How do you Measure the Risk in a Stock Portfolio

Under the Capital Asset Pricing Model (CAPM) the Beta of a particular stock is defined as the relative risk of that stock compared to the risk of the market as a whole.

Theoretically, beta = (std deviation of the stock / std deviation of the reference index) *(correlation between the stock and the reference index).  This equation has two main aspects: the first is the measure of volatility of a particular stock as a ration to the volatility of a reference index (calculated as the ratio of the standard deviations) and the second is the extent to which the particular stock moves in tandem with the reference index (as calculated by the price correlation).

Before discussing the meaning of beta, we need to make two points.

The first is the ‘reference index’ that is used for comparative purposes. The CAPM is used, amongst other things, to manage the risk of a portfolio of investments with the aim being to get the maximum return with the minimum risk.  Ideally therefore the reference index is made up of a whole portfolio of different investments – bonds, equities (local and internationally), etc. Traditionally, however, it is made up of the most significant index of the local stock market, which in this case would be the S&P 500.

The second point to make is that this value is historic, and is based on returns over specified time period. Normally this would be the preceding three years, but even so it is obvious that the upheavals in the recent past would distort values from their historic returns.

Beta is commonly used as a proxy for two things, both relating to market risk.  In the first case beta is a measure of volatility. A high beta (greater than 1) implies the returns of the stock are far more volatile than that of the reference index. The price varies drastically. The second implication is that the returns may be tracking the overall index, but more amplified. A beta of 1.5 would imply if the reference index rises 10%, the stock would rise 15%, and similarly a price fall would be magnified.

The Adjusted Beta

The Adjusted Beta is a consequence of the Efficient Market Theory that states that as all information becomes known, the market will settle to its proper level as everyone will be able to make correct choices.  This implies that the return of any stock that is out of line with the returns of the market will rise or fall to bring it into line with the market.

The formula is then

(Adjusted Beta) = (Theoretical Stock Beta)*0.67 + (Theoretical Market Beta)*0.33.

This is used as a forward looking Beta to estimate risk. As the (Theoretical Market Beta) is generally normalized to 1, this becomes (Adjusted Beta) = 0.67*(Theoretical Stock Beta) +0.33

The problems with this formulation are self-evident. Beta, while useful in comparing risk is already problematic as it depends on specific time frames and specific indices. Adjusted Beta takes the assumption one step further by assuming both that the historical Beta is an accurate reflection of the risk in a stock, and that the stock will normalize against the market.