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
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 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
||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
- 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
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.