subject: Portfolio and Component Securities [print this page] Portfolio and Component Securities Portfolio and Component Securities
Portfolio and Component Securities
Let us now examine the relationship of a portfolio to its componentsecurities. First, what is the relationship between the return on a port folio and the returns on the component securities? Fortunately, thisrelationship is quite simple. The return on a portfolio is simply theweighted average of the returns on its component securities, the weightof each security being the fraction of the total value of the portfoliowhich is invested in it.
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A complication arises because portfolio managers are concernedwith future outcomes. If the rates of return on individual securitiescould be known with certainty, the rate of return on any portfolio could be predicted accurately and rates on all securities would beequal. Since the future is uncertain, portfolio managers must basetheir selections on forecasts of future outcomes. Suppose an analystmade the following forecast for a specific security:
This "probability distribution" represents the probabilities that thesecurity will provide specified rates of return over some designatedfuture period. The probabilities must, of course, sum to one.
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Unfortunately, the relationships between estimates of risk for individual securities and estimates of risk for portfolios are not so simple. For the time being, the measure of risk which we will use is variabilityas measured by the variance. This is defined as the weighted sumof the squared deviations of a variable around its expected value wherethe weights are the probabilities that the deviations will occur. It provides a measure of the spread or dispersion of the distribution.
The square root of the variance is the standard deviation. Its meaning is straightforward for normal (bell-shaped) distributions. Thechances that an outcome will be in the range of the expected value(E) plus or minus one standard deviation (cr), are about two outof three. The chances that it will be between(E + 2cr) and(E 2
