing in more than one asset). The videos below demonstrate this simple process. The first video deals with return and the second one deals with risk.

Return of a Single Asset

Risk of a Single Asset

Homemade Dividends

Dividends are the distributed part of a company's profit and are one of the major ways (apart from a share repurchase program) in which a company offers cash rewards to its shareholders. The alternative is to retain the earnings in a hope of faster growth or to save for the rainy day. The company can also choose to offer non - cash rewards to the shareholders through stock - dividends or stock - splits.

I am focusing only on cash dividends here and there are a number of school of thoughts that consider the dividend policy of a company as an (un)important factor affecting its value. It should be remembered from the outset that dividends are always important. The debate is about the dividend policy. What is dividend policy?

Dividend policy is the choice between paying the dividends now or later and the literature offers arguments both for the relevance (for example, the signaling theory, the Walter model, the traditional position advocated by Graham and Dodd) as well as irrelevance of dividend policy (for example, clientele effect, Miller and Modigilani argument). Apart from these clear - cut 'yay' and 'nay' positions, we have some arguments which seek a middle ground. For example, Myron Gordon's classification of firms as 'growth' firms, 'normal' firms and 'declining' firms and the (ir)relevance of dividend policy to each one of them. We also have J. F. Muth's Rational expectations hypothesis. It proposes that what is important is not what really happens but what was expected to happen. For instance, if you expected the company to announce a high dividend but it didn't do so, you may revise your assessment of the company downwards and vice - versa.

In this post, we talk about the concept of homemade dividend (Miller and Modigilani), which simply means creating a personal dividend policy and ensuring the desired cash inflow in a given period(s). For example, if your company is paying more dividend than you need (well, you may want a lesser dividend receipt due to tax implications), you can receive the dividend check and reinvest the money back in the company (by buying additional shares through a DRIPS program) or anywhere else (perhaps in a tax saving scheme). And if your company is paying you less dividend than you need, you can make up for the shortfall by selling some shares.

If you can achieve your desired cash flow position on your own, then it does not matter to you what kind of dividend policy the company is following and unless you are affected, you are indifferent between quitting or staying with the firm. So, you might as well stay [If you stay, you don't cause a ripple. If you leave (and like you, others do too), then there is a selling pressure on the company's stock, causing it to turn southward].

Of course, this is an over - simplified way of looking at things because it does not consider factors like transaction costs and differential taxation treatment of dividend and capital gain income. However, it is important in understanding just how much relevance dividend policy has on its own, without the distortions caused by market imperfections and for that purpose (which is quite important), the procedure is helpful. Why I say this is because once you establish the pure relationship between the dividend policy and the value of a firm, you can then begin to factor in the imperfections and see how this relationship changes as each imperfection creates its own effect. It may very well be that it is the imperfect market conditions that cause the dividend policy to be relevant and without them, any policy does not have enough teeth to make an impact.

One can get a little philosophical here and muse: In a perfect world, no policy is needed. Everything takes care of itself on its own. Wow!!!

In the following video, I demonstrate the concept of homemade dividend:

Thursday, December 17, 2009

Homemade Leverage

In the world of finance, leverage means using either fixed cost assets or fixed cost funds. When fixed cost assets are used, the resulting leverage is called the operating leverage and when fixed cost funds are used, we have financial leverage.

We will refer to financial leverage in this post, which is created when a firm (or a person) uses borrowed funds (debt).

Homemade means something personal. Therefore, homemade leverage means personal leverage. Just like when companies borrow and create corporate leverage, individuals, when they borrow on their personal account, create homemade leverage.

Of course, a company can reduce its leverage by retiring some of its debt. Likewise, individuals can undo  the effect of corporate leverage (at least for themselves) by doing the exact opposite of borrowing, that is lending, which practically means investing in an interest bearing security.

The concept of homemade leverage emanates from the Miller and Modigilani propositions on capital structure, where they demonstrate that investors can substitute homemade leverage for corporate leverage, when they move from one firm to another to ensure that their return and risk exposure remains unchanged.

In an ideal world, investors can render the capital structure policy of a firm irrelevant through homemade leverage because they can create their own desired leverage status independent of what the company does.

However, we live in a world that is not perfect or ideal by any means. One of the major assumptions for homemade leverage to work is that individual investors can borrow and lend at the same rate of interest as corporations. We know that this is not possible. Also, the taxation rates applicable to corporate and personal incomes are different. With these imperfections entering in, the mechanism does not work as well as it is presented in theory.

