Lesson 11 - Investment Portfolios

This lesson introduces investment portfolios and how to calculate market Beta. Investors use Beta to determine which financial securities to include in a portfolio that reduces risk.

Investing in Financial Securities

Looking at the Table below, we have four returns from financial securities with the four possible outcomes

  • Each investment has a letter
  • Each outcome is equally likely
  • Each outcome has 1/4 probability
Scenario Investment
Outcome 1 10% 8% 3% 2%
Outcome 2 2% 4% 4% 2%
Outcome 3 12% 2% 5% 2%
Outcome 4 3% 5% 4% 2%
Average 6.75% 4.75% 4.00% 2.00%
Variance 18.69%% 4.69%% 0.50%% 0%%
Standard Deviation 4.32% 2.17% 0.71% 0%

Note:- Variance has two percentages to indicate the unit is squared 

Note - If percentages are converted to decimals, the average and standard deviation is the same, but the variance would be different.

Calculations for Investment A

The expected value

Calculating the expected return for Investment A


The variance

Calculating the variance for Investment A


The standard deviation


  • The reward of the investment is the expected value while the risk is the standard deviation
    • Investment D
      • Has lowest reward, but lowest risk
    • Investment A
      • Has highest reward, but also highest risk
  • What happens if you invested all your funds into Investment A and this investment bankrupts?
    • You loose all your money
    • Diversification - spread your investments over many financial securities
      • Reduces risk
      • "Do not put all your eggs into the same basket"
    • Market Portfolio
      • Investor has a portfolio of a variety of securities
      • Reduces risk
      • Some securities increase while others decrease, but the portfolio earns a rate of return
    • Imperfect correlation
      • Some returns on securities increase while others decrease
      • Securities do not move exactly together
      • Diversification works by mixing securities with imperfect correlation
    • Perfect correlation (or co-movement)
      • Securities move up and down together
      • Diversification does not work in this case
    • Market Index
      • Dow Jones Industrial Average
      • Standard and Poor's 500 (S&P 500)
      • Use these market indices to indicate the average return of market
Blue arrow Rates of return and risk tradeoff - higher rates of return entail higher risks.

At this point, you cannot combine the investments A, B, C, and D into a portfolio using the standard deviation. You have to include how each investment changes in regards to other investments.

Market Beta

Market Beta is estimating a linear relationship between your investment and the market
  • Linear regression - Econometrics
    • Use historical data to indicate how investments are doing
    • Easily estimated in Excel, and other programs
  • rinvest is dependent variable
    • Tilde means an estimate
    • This is your investment return
  • rmarket is independent variable
    • This is a market return
    • Return from market index
  • Beta, b, is the slope of the line
  • Alpha, a, is the intercept of the line

Calculate rate of return from market beta

  • Compare two investments to market
  • Investment Q
  • b = 1
  • Do not gain from diversification; moves in same direction as market

Return to Investment Q

  • Investment R
  • Moves in opposite direction of market
  • b = -0.5
  • Gain from diversification by adding Investment R

Return to Investment R

  • Which is the best beta?
    • Beta is rarely negative
    • Choose the lowest beta
      • Lowest risk
      • Helps in diversifying portfolio
    • Higher betas indicate higher risk
  • How to measure beta?
  • Include the last 3 to 5 years of historical data
    • Times change and going to far back may estimate the wrong beta
  • Include betas from similar projects and/or investments
    • Compare betas to similar projects in the same industry
  • Adjust market beta to one for historical data and then include forecasts
    • Minimizes errors

Below is a chart from Yahoo Finance for historical betas

Company Ticker Beta Mkt Cap.
AMD AMD 2.7 5.4
Agilent Tech. A 2.5 16.2
Barnes Group B 0.2 0.7
Citigroup C 1.4 261.4
Dominion Resources D 0.2 20.5
Ford Motor F 1.3 30.1
Gilette G 0.3 36.7
Intel INTC 2.1 206.6
Kellogg Co. K 0.0 15.4
Microsoft MSFT 1.7 302.9
Sears, Roebuck S 0.5 12.1
AT&T T 0.8 16.1
Starbucks SBUX 0.6 14.1
Sony SNE 1.1 38.2

Source: Welch,, Ivo. 2007. Corporate Finance. p. 186

�Mkt cap� is equity stock market value in billions of dollars. Betas were reported by Yahoo!Finance, and explained as follows:

The Beta used is Beta of Equity. Beta is the monthly price change of a particular company relative to the monthly price change of the S&P500. The time period for Beta is 5 years when available, and not less than 2.5 years. This value is updated monthly.

Blue arrow You can subtract the interest free interest rate from both the investment and the market return.

Expected Returns for Portfolios

Using the first example with the four investments

Average 6.75% 4.75% 4.00% 2.00%
Variance 18.69%% 4.69%% 0.5%% 0%%
Standard Deviation 4.32% 2.17% 0.71% 0%

We can create a portfolio

  • Value-Weighted Portfolio - have different mixes of investments
    • Investment A - Portfolio is composed of 40%
    • Investment B - Portfolio is composed of 30%
    • Investment C - Portfolio is composed of 20%
    • Investment D - Portfolio is composed of 10%
      • All weights sum to one

Calculate the average weighted return

Calculating the return for a portfolio

  • Equal-Weighted Portfolio - have equal proportions of all securities
    • Investment A - Portfolio is composed of 25%
    • Investment B - Portfolio is composed of 25%
    • Investment C - Portfolio is composed of 25%
    • Investment D - Portfolio is composed of 25%
      • All weights sum to one

  • Beta's can be weighted and averaged
  • Why?
    • Average function and linear regression are linear equations
    • Standard deviation and variance cannot be averaged or weighted
      • Not linear functions