Portfolio Management Flashcards
Intro
What is the purpose of portfolio investing?
To maximise an investments expected rate of return for a given level of risk (or minimise risk for a given rate of return), through diversification.
Intro
Endowment or Foundation
Definition
This is an investment fund set up by an institution from which regular withdrawals are made to fund ongoing operations.
Often set up by universities, hospitals or churches.
Intro
Steps
What are the 3 steps in portfolio management?
- Planning step - understand clients needs and develop an Investment Policy Statement (IPS)
- Execution step
- Feedback step - including rebalancing the portfolio, and adjusting the IPS if necessary
Intro
Fund Charges
Load fund
Redemption fee
Use of annual fees
A load fund is one with initial sales commission charges.
A redemption fee is a back-end load, a charge to exit the fund.
All funds charge annual fees
Portfolio
Standard deviation of portfolio of 2 shares
Portfolio
Standard deviation of portfolio of 3 shares
Portfolio
2 assumptions in investment analysis
- Returns are normally distributed
- Markets are operationally efficient
Portfolio
Utility Theory
Definition
Utility theory involves allocating a utility score to each investment based on a function of the expected return and variance.
eg Utility Score = Expected Return - 0.5*A*σ2
In this case A is the risk aversion coefficient, positive for risk averse investors, zero for risk neutral and negative for risk seekers.
Portfolio
Utility Theory
What are indifference curves in the context of utility theory?
Based on the utility score/formula used, an indifference curve can be drawn for a given risk aversion level (based on risk aversion coefficient A). This reflects investments which would be equivalent for that investor, based on the expected return and standard deviation levels.
Portfolio
Capital Allocation Line
Definition
Formula
Name of the slope/ratio
This represents the relationship between E(rp) and σp, the expected return and standard dev of a portfolio.
E(rp) = rf + E(ri - rf) * σp/σi
This is in the situation where we invest w1 in risk free asset rf and the rest in risky asset ri.
Exp portfolio return is E(rp) = w1 * rf + (1-w1) * E(ri)
and standard dev is σp = (1 - w1) * σi
So in short, the expectation of the portfolio is a linear function of the standard deviation of the portfolio, with slope E(ri - rf)/σi being the Sharpe measure, or reward-to-variability ratio.
Portfolio
Optimal Capital Allocation
Given the capital allocation line and indifference curves based on utility theory, how is optimal capital allocation determined?
Select the highest (i.e. most return for variability) indifference curve which touches the capital allocation line. The point at which the CAL touches the indifference line is the optimal capital allocation.
Portfolio
Covariance
Relationship between covariance and correlation coefficient
The correlation coefficient is the standarised version of covariance, calculated as follows:
p(1,2) = cov(1,2)/σ1σ2
Correlation coefficient represented by greek letter phi and ranges between -1 and 1.
Portfolio
Covariance
How do you calculate covariance from probability data?
Σpi*(Ri(A)-E(A))*(Ri(B)-E(B))
In the below example:
35%*(10%-4.8%)*(7%-2.05%) +
35%*(-4%-4.8%)*(4%-2.05%) +
30%*(-9%-4.8%)*(-6%-2.05%)
=0.0714%
Portfolio
Efficient Frontier
What is it?
The Minimum-Variance Frontier is built by using a computer to calculate the portfolio weighting with the lowest variance for each given level of expected return.
The efficient frontier is the upper section of that line, above the minimum-variance point. The lower section will never be chosen since for the same level of variance a higher return can be achieved with a different weighