Week 2- Portfolio Theory Flashcards
What are the two types of risk?
Systematic risk and unsystematic risk
What is the difference between speculation and gambling
Speculation occurs in spite of risk due to the perception of a favourable risk-return trade off, whereas in gambling risk is assumed for the enjoyment of risk itself. Effectively the central difference is the lack of βcommensurate gainβ
What is the utility function we assume that investors assign to their competing portfolios?
π = πΈ(π) β 1/2π΄π^2
In the utility function: π = πΈ(π) β 1/2π΄π^2, what does everything stand for?
- π = Utility value
- πΈ(π) = Expected return
- π΄ = Index of the investorβs risk aversion
- π2 = Variance of returns
- Β½ = Scaling factor
What are the 3 kinds of investors? How does their A index demonstrate this?
- Risk Averse (A>0)
- Risk Neutral (A=0)
- Risk Loving (A<0)
How do risk averse individuals view risk?
Risk-averse investors consider risky portfolios only if they provide
compensation for risk via a risk premium.
How do risk neutral individuals view risk?
Risk-neutral investors find the level of risk irrelevant and consider
only the expected return of risk prospects.
How do risk loving individuals view risk?
Risk lovers are willing to accept lower expected returns on
prospects with higher amounts of risk.
How do we find the risk-free rate?
Risk-free Rate = Expected Return - Risk Premium
What is the portfolio return?
A simple weighted average of the proportion invested in each stock
What does the risk of a portfolio depend on?
- The risk of the individual stocks in the portfolio; and
- T he correlations between the stocks.
So how do we work out the return of a portfolio, say of in a portfolio with an 80:20 split between stocks A and B, stock A with 5.96% return and stock B with 9.10% return?
portfolioAB= (0.8 Γ 5.96) + (0.2 Γ 9.1) = 6.59%
For a portfolio with 2 Stocks, A and B, what is the covariance of Stocks A and B? How about the covariance between Stocks B and A?
ππ΄B = ππ΄Bππ΄πB
πBπ΄ = πBπ΄πBππ΄
Note that these are identical
Additionally, if there are multiple events with different probabilities, these all need adding up
What is the covariance a product of?
Covariance can be expressed as the product of the correlation coefficient ππ΄B and the two standard deviations π.
What is the purpose of diversification?
Diversification is the process of combining securities in a portfolio with the aim of reducing total risk, but without sacrificing the portfolio return.
What is key for why diversification works?
Diversification works because stock prices do not move in perfectly in phase with one another.
As some stock prices are moving upwardly others are moving in the
opposite direction.
What happens to unsystematic risk as the number of investments in a portfolio increases?
It decreases, this is called portfolio diversification of risk
What is the difference between systematic and unsystematic risk?
Unsystematic risk is a risk specific to a company or industry, while systematic risk is the risk tied to the broader market, such as changes in business cycles or govt policy.
What are other names for systematic and unsystematic risk?
Market and Unique risk
What does total risk =?
Total Risk = Systematic (market) Risk + Unsystematic (unique) Risk
What must the correlation coefficient ππ΄B stay between?
-1 < ππ΄B < 1
Can unsystematic risk be diversified away if ππ΄B = +1?
No unsystematic risk can be diversified away in this situation (however this rarely happens)
Can unsystematic risk be diversified away if ππ΄B = -1?
In this situation, all unsystematic risk will be diversified away
Can unsystematic risk be diversified away if ππ΄B = 0?
In this situation there is no correlation between the returns of the 2 securities.
How much risk roughly on a single share is based on systematic risk?
About 35%
When creating a 2 stock portfolio, do we want ππ΄B to be +1 or -1? Why?
-1, so we can diversify all unsystematic risk as the stockβs performances alter perfectly with each other, ie as one goes up, the other falls by an equal amount.
What do the size of diversification benefits depend on?
The correlation between the 2 stocks
Why are downward-sloping portfolio possibility curves inefficient?
As they are obtaining a lower return for the same amount of risk than upward-sloping portfolio possibility curves.
What does the Efficient Frontier consist of?
The Efficient Frontier consists of an envelope of all portfolios that lie between the minimum variance and maximum return portfolios.
Name 3 features of Markowitzβs Portfolio Theory (1952):
- Portfolio consisting of N stocks
- Efficient set when there is a riskless asset
- Market equilibrium
In a portfolio with a risky and a risk-free asset, what is the expected return? What does the slope mean?
π
π = π
π +((π
Μ1 β π
π)/π1) * πp
- The slope (π
Μ1 β π
π)/π1) os the extra unit per additional unit of risk (ie the Sharpe ratio)
In a portfolio with a risky and a risk-free asset, what is the standard deviation?
ππ = π1π1 where π1 is the proportion of wealth held in the risky stock
What does the Capital Market Line (CML) show?
That investors can both lend and borrow at a risk-free rate of return
What is true about the market portfolio (m)?
There are no risk-free assets, only risky assets.
Why would leverage be employed?
To enhance return
What does the market portfolio maximise, and what is it on a diagram?
The market portfolio will maximise the Sharpe ratio and lies at the point of tangency
between the Capital Market Line and the Efficient Frontier.
What about portfolios on the CML derived by?
/borrowing and lending at the riskless rate of interest in the capital market.
What is the optimal portfolio?
This is specific for each investor, given their level of risk.
What does the Separation Theorm (Tobin, 1958) state?
Whatever the risk preferences of individuals, in equilibrium, all investors hold portfolio m (the market portfolio) then either borrowing or lending at the riskless rate.
What is the market portfolio?
The market portfolio is the portfolio of all stocks in the economy with weights equal to their relative market values.
What are 2 criticisms of the Separation Theorem?
- Itβs unrealistic for an investor to hold every single stock
- It is unrealistic for investors to be able to borrow or lend at the risk-free rate
What is the market price of risk equal to? So what is the equation?
- The market price of risk is equal to the slope of the CML.
- π π = π π +((π Μm β π π)/πm) * πp
How do we calculate the correlation between stocks A and B?
Work out the covariance between A and B and divide by the total of the standard deviations of A and B
How do we work out portfolio variance?vGive the steps. What about for standard deviation?
- (Decimal percentage invested in Stock A multiplied by deviation of A)^2
- (Decimal percentage invested in Stock B multiplied by deviation of B)^2
- 2 x decimal invested in A x decimal invested in B x covariance of AB
- Add all these up
If you have multiple portfolios, each with different risk premiums per unit of risk, which is most likely to be the market portfolio?
The portfolio with the highest risk-free premium per unit of risk is most likely to be the market portfolio.
What is the Sharpe ratio?
Risk premium/Standard deviation
