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College aantekeningen Investment Analysis (323060-M-6)
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Investment Management Summary
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Refresher slides:Expected return, Variance, and Standard Deviation:
Historical returns of stocks and bonds:
Computing Historical Returns:
- Realized Return:
→ The return that actually occurs over a particular time period.
Average annual return:
Variance and Volatility of returns:
Variance Estimate using realized returns:
The estimate of the standard deviation (SD) is the square root of the variance.
Common vs. Independent risk:
- Common risk:
Risk that is perfectly correlated
→ risk that affects all securities
- Independent risk:
Risk that is uncorrelated
→ risk that affects a particular security
- Diversification:
The averaging out of independent risks in a large portfolio.
,No Arbitrage and the Risk Premium:
- The risk premium for diversifiable risk is zero, so investors are not compensated for
holding firm-specific risk.
- The risk premium of a security is determined by its systematic risk and does not
depend on its diversifiable risk.
Historical volatility and return for 500 individual stocks, ranked annually by size:
Measuring systematic risk:
- Efficient Portfolio:
A portfolio that contains only systematic risk. There is no way to reduce the volatility
of the portfolio without lowering its expected return.
- Market portfolio:
An efficient portfolio that contains all shares and securities in the market.
The expected return of a portfolio:
Then the return on the portfolio, Rp, is the weighted average of the returns of the
investments in the portfolio, where the weights correspond to portfolio weights.
The volatility of a two-stock portfolio:
- Combining risks:
By combining stocks into a portfolio, we reduce risk through diversification.
The amount of risk that is eliminated in a portfolio depends on the degree to which
the stocks face common risks and their prices move together.
,Determining Covariance and Correlation:
Covariance: the expected product of the deviations of two returns from their means.
Covariance between returns Ri and Rj:
Estimated covariance from historical data:
- If the covariance is positive, the two returns tend to move together.
- If the covariance is negative, the two returns tend to move in opposite direction.
Correlation: a measure of the common risk shared by stocks that does not depend on their
volatility:
Computing a portfolio’s variance and volatility:
- For a two-security portfolio:
- For a large portfolio:
The variance of a portfolio is equal to the weighted average covariance of each stock
with the portfolio:
, Risk versus Return: Choosing an efficient portfolio.
- Efficient Portfolios with two stocks;
In an inefficient portfolio, it is possible to find another portfolio that is better in terms
of both expected return and volatility.
Volatility versus expected return for portfolios of two stocks – an example:
Effect on volatility and expected return of changing the correlation between two stocks:
Risk free saving and borrowing:
- Risk can also be reduced by investing a portion of a portfolio in a risk-free
investment, like T-bills. However, doing so will likely reduce the expected return.
- On the other hand, an aggressive investor who is seeking high expected returns
might decide to borrow money to invest even more in the stock market.
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