2. Portfolio Theory Flashcards
What are the three key assumptions around Portfolio Theory
- Investors are risk averse
- Security returns are Normally distributed
- Investors only care about financial risk & return
What is the utility function?
Portfolio theory
What is an indiference curve?
Indifference curves indicate the investment opportunities in mean variance space that give an investor the same level of utility.
Suppose an investor identifies all portfolios that are equally attractive as portfolio P. Starting at P, an increase in standard deviation lowers utility; to compensate, expected return must be higher. Thus, point Q in Figure 6.2, with higher risk but higher expected return, is equally desirable to this investor as P. Equally preferred portfolios lie in the mean–standard deviation plane on a curve called the indifference curve, which connects all portfolio points with the same utility value (Figure 6.2).
What do we see here?
Systematic vs nonsystematic risk
What is the tangency point?
A tangency portfolio is a portfolio that lies at the point where the efficient frontier is tangent to the highest possible capital market line (CML) in the risk-return space. This portfolio offers the highest risk-adjusted return for a given level of risk, combining optimal diversification and asset allocation.
The tangency point is the optimal portfolio of risky assets, known as the market portfolio.
What are two Modern portfolio theory implications
- Capital/asset allocation: how to optimally allocate your wealth over different
assets - Asset pricing: the effects of investor decisions on security prices; specifically,
the relation that should exist between the returns and risk
What is the goal of portfolio theory?
The best tradeoff between risk and return
What is the Sharpe ratio formula
What is the reward to volatility
Reward-to-variance ratio
What is the optimal portfolio formula with one risky asset and one Rf asset
What is slope of the CAL?
- Sharpe ratio
The CAL is basically a line that represents all the possible combinations between the
Risk Free asset and the optimal mix of risky assets.
What is the two-fund separation
Statement: The CAL is also called the efficient frontier of risky assets in the absence of a risk-free asset.
True or false
False
The CAL is also called the efficient frontier when risk free asset is present.
Statement 2: When borrowing and lending at a risk-free rate are allowed, investors should choose the Capital Allocation Line (CAL) with the steepest available slope
True or false
True
Highest slope of the CAL offers highest reward to variability ratio and identifies the
set with efficient investment opportunities.
Statement 3: An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the Capital Allocation Line must borrow some money at the risk-free rate and invest in the optimal risky portfolio.
True or false
True
The portfolios that lie along the CAL consists of the risk free asset and an optimal risky portfolio. The portfolio that lies on the y-axis invests 100% in the risk free asset. In between the portfolio on the y-axis and an optimal risky portfolio the wealth is split between risk free asset and the optimal risky portfolio. All the portfolios to the right of the optimal risky portfolios consists of lending at the risk free rate and taking a leverage position in the optimal risky portfolio.
Indifference curves are more steep when an investor is..
MORE risk averse
More risk averse: more steep, all else equal, the more risk averse you are, the more your indifference curve will be tangent on the left of the investment opportunity set. More conservative investment strategy.
Less risky averse: less steep indifference curve
What is the main investment advice from MPT
The optimal position, y* formula
Where can you find this point in the graph?
How do you calculate the optimal portfolio with two risky assets and rf?
1. Specify the return characteristics of all securities (expected returns, variances, covariances).
2. Establish the risky portfolio (asset allocation):
a. Calculate the optimal risky portfolio, P (Equation 7.13).
b. Calculate the properties of portfolio P using the weights determined in step (a) and Equations 7.2 and 7.3.
3. Allocate funds between the risky portfolio and the risk-free asset (capital allocation):
a. Calculate the fraction of the complete portfolio allocated to portfolio P (the risky
portfolio) and to T-bills (the risk-free asset) (Equation 7.14).
b. Calculate the share of the complete portfolio invested in each asset and in
T-bills.
