All Business & Investing Science

Risk, Diversification & Asset Pricing

Fair warning that the following gets technical at times but I hope it’s not too dense. Risk and Diversification underpin the theory of asset valuation as well as risk management. Understanding these helps make informed decisions and not taking on too little or too much risk in investing and life in general.

Risk & Diversification

Depending on personal tastes, we can be risk-seeking and go for the stocks that have large swings with potentially large payoffs, or risk-averse and prefer government bonds. Regardless of individual preferences, one of the biggest mistakes people make is putting all their eggs in one basket.

Diversity reduces risk and it can be seen all over the natural world. Mixed breed dogs live longer than pure breeds. Biodiversity grows stronger ecosystems. Charles Darwin proposed that the environment changes over time and different traits are favored to multiply through natural selection. Similarly, in investing, diversification reduces risk – although you may not make as much, you also lose less. Mathematically speaking, you can gain more return per unit of risk this way.

The theory of finance is prefaced on the argument that investors want to earn in proportion to the amount of risk they take. Risk is measured as the standard deviation of returns over a period of about 3 years. While historical risk is simple to calculate, predicting future returns is more difficult for risky assets.  The least volatile asset is the “risk free asset.” For people in America, this is the 3-month Treasury bill that which pays the least but is most likely to be repaid.

Risk is a biggest issue in the near to medium term. Usually, asset prices will not drop by a large amount in a single month, but it’s unclear what will happen over three years. Reviewing historical trends gives some insight but is by no means a proof. Over the longer term, however, price trends are positive – making a strong argument for ‘buy and hold’ investing. Image result for S&P time frame negative positive

For other assets, having a portfolio of two or more reduces the overall risk to less than the riskiest asset. The more different the assets and the more in the portfolio, the greater the benefits of diversification. The reason for this is security prices generally do not move in sync with one another (correlations are not equal to 1). So when one asset performs poorly, others perform better and negate the volatility of the portfolio.

Empirical research has found that it takes about 15-30 stocks to reduce total risk to its minimum by neutralizing company-specific risks. The remaining risk is not diversifiable and reflects the systemic risk of that asset class. If all 20 stocks are tech stocks, the market you reflect is the tech market and not the construction market or the broader large caps asset.


The risk and return of any individual security is related to that of its asset class (market). The strength of that relationship is called the ‘market beta’ and is calculated through statistical regressions. A market beta of 0 means that there’s no relationship while that of 1 means that they move in tandem. Market betas can also be negative (when the stock and market move in opposing directions but this is unusual) and greater than 1 (when the stock moves in multiples of the market).

Market Betas

Market betas got their names from regression terminology. Regressions are tools for finding the relationship between explanatory variables and something that depends on them. To explain stock returns using the market’s returns, we can run a regression with the explanatory variable being the daily market returns while the stock returns is dependent variable. The regression results estimate the stock return the product of the explanatory variable (the market return) and a coefficient – plus a remainder. The coefficient, identified by the Greek letter ‘beta’ in the equation, represents the sensitivity of the stock to the market. The remainder cannot be attributed to the market and so is ‘alpha’. This is roughly the Capital Asset Pricing Model (CAPM) introduced during the golden years of theoretical finance in the 1960s.

The CAPM argued that the historical risk of a stock (the beta) determines how much investors should demand for a stock – or any security – to return over a period.  A stock that has a beta of 1.5 is more volatile than the market and so needs to compensate investors by approximately that much more investment return.

The reason betas are used (as opposed to total risk) is because the market should not compensate investors for not diversifying out non-systematic risk.

Risk Factors

As technology allowed finance to become empirical, other variables were identified that influence stock prices. Along with the market, these were called “risk factors”, and include descriptive information, such as the company industry and size, and other metrics, such as financial ratios. By adding additional explanatory factors to the CAPM model, there was no longer one beta but many. A single company can be exposed to risk from different sources: small cap, biotech, low sales relative to equity (value), price momentum, and so on. This gives us the ability to invest not only in the ‘market’ but a range of betas from risk factors, such as value and momentum.

For this, the index makers created alternatives to market weighted indices to increase exposure to these other factors and called them “Smart Beta”. In addition to the better-known Value and Dividend, other varieties include Quality (how much is net profit dependent on cash flow rather than estimates) and Minimum Volatility. The later caused a stir among practitioners because it violates the CAPM: volatile stocks with higher betas generally and consistently underperform less volatile stocks. These are betas are distinct from the capitalization weight beta and act as separate asset classes (or at least sub classes).

One argument holds that the reason some of these risk factors outperform is that they are more illiquid (since they do not weigh by market demand) and that may be become a problem if much, much more people try to use them. Moreover, products such as Barra and Axioma use multi-factors to decompose stocks and then optimize the portfolio. Optimization weighs a portfolio to diversify and lean towards the risks you want. Risk attribution exist that estimate the portfolio risk (what bets are being made) and decompose historical returns by risk category (what risk bets paid off).

Take Aways

Ancient mysticism held that knowing the name of something or someone gives one power over that thing or person. Less fantastical is the belief that understanding and being mindful of our anxieties and dreams guides us along a straighter path. Expressing our thoughts through meditation, journaling, or therapy increases self-awareness; without conceptualizing our fleeting thoughts can be formless tormentors.

Unlike investment risk, the risks in our lives are more difficult to quantify. Still, the methodologies of diversification and risk management can be called upon.

What do you think?


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