Asset Allocation(two risky) Flashcards
Why do we diversify?
When 2 risky assets and risk- free rate, we choose the best portfolio obtained combining the risk-free and the tangency portfolio.
Why diversification works?
Because of negative correlation, diversification works.
Idiosyncratic and systematic risk
There are limits of diversification: idiosyncratic risk(sth different) can be diversified, systematic risk(sth the same) can not
Classify world, country, industry and firm sources of risk
Total risk = idiosyncratic risk + systematic risk
Efficient diversification
optimal weights that provide the lowest possible risk
Covariance of a random variable with itself.
The variance of the portfolio os a weighted sum of covariances, and each weight is the product of the portfolio proportions of the pair of assets in the covariance
Covariance of a random variable with itself, it is variance
The variance of the portfolio os a weighted sum of covariances, and each weight is the product of the portfolio proportions of the pair of assets in the covariance term
The efficient frontier of risky assets is
the portion of the investment opportunity set lies above the global minimum variance portfolio.
Portfolios on the efficient frontier are those providing the greatest expected return for a given amount of risk. Only those portfolios above the global minimum variance portfolio meets the criterion.
The capital allocation line provided by a risk- free security and N risky securities is
the line tangent to the efficient frontier of risky securities drawn from the risk- free rate.
Portfolios that are efficient are those that
provide the highest expected return for a given level of risk
An investor who wishes to form a portfolio that lies to the right of optimal risky portfolio on CAL must
both borrow some money at the risk- free rate and invest in optimal risky portfolio and invest in risky securities(will not hold any risk- free assets).
Portfolio theory as described by Markowitz is most concerned with
the effect of diversification on portfolio risk. He concerned with reducing portfolio risk by combining risky securities with differing return patterns.
The measure of risk in a Markowitz efficient frontier is
sd of return
The individual investor’s optimal portfolio is designated by
The point of tangency with the indifference curve and the capital allocation line.
The indifference curve represents what is acceptable to the investor; the capital allocation line represents what is available in the market. The point of tangency represents where the investor can obtain the greatest utility from what is available.
The line representing all combinations of portfolio expected returns and sd that can be constructed from two available assets (a portfolio of risky assets) is called
the portfolio opportunity set
The sd of a 2-asset portfolio is a linear function of assets’ weights when the assets have a correlation coefficient equal to
one.
When there is a perfect positive or negative correlation, the equation for the portfolio variance simplifies to a perfect square. The result is that portfolio’s sd is line relative to assets’ weights in portfolio.
The separation property refers to the conclusion that
the determination of the best risky portfolio is objective and the choice of the best complete portfolio is subjective.
The determination of the optimal risky portfolio is purely technical and can be done by a manager. The complete portfolio, which consists of the optimal risky portfolio and the risk- free asset, must be chosen by each investor based on preferences.
Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global minimum variance portfolio has a standard deviation that is always
equal to zero
The efficient frontier of risky assets is
the portion of the investment opportunity set that lies above the global minimum variance portfolio.
Portfolios on the efficient frontier are those providing the greatest expected return for a given amount of risk. Only those portfolios above the global minimum variance portfolio meet this criterion.
Why tangency portfolio is the best portfolio to combine with risk- free?
Because the portfolio has the highest sharpe ratio.
