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