|Security A||Security B|
Expected return = WArA + WBrB where "W" is the percentage of all money invested in a security (expressed as a decimal) and "r" is the security's expected return.
|Portfolio||Percentage of money invested in security A WA||Percentage of money invested in security B WB||Portfolio's expected return||Portfolio's standard deviation (correlation coefficient is +1.0)||Portfolio's standard deviation (correlation coefficient is 0.0)||Portfolio's standard deviation (correlation coefficient is -1.0)|
|1||1.0 (100%)||0 (0%)||5%||4%||4%||4%|
The relationship between expected return and standard deviation is graphed below for the seven portfolios assuming three different degrees of correlation between securities A and B. Point A represents portfolio #1, and Point B represents portfolio #7. As you go from portfolio #1 to portfolio #7, you take a path from point A to point B. The three paths reflect the three different correlation coefficients assumed in the example.
When a financial security is added to a portfolio, its risk can no longer be measured by standard deviation because some of its risk has been eliminated. In a portfolio the variation in a security's return associated with company-specific factors can be offset by including securities with different company-specific factors. However, because the returns of all securities tend to be positively correlated, some risk remains. This is labeled market risk. In a portfolio the risk of a single security is measured by beta, which measures the correlation of a security's return with that of the entire market. A security with a beta equal to 1.0 means that its return is perfectly positively correlated with the return of the market as a whole. If the market return goes up or down by 6%, the security's return will go up and down by the same 6%. A beta greater than one means that the security's return fluctuates more than the market return. If the market return goes up by 4%, the security's return will go up by more than 4%. A beta of less than one means that, if the market return goes up by 10%, the security's return will go up by less than 10%. The required return of a security in a portfolio is equal to the risk-free return, usually measured by the return on 90-day Treasury bills, plus a risk premium, measured by the market return minus the risk-free return, multiplied by beta. This relationship is known as the Capital Asset Pricing Model:
Last Update: 6 September 2000