L7 - Portfolio Analysis Flashcards
How can you calculate the expected return of a share?
What is the most basic measurement of risk on stocks?
- The standard deviation is a measure of the dispersion of outcomes around the expected value. It is the most common measure of risk used in the theory of investment.
- If security return distributions are normal, we need only standard deviation and variance to describe fully the probability distribution of any security;
- Most frequency distributions of past security returns appear to be normally distributed;
What are the different percentages of Standard Deviation?
1 S.D. –> 68.26%
2 S.D. –> 95.46%
3 S.D. –> 99.72%
How do you calculate the expected return on a two-asset portfolio?
How can the Standard Deviation of the Expected return of a two-asset Porfolio be calculated?
How can the Covariance of a two-asset Porfolio be calculated?
if returns move in the same direction we have positive covariance, if in opposite directions, its negative
How can Correlation be used to simply the Standard Deviation of Expected Return of a Two-asset portfolio?
What happens when Correlation is 1 and -1 in a two-asset portfolio?
Correlation = 1
Standard Deviation (risk) becomes a weighted average of the two shares
Expect Return E(r) = ωARA + ωBRB
Standard deviation σp =ωAσA + ωBσB
As the stocks become less correlated, the standard deviation decreases thus expected risk does too, this can happen when you add more stocks to a portfolio (diversification)
Correlation = -1
Expect Return E(r) = ωARA + ωBRB
Standard deviation σp =ωAσA - ωBσB
In this case, you can find a the weighted value of A ( the portion of share A of the porfolio) in which is cancels out the risk making standard deviation = 0 –> effectively no risk
When does Risk in a Portfolio Reduce?
The degree of risk reduction depends on:
- the extent of statistical interdependence betweenthe returns of the different investments
- the number of securities over which to spread the risk
What does Risk Return Profile Look like on a graph?
If you choose a Porfolio it will always been from the efficient frontier
The graph also highlight that if you want a greater return it is at a greater risk
What is the Efficient Frontier?
The efficient frontier is 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. Portfolios that cluster to the right of the efficient frontier are sub-optimal because they have a higher level of risk for the defined rate of return.
What does the indifference curve to an investor look like?
- in order for an investor to take more risk (standard deviation) they need a higher return
- any point vertical above a portfolio gives a higher return at the same risk so it is preferred
- all points to left of a portfolio give the same return at a lower risk thus are preferred
thus more utility towards the north west
How can risk aversion affect an investor indifference curve?
- at higher level of risk aversion the slope of the indifference curve is more steep, thus to take more risk they need a larger amount of return compared to those with low risk aversion
How do Investors choice a portfolio?
The optimal combination is when an investors indifference curve is at a tangent to a the efficient frontier
What does the efficient frontier look for a two asset portfolio with a correlation coefficient of 0?
- shaded area are all the portfolio combination where the correlation coefficient is between 0 and 1
- it shows do for a given level of risk, for portfolio combinations that are less correlated (tend away from 1 towards zero) you will get a higher return
What does the Risk-return graph look like for a three-asset porfolio?
- the line between 1( A and B), 2(B and C) and 3(A and C) shows the efficient frontier of portfolio containing only those assets
- the line 4 shows the effcient line for a portfolio containing all three assets
- as you can see this portfolio dominates all the other combination of assets giving a much higher reward than a two asset model for the same amount of risk
What does the risk-return profile look like for a multi-security portfolio?
- the inefficient region (shaded) are the combination of shares that for a certain level of risk, do not give the maximum return possible
- someone with low levels of risk aversion will pick a combination with high risk-high reward, while someone with a small amount would pick low risk- low reward
How can diverifiable and non-diversifiable risk be represented on a graph?
- by adding more shares to your portfolio you have different covariance between shares reducing your risk
= most of your risk comes from the first 4 shares –> add 10-15 shares to your portfolio and it gets rid of significant amounts of risk
- however cannot get risk of non-diversifiable risk (changing in taxes, interest rates, GDP growth)
Benefits of international diversification?
- vastly reduces risk by holding internation shares that are not effected my domestic monetart and fiscal policies.
What is the capital market line when combining risk-free and risky investments?
- at point A risk is minimised in the porfolio but returns are low.
- by including government bonds at the risk free rate (rf with a standard deviation of 0) and connecting them to a porfolio on the line, we get a new efficient frontier for a profolio containing risk and non risk assets
- thus connecting it with point M which is a relatively riskier combination of assets than A and changing a proportion of the porfolio to government bonds, we can now take the porfolio F than has the same about of risk as A but a higher return
