The Relationship Between Risk and Reward

The first thing we need to know about risk and reward is that under certain limited circumstances, taking more risk is associated with a higher expected return.

The second thing we need to understand about the relationship between risk and reward is that there in many cases there is no relationship.

It has been well established that on average stocks have a higher return (reward) than treasury bills or bonds and that this extra reward comes at the expense of a higher standard deviation of return than treasury bills. For example stocks might have an average annual return of 11% but in any one year the range might fall within say -10% to 20% two thirds of time and the range would be outside of that range the other 1/3 of the time. Meanwhile treasury bills might average only 5% but might have an expected range of plus or minus 1%. Further it is well established that on average small company stocks are expected to have a higher return than large company stocks and that this comes at the expense of yet a higher standard deviation in annual returns.

One of the most widely accepted theories about risk and return holds that there is a linear relationship between risk and return But there are many fallacies and misconceptions about risk.

The fact that a relationship between risk and reward exists on average does not mean that the same relationship holds for individual stocks.

  • Risk Fallacy Number 1: Taking more risk will lead to a higher return. False, if a higher return was assured than it would not in fact be risky. The theory states that the average or expected return should be higher. Due to the existence of risk the actual result could be a much lower return
  • Risk Fallacy Number 2: All types of risk will lead to a higher expected average return. False, the Capital Asset Pricing Model (“CAPM”) indicates that the only risk that is expected to lead to a higher return is the non-diversifiable risk that is correlated with overall market risk. CAPM indicates that taking risks that could be diversified away will not be rewarded. My own theory is that stupid risks will not be rewarded. If you take a stupid risk by putting all your money into one company that is over-valued then you will not be rewarded. And, Warren Buffett has argued that there are cases where taking less risk leads to higher returns. If one can identify under-valued stocks then Buffett argues convincingly that this will both lower your risk and increase your return as compared to the overall market.
  • Risk Fallacy Number 3: That risk can be measured. False, at least it can’t be measured precisely. Most work on risk assumes that historic nominal (before adjusting for inflation) volatility of the stock market price or the historic correlation (beta) of an individual stock with the market are good measures of risk. Beta may capture the market related risk and under CAPM that is the only risk that matters since all other risk can and should be diversified away. But studies have shown that beta varies over time, therefore it is not clear that beta can be actually measured. And calculations of beta vary dramatically depending if one works with monthly, daily, weekly or annual returns. And if one believes that diversifiable risks are also relevant then it is clear that those cannot be so easily measured. How can you measure the chance that completely random events will occur?

In addition some investors are not so concerned about volatility but are much more concerned about the risk that their long term wealth will be below an acceptable level. Short term volatility does not address very well the risk of long term purchasing power. For example treasury bills are not risky in the short term but putting all funds into Treasury bills would cause a large risk of insufficient long term purchasing power, as the returns barely keep up with inflation.

My belief is that at best we can get a rough qualitative sense of the risk but we cannot precisely measure it. I also believe that their is too much focus on short term volatility and not enough focus on the risk of long term real (after inflation) wealth risk.

  • Risk Fallacy Number 4: That you can compare various investments on a “risk adjusted basis”. False, this theory holds that on a risk adjusted basis the expected return on the market (say 11%) is equivalent to a risk free return (say 6%), and that an expected return of 16% gained by using borrowing to create a portfolio twice as risky as the market is also equivalent to a risk free return. This fallacy is based on the fact that 6%, 11% and 16% are the market rates of return for this risk level as set by CAPM or the Security Market Line (“SML”). Well, they might all be market returns but they are not equivalent in any sense. The person who invests in the market at 11% and earns that over a lifetime expects to end up with a lot more money in the end but puts up with more volatility along the way. And there is some small chance that even over many years the risk free rate will actually turn out to beat the market return.

A mythical average investor might be indifferent to the two positions along the SML. But realĀ individual people will typically have very strong preferences for one position or the other. I may choose the safe route and expect a lower return. You may choose to take a maximum amount of risk and its expected far superior return. There is nothing equivalent about this. Neither of us would be willing to trade places. You might have been willing to take on all that risk for a much lower risk premium than the market is currently paying. I might not have been willing to take on the risk even if the market risk premium was significantly larger. This is based on individual preferences and the average market risk premium does not imply that individuals should accept that level of premium as creating an equivalency.

Another problem with the concept of talking about a risk adjusted return is that it would be necessary to be able to measure the risk of an investment before we could state what its risk adjusted return is. As discussed above the concept of being able to accurately and quantitatively measure risk is more false than true.

It is true that an investment should always have an expected return that is at least as high as the market return for that level of risk. The problem is we can’t measure accurately measure the risk of any investment and we also don’t accurately know the market return for any given level of risk.

InvestorsFriend Inc. (Dated approximately 2001)