7-4 How Individual Insecurities Affect Portfolio Risk

Remember

The risk of a well-diversified portfolio depens on the market risk of the securities included in the portfolio.

🅱️ Market Risk Is Measured by Beta

It is not a good practice to measure risky a security is if held in isolation. You need to measure its market risk. You do this by measuring how sensitive it is to market movements. This sensitivity is called beta $\beta$.

• Beta > 1.0 -> amplify the overall movements of the market
• 0 < beta < 1.0 -> move in the same direction as the market, but not as far.

The market is the portfolio of all stocks, so the "average" stock has beta = 1.0

Many of the stocks with high standard deviations also have high betas, but this is not always the case.

⁉️ Why Security Betas Determince Portfolio Risk

Review

• Market risk accounts for most of the risk of a well-diversified portfolio.
• The beta of an individual security measures its sensitivity to market movements.

In a portfolio context, a security's risk is measured by beta.

Better diversification makes the portfolio risk declines untill all specific risk is eliminated and only the bedrock of market risk remains.

The bedrock depends on the average beta of the securities selected.

Portfolio beta 1.0

• portfolio containg 500 stocks drawn randomly from the market
  • results in a portfolio very similar to the whole market. So beta is 1.0
• standard deviation of the market is 20%
  • so portfolio standard deviation is 1.0 x 20% = 20%

Portfolio beta 1.5

• portfolio containing 500 stocks with virtually no specific risk
  • beta of the portfolio is 1.5
• standard deviation of the market is 20%
  • so portfolio standard deviation is 1.5 x 20% = 30%
  • portfolio will amplify every market move by 50%
  • portfolio with 150% of the market's risk

Calculating Beta

Beta of stock i

• ${\sigma }_{im}$ = covariance between stock returns and market returns
• ${\sigma }_m^2$ is variance of the return on the market

${\beta }_i={\sigma }_{im}/{\sigma }_m^2$