Betas and definition of risk:
Although I disagree with the use of betas to identify the level of risk an investment carries, it is understandable. At bottom using betas as a gauge of risk says your’ definition of risk is volatility. This fits with the reasoning that the more uncertain a future benefit is the more risk it carries and the more it should be discounted today, which is correct. The issue becomes whether variance or volatility and uncertainty are the same thing. The answer is inseparable from your investment time horizon. If for example you had a strong conviction that the competitive strengths of an investment would produce a very good return over the next 10 years, but there could very well be a terrible two or three years during that time (and maybe that’s the case at time of purchase which makes the price appealing), if your horizon was 10 years, you don’t care about the volatility, because you feel there is a high degree of certainty that it will perform well over your ownership period. If, however, your time window was 6 months, volatility would more equate to uncertainty. This concept has similarities to the concept of “probability as a limit” or “relative frequency”. The probability of rolling a 3 on a six sided die is 1 in 6 or 16.6%. It is however possible to roll a die 20 times and not get a 3 once. But eventually, as more and more rolls are made the probability of 1 in 6 will take affect. If the time horizon was 3 rolls, the volatility would dictate your level of certainty, however if the time horizon was 200 rolls, the degree of certainty would be less affected by variance.

