week 7 Flashcards
How do we calculate the expected return on a two asset portfolio?
R(bar)P = WaRa +WbRb
Where: R(bar)p = Expected return on Portfolio Ra = Return on Security A Rb = Return on Security B Wa = Share of Security A in portfolio Wb = Share of Security B in portfolio
How do you calculate the standard deviation of a two asset portfolio?
σp = Square root of (W2Aσ 2A + w2B σ 2B + 2WaWb COV (RA,RB)
Where: σp = Portfolio Standard Deviation σA2= Variance of Investment A σB2 = Variance of Investment B COV(Ra,Rb) = Covariance of A and B
How do we calculate the Covariance of A and B?
COV(Ra,Rb) = SIGMA (Ra - R (bar)a) (Rb - R(bar)b)pi
Where:
R(bar)a = Expected Return on A
R(bar)B = Expected Return on B
How do we calculate the correlation coefficient?
P a,b = COV (Ra,Rb) / σa σb
What is the correlation scale?
Ranges from -1.0 to +1.0.
The closer r is to +1 or -1, the more closely the two variables are related.
If r is close to 0, it means there is no relationship between the variables.
What does the degree of risk reduction depend on?
the extent of statistical interdependence between the returns of the different investments
the number of securities over which to spread the risk
What is the general rule in portfolio theory?
Portfolio returns are a weighted average of the expected returns on the individual investment . . .
BUT . . .
Portfolio standard deviation is less than the weighted average risk of the individual investments, except for perfectly positively correlated investments.
what is the efficient frontier for portfolio analysis
set of optimal portfolio that offer the highest return for a defined level of risk or the lowest risk for a given level of expected return
what is the indifference curve for portfolio analysis
describe investor demand for portfolio based on the trade-off between expected return and risk
its convex curve
upward sloping where it will meet the efficient frontier there is a match between supply and demand
how are varying degrees of risk displayed in the indifference curve
documents
How do you plot the points of a two asset model where both assets are perfectly correlated?
It is only possible to create along a straight line between the 2 assets
how do you plot the points of a 2 asset model where both assets are uncorrelated
only possible to create a 2 asset portfolio with risk return along a line between either asset
how do you plot points of a 2 asset model when both assets are correlated
only can create a 2 asset portfolio between the 1st 2 curves
diagram
how do you plot the points of a 2 asset model where both assets are negatively correlated
possible create a 2 asset portfolio with much lower risk than eitheir asst
how do you calculate the correlation coeffcient
cov(Ra,Rb)/(stnd_A*stnd_ B)
how do you plot the points of a 2 asset model where both assets are perfectly negative
possible create a 2 asset portfolio with almost no risk
what are the three varying degrees of risk aversion represented by indifference curve
moderate risk: this is a 45 degree line
low risk line: below 45 degree’s (becoming horizontal)
high risk: greater htan 45 degree (becoming vertical)
why are indifference curve increasing
as risk increases, the investor is expected to be comepsated by a higher return
what is the inefficient region
anything to the left of the efficient frontier look at notes, its usually shaded in grey or purple
how can you know if there is diversifiable risk
look if it is the portfolio is above the asymtope if it is not then it is a un-diversifiable risk.
there will always be a degree of un-diversifiable risk present.
- so if you add 10-15 shares to your portfolio research show 90% of risk is diversified
what would the un-diversifiable risk represent?
changes in tax and interest rate
why does diversifiable risk decrease
you own more companies shares, these companies would be affected by random shocks –>lower return for that share. an individual decision would cancel out e.g. a manager making crappy decison.
what is the benefit of international diversification?
International shares may provide a lower risk as a percentage of the risk on a single share
business cycles are different from country to country, so a decline in a country wouldn’t be great of a loss to you if you have countries doing well.
