Value at Risk or Beta: Which is BetteR?

Professor Grace once asked us a question on which company was riskier: a company with a VaR of $2 bil and a Beta of 1, or a compnay with a VaR of $2 mil and a Beta of 2? Well, which one is it? Answer: It all depends on which view you're looking from AND which measure of risk you're using. Those looking in terms of VaR would say that company #1 is riskier than the second. Those looking at Beta would say the opposite. We'll look at each view and then compare and contrast the two measuring options.

First we look at VaR, which stands for Value at Risk. What is Value at Risk exactly? There are many definitions, but the concept is the same. Computing a firm's Value at Risk allows them to answer the following questions: "What is my exposure for tomorrow, especially if tomorrow is my worst day?" and "What is the worst lost that could occur x% of the time?" In addition, firm's will be able to make the statement, "We are X% certain that we will not lose more than $V in the next N days!" But if we must give some definitions of the term, here are a few: 1) the value of loss to the firm, and 2)an attempt to provide a single number summarizing the total risk in a portfolio. Firms that calculate their VaR are able to find the distribution of their returns and see what their worst possible lost is for a given percentage level so that they can implement the appropriate risk management techniques. For example, banks use VaR to determine how much capital is needed to bear future risks (also known as reserves). One could calulate the VaR using this formula:
VaR (C%) = u +/- sigma * zc . C% represents the percentage (level of confidence) the firm wants to be sure about. With that, zc is the corresponding z-score for the confidence level. u is the mean while sigma is the standard deviation (or volitality). All of these components help companies determine their Value at Risk.

Now, we'll examine Beta. Beta is another way to measure risk. However, it doesn't look at a percentage level; instead, it looks at a relationship between the firm and the market. First, let's determine how to calculate Beta.
Beta = Cov(X,Y)/Var(Y). (Before I go any further, please note that the denominator is the variance of firm Y, not the value at risk of firm Y). Cov(X,Y) represents the covariance between firms X & Y. This basically let's us see how closely related the two firms are, as well as their movement with each other. (This is done by dividing the covariance by the product of both firms' standard deviation; this in turn gives you the correlation). Doing the formula gives you the Beta, the sensitivity changes in X related to the changes in Y. Basically, the sensitivity between X and Y. Another formula would be rs-rf = alpha + Beta(rm-rf); however, this is used in relation with CAPM. From the first formula, we mentioned the word "sensitivity" and how this formula allows you to see the sensitivity between the two variables. This is important because firms can determine their sensitivity in relation to the market. Firms with a Beta>1 are sensitive to the market. This means that whenever the market moves, and in the same direction, that firm will move just the same. For example, Home Depot with a Beta=2 will a movement twice as much as the market. Therefore, if the market's price moves up 10%, Home Depot's will move 20%. For firms that have a Beta=1, they are considered neutral. Meaning, they are in exact alliance with the market. If the market moves up one, they move up one, if the market moves down .17894, that firm moves down exactly .17894. Lastly, if a firm has a Beta<1,>

So, back to the original question, which firm is riskier? With all the information given, some might have changed their answer. However, the answer is still the same. When a firm's VaR is high, they have greater risks. When their Beta increases and gets higher, they have a greater risk. Therefore, the two measuring tools share one common aspect; WHENEVER THEY ARE HIGH, THE COMPANY HAS A LOT OF RISK. So for the question asked, your answer may forever differ from mine because....it all depends on which view we're using!