Nevertheless, it should be kept in mind that the motivation for the homemade leverage argument is not to give us some unrealistic ideas but to suggest that the capital structure policy of a company on its own can not have any effect on its value. It is only when the market imperfections appear on the scene, the  capital structure policy of a firm starts making a difference to its value.

In order to impact the value, the corporate policy on how it finances it business must be something that can not be mimicked by individual investors for financing their personal investment in the company. If individual investors can undo the effect of corporate policy by their own actions, it loses relevance. As I said before, in real world, many imperfections enter the picture, preventing individual investors in imitating corporate leverage. If they are to do that, they can only do so at different borrowing and lending terms.

In this post, we are going to assume an ideal world, not because it exists, but because we wish to see if corporate leverage is potent enough on its own to affect a firm's value.  Or is it that the existence of an imperfect world makes the capital structure policy relevant. The underpinning is that if in an ideal world, investors can switch between companies and policies on their own without changing their risk - return profile, capital structure (the mix of debt and equity capital) would then be an irrelevant item on and of its own.

The following two videos explain how the mechanism of homemade leverage works in an ideal world. In the first video, we assume an investor who wants to move from a levered firm to an un - levered firm and in the second one, we look at the opposite case, where an investor wants to move from an un - levered to a levered firm without affecting his / her return, risk and proportional ownership in companies.

Moving from a Levered to an Un - levered firm:

Moving from an Un - Levered to a Levered firm:

Stock Valuation: The Variable Growth Case (Gordon Model)

Financial Instruments are valuable because we derive some benefit from them in the form of return. It goes to say that higher the expected benefit from an asset, higher should be its value. Shares of stock are no exception. We expect to earn a return on them in two ways: 1) Dividends and 2) Capital gains (difference between the buying and selling prices).

We can see capital gains also as a function of expected future dividends. We know that a capital gain arises if the selling price of a stock is more than its buying price. It should lead us to think in terms of what affects the price of a stock. Well, there can be a host of factors, one of which is the dividend that we expect to get on it. Intuitively, if we expect to earn a higher dividend, we believe that perhaps the company in which we have invested is a profitable one. How else would it be able to afford a higher dividend payment? This perception can have a favorable impact on the stock price of the company, thereby creating an opportunity for a capital gain.

In essence therefore, we can look at the value (price) of a stock as simply a function of its expected dividends. Higher expected dividends create an upward pressure on the price and vice - versa.

We also know that expected dividends are receivable on future dates. Therefore, the value (price) of a stock should be the discounted value of these dividends. What we have now is the understanding that if we find the present value of expected dividends of a company, we can have an estimate of the current stock price. It should be kept in mind that this argument is valid only for dividend paying companies and for this post, I am sticking to a dividend paying company.

Of course, the price estimate can vary from person to person because people have different estimates of expected dividends and the required return (discount rate). Therefore, what we get from a stock valuation model of this type is an estimate of the intrinsic value of a stock, which can differ from its market value. Depending on who had a better idea about future expectations and the required rate of return, he / she will be that much closer to the real intrinsic worth of the stock. Needless to say that if we provide inputs to a model that are not in touch with the pulse of the company and the market, we will find ourselves gaping at some strange results. The fault may not be that of the model but in the inputs provided to the model. It works the same way as a computer does, that is, on the GIGO (garbage - in - garbage - out) principle.

We also know that the world is a flux. Therefore, like everything else, dividends also keep on changing over time. For a given time period, they grow (or fall) at a certain rate and then this rate can change as we move into another time period. In short, the growth rate (either positive or negative) keeps varying and when that happens, we start talking in terms of a stock valuation model that can account for changing growth in dividends.

For the sake of simplicity, let us assume that the dividends on a certain stock grow at a 5% p.a. rate for the first two years from now. After the first two years, the growth rate will change to 7% p.a. for an indefinite period of time.

Let us say that the current year's dividend was $1 per share. It will mean that the dividend at the end of the next year will be 1 x 1.05 = $1.05 and the dividend at the end of the second year will be 1.05 x 1.05 = $1.1025. If we find out the present value of these two dividends at some discount rate k, we will get a part of our answer. Why a part? Because we still need to account for 7% growth in dividends from the third year onwards. Once we do that, we can have the final answer for what is the value of this stock.

In the following video, we take up some data and arrive at the value of a stock assuming varying growth rates in dividend: