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.

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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:

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:

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