Risk Adjusted Returns: Risk

Posted By: Advisor Analyzer Team

Anyone who’s visited a casino and played roulette knows that there are different odds and payout structures to the game. Taking outside bets (red or black) has a payout scheme of 1 to 1, while playing a single number (inside bet) pays at a rate of 35 to 1. So, given the huge discrepancy in payouts, why would anyone take outside bets? The obvious reason is due to probabilities; although the payout itself is higher, the likelihood of having your number hit is much lower than betting on a color. Therefore, after adjusting for these differences in probabilities, the expected return on a dollar bet for any number and the return on a color are identical (-$0.053).

 

A similar comparison can be made in the investment world: in general, every stock has a different risk and return scheme relative to another. Some investments are similar to betting on 22 black, while others are akin to betting odd or even. Unfortunately, most investors only examine the returns of an investment without any consideration to the risk involved with that investment. In their eyes, 22 black is a better investment than red due to the higher payouts (returns). However, in actuality the odds are sometimes the same or more oftentimes much worse.

Market Capitalization

Generally, companies with smaller market capitalizations experience higher absolute returns and volatility than larger firms. Very simply, market capitalization is the product of the price of a stock and the number of shares outstanding: · Market Capitalization = Stock Price X Shares Outstanding

 

For example, on 9/17/08, CROCS Inc. (CROX) had a market cap of 320.60 million. To calculate this amount, we take the product of the number of shares outstanding (84.84 million), and the closing price (3.87) a share.

 

· (CROX) market Cap = 3.87 X 84.84 million = 320,590,800

 

So how does market capitalization affect the price fluctuation of a stock? Since stock prices go up when there are more buyers, and down with more sellers, a stock with less shares outstanding will require fewer buyers to push the stock price higher, and fewer sellers to push the price lower.

 

As an extreme example, suppose a company only had 5 shares outstanding, but 100 people would like to purchase the stock. The buyers must aggressively compete with one another, thus increasing the price of the stock fairly quickly. If there were 5 million shares outstanding the 100 buyers can cherry pick who they buy from, and these transactions would have a negligible effect on the stock.

 

Therefore, as the number of shares outstanding increases, the shares required to move the stock one point increases, and vice versa. Usually, larger cap companies have more shares outstanding thus experience smaller price moves than smaller cap firms.

 

While not a direct risk measure in the conventional sense, market capitalization is a useful tool in comparing returns of different size companies. In general, small cap stocks are more volatile than large cap stocks, and a 1% return should be assessed differently. Although there are ways to compare stocks after adjusting for market cap, we will not address this portion. We only bring it up to identify the differences in volatility that are attributable to the size of the company.  

Beta (bi)

Theoretically, Beta is a measure of a stock’s volatility (market risk or systematic risk) relative to the overall market. Basically, it measures the price fluctuation of an investment relative to a 1% change in the overall market. For example, a beta coefficient of 1.2 signifies a stock will, on average, increase 1.2% when the overall market increases 1%. Conversely, a 1% decline in the market depreciates the investment by 1.2%.

For the sake of simplicity, we will save the actual calculations behind beta (as they usually require statistical and linear regression analysis). For those who are interested, one method to calculate beta is:

 

· bi = (COV (I,M)) / Variance (M)

 

Before continuing, a few words of caution: Beta uses historical prices to measure a stock’s volatility. As we all know, past performance does not guarantee future performance. Therefore, while a useful tool, it is not fool proof.

 

Also, beta measures volatility relative to the overall market and fails to capture firm specific risks. A stock with poor earnings can depreciate to a greater extent than was indicated by beta, and vice versa. The fact that idiosyncratic events are not recognized also emphasizes the incomplete nature of beta as a risk measure.

 

Despite its shortcomings, investors can better assess price fluctuations of a stock when using beta to gauge risk. Those with lower risk appetites would prefer stocks with lower betas, while investors who can stomach higher volatility would invest in higher beta stocks.

 

An advantage of beta is that it is very simple to use and understand. Also, beta estimates are abundant and readily available, sparing investors from tedious calculations. However, one must always keep in mind when using beta, they are only viewing the tip of the iceberg of a stock’s overall risk.

Standard Deviation (si)

For most investors, the word standard deviation sends chills down their spine. It’s a word many investors omit from their vocabulary due to its statistical nature and complexity in calculation. In actuality, however, standard deviation is a fairly simple concept to grasp. To avoid delving too much into statistics, I will use a simple example to clarify.

 

Suppose a stock only has two options: it can go up 1% or down 1%. The expected value (or average) of this stock would be 0% {= [1 + (-1)]/2}. The standard deviation would be 1%, meaning it can go up or down 1% from the mean (=0). Therefore, someone investing in this stock would either gain 1% or lose 1%, but on average would have a return of 0.

 

Standard deviation provides information of the fluctuations from the mean.  Therefore, investors are able to infer the degree of change in an investment over time. It measures the total volatility (or total risk) of a stock’s return.

 

In fact, there is a mathematical relationship between beta and standard deviation (but we won’t go into that here). Basically, standard deviation measures the total fluctuation of the stock, and beta reflects only that portion of the stock’s volatility that’s attributable to the market.

 

However, as with beta, there are similar caveats to note. We are using historical data, and should not expect that past conditions to repeat in the future. Also, there are certain statistical assumptions (i.e. symmetry and normal distribution) that must be met for standard deviation to be a reliable measure of volatility and forecasting.  

Conclusion

In the first part of our two part series, we discuss some factors that affect stock price fluctuations (such as market capitalization) as well as some basic measures of volatility and risk. In the second section, we will examine how these measures can be used to obtain risk adjusted values. Much like betting on 22 black, a higher payout does not necessarily indicate a better bet.