Implications Across Portfolios

Read this section and learn more about risk and return, implications across portfolios, and the beta coefficient for portfolios. Why are these topics important to businesses? The answer is contained in this section. This section discusses how a beta coefficient compares how much a particular stock fluctuates in value daily.

Beta Coefficient for Portfolios

A portfolio's Beta is the volatility correlated to an underlying index.


LEARNING OBJECTIVE

  • Calculate a portfolio's beta

KEY POINTS

    • In individual stocks, a beta coefficient compares how much a particular stock fluctuates in value on a day-to-day basis.
    • A beta coefficient for a portfolio of assets measures how that portfolio value changes compared to a benchmark, like the S&P 500. A value of 1 suggests that it fluctuates as much as the index and in the same direction.
    • A beta coefficient of less than 1 suggests a portfolio that fluctuates less than the benchmark. A negative beta is an indication that a portfolio moves in the opposite direction of its benchmark.

TERM

  • Normalized variable

    In statistics, a normalized variable is one that is calculated using a ratio of itself and some benchmark figure. Normalized figures tend to be smaller than the original values.


In this section, we will discuss the idea of calculating a Beta coefficient to help investors measure the risk-reward trade-off for a blended pool of investments.

In this case, it is important to remember that a portfolio may represent the seller side of the market and the buyer can be thought of an institutional investor or a mutual fund. A portfolio's Beta is the volatility correlated to an underlying index. If we think of the S&P 500 as the index, a portfolio that fluctuates identically to the market has a Beta of 1. What would the following portfolios have for Beta values?


Calculating Beta:  Two hypothetical portfolios; what do you think each Beta value is?

Do you have an answer? Beta is a normalized variable, which means that it is a ratio of two variances, so you have to compare the volatility of returns to the benchmark volatility. Portfolio A has a direct relationship with the S&P 500 – it is scaled by three times each day. When the market is up 2%, it is up 6%. Thus, the portfolio would have a Beta value of 3. Portfolio B is a different situation; it is also directly proportional, but in the negative direction. Every time the market is up 1%, the portfolio is down half a percent. The Beta for this portfolio, when compared with the S&P 500 benchmark, would be -0.5. A Beta of zero in this situation doesn't necessarily mean a risk free asset, it simply means that it is not correlated with the benchmark.

In reality, the numbers would rarely work out this cleanly, but this is a good model to demonstrate some key concepts. A pension fund that seeks to maximize its reward and limit its risk might be interested in each of these portfolios. If you invested equal amounts in each portfolio, it would leave you over-exposed to the market because it would have a Beta of 1.5. But let's say you have $300,000 to invest; you could put that in a fund that is indexed to the S&P 500 and is perfectly correlated with it.

Every time the S&P gains 1%, your fund nets you 100,000 in fund A and S Misplaced &3,000 and your position in fund B pays you 2,000, which is less damage than you would have suffered on your position in the S&P index fund. On days when the S 3,000 and your fund A position loses 2,000 and your upside is limited by the same amount, your downside is reduced.

A pension fund is a good example of an institutional client that could extend the principles of diversification to a pool of blended portfolios. A city with an aging workforce needs to be protected from downside risk. It is the same principle as an employee approaching retirement; it can afford to have a heavier position in the S&P 500 if it has a position in portfolio B.