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# 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
A
Investment
B
Investment
C
Investment
D
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

The variance

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
• Reduces risk
• 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
 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

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

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

 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

 InvestmentA InvestmentB InvestmentC InvestmentD 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

• 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

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