chapter 7 powerpoint (lessons 3 and 4) Flashcards
Investment decisions fall into which three types
Capital Allocation
Asset Allocation
Security Selection
Capital Allocation
Determines investor’s exposure to risk
Asset Allocation
Optimal portfolio with respect to risk-return tradeoff
–> Across broad asset classes Bills, Bonds, Stocks, etc
Security Selection
Individual assets within a class
–> Which bond in particular to pick?
What type of risk can be reduced through diversification
Firm-specific risk
Two main types of risk
Market risk
Firm-specific risk
Market risk
Reflects the conditions in the general economy
systematic risk
non diversifiable risk
Firm-specific risk
Reflects the conditions of the company itself
Unsystematic risk
diversifiable risk
Unique risk
Idiosyncratic risk
a well diversified portfolio would mainly bear which type of risk?
market risk only
Total risk
Market risk + Firm-specific risk
An efficient portfolio
the one that provides the lowest possible risk for the required level of expected return
Covariance
the measure of comovement between instruments
What does Cov(rD,rD) mean
How does asset D move with asset D
so how does asset D move with itself
The variance of a portfolio
a measure of risk of the portfolio
a weighted sum of covariances
what is the formula for the standard deviation of a portfolio with two risky assets?
the same as comm 308
it has way better formulas and you already have a good idea of it
what is the formula for the standard deviation of a portfolio with two risky assets?
the same as comm 308
write it on a cheat sheet
Correlation coefficient of returns
measures degree of association between
assets – has a direction
symbol: p
formula for correlation coefficient
same as comm 308
is the variance of a portfolio a simple weighted average of the individual asset variances?
nah brooo
it has the weird formula with either the covariance or the correlation coefficient
if p = 1 when we have two risky securities?
perfectly positively correlated
standard deviation is just the weighted average of the standard deviations of the risky securities
if p is not = 1 when we have two securities, is the portfolio standard deviation bigger or smaller than the weighted average of the standard deviations of the risky securities?
smaller
when we have two securities, how can we find the weight of security A if our p = 0 (securities have zero correlation)
wA = 𝜎B / (𝜎A + 𝜎B)
What is hedging?
Sets the variance to minimum, elimination risk, perfect hedge
a risk management strategy employed to offset losses in investments by taking an opposite position in a related asset
also typically results in a reduction in potential profits
Hedging strategies typically involve derivatives, such as options and futures contracts
when put in graphs, as we reduce the correlation, of our portfolio what happens to our returns in regards to our portfolio standard deviation and weights of securities?
two security
the lower the correlation coefficient, the lower the standard deviation for the same returns when the weight of stock A is between 0 and 1
–> also when the weight of stock B = 1 - wA
when wA < 0 or > 1, then the opposite happens
–> the lower the correlation coefficient, the higher the standard deviation for the same returns for p = 1
the efficient frontier
the set of optimal portfolios that offer the highest expected return for a defined level of risk or the lowest risk for a given level of expected return.
Portfolios that lie below the efficient frontier
are sub-optimal because they do not provide enough return for the level of risk
The lower the correlation between A and B, the more efficient or whack the diversificiation?
the more efficient
the Minimum Variance Portfolio (MVP)
the portfolio that has the lowest variance among all other portfolios obtained by changing wA
we ask ourselves the following question:
What value of wA will minimize our variance?
for two risky assets, how is our utility function considering we are risk averse investors?
U = ERp - 0.5 · A · 𝜎p^2
how do we choose our portfolio with two risky assets and a risk free asset?
At first, we form a new opportunity set: a new efficient frontier
–> the new CAL line
–> the spot where it is tangent to the old efficient frontier (with only two risky assets) is portfolio P
–> This is where the risk is optimized between our two risky and risk free assets
step 2: we check where our utility curve is tangent with our new CAL line (our new efficient frontier)
the old efficient frontier contains the mix of only the two risky assets, which from a portfolio
the point where the new CAL line is tangent to the old efficient frontier is the optimal mix between the two risky assets and our risk free asset with no regard for our utility
how can we find the portfolio P that is the tangency point between the new CAL line and the old efficient frontier?
Optimal Asset Allocation between Two Risky Assets and a Risk-Free Asset
we need to select the weight wA that maximizes the Sharpe ratio for the new CAL line
Sharper ratio = (ERp - RF) / 𝜎p
we need to find wA that maximizes the sharpe ratio
the part of the minimum variance frontier that lies on and above the global minimum variance portfolio
The efficient frontier
The Markowitz Portfolio Selection Model steps
Build the efficient frontier of risky assets
Find the CAL(P): the line that passes through the risk free rate and intersects the frontier on portfolio P
Choose the optimal portfolio that maximizes the investors utility through the proper
allocation of funds between the risk free asset and the optimal risky portfolio
How to build the efficient frontier of risky assets?
The Markowitz Portfolio Selection Model
We need to determine the possible risk return combinations of our assets
we have to find the minimum variance frontier and the minimum variance portfolio
how to to find the minimum variance frontier?
The Markowitz Portfolio Selection Model
follow to formulas
have to find ERp
have to find the 𝜎
have to make sure the weights of all securities are equal to 1
the construction of the minimum variance frontier and consequently the efficient frontier is based on our estimates of expected returns, variances, and covariances
When short selling is allowed, single portfolios lie to the right or left side of the efficient frontier?
The Markowitz Portfolio Selection Model
lie to the right side
The more the constraints the efficient frontier is subject to, the less or more its reward to variability ratio?
The Markowitz Portfolio Selection Model
the less
the portfolio choice problem is divided into which two independent tasks?
The Markowitz Portfolio Selection Model
The formation of the risky portfolio
The allocation of wealth between risky and risk-free asset
this is the basis of the separation property
the separation property
The Markowitz Portfolio Selection Model
clients will not have to same portfolios because different constraints will lead to different optimal risky portfolios (P)
different preferences will lead to different allocations of P and the risk free asset
As the number of securities (n) increases, the contribution of individual variances increase or deacrease?
decrease
–> If ‘n’ is big enough and the average covariance of our securities is zero, then we can bring our portfolio variance to near zero level
The Markowitz Portfolio Selection Model
effect of diversification on the standard deviation of our portfolio
–> the new formula(s)
𝜎p^2 = 1/n · 𝜎^2 + (n - 1)/n · p · 𝜎^2
𝜎p^2 = 1/n · 𝜎^2 + (n - 1)/n · Cov
the importance of the correlation coefficient on our total portfolio variance if all our stocks are uncorrelated, p = 0
The Markowitz Portfolio Selection Model
(an unrealistic case for ‘n’ > or = 3)
we can obtain the insurance principle
our portfolio variance approaches zero as n increases
the importance of the correlation coefficient on our total portfolio variance if all our stocks are uncorrelated, p > 0
The Markowitz Portfolio Selection Model
(a realistic case for n > or = 3)
our portfolio variance remains positive
the bulk of the portfolio variance would be attributed to the covariance term as ‘n’ increases
the importance of the correlation coefficient on our total portfolio variance if all our stocks are uncorrelated, p = 1
The Markowitz Portfolio Selection Model
(an unrealistic case for ‘n’ > or = 3)
our portfolio variance would be equal to the average individual variance
There is no benefit from diversification
While adding a new security to our portfolio, what matters is the covariance of this security’s returns with the returns of other securities in our portfolio or the new security’s variance?
the covariance or the correlation between other securities
