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
 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 comovement)
 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 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
 r_{invest} is dependent variable
 Tilde means an estimate
 This is your investment return
 r_{market} 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
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. 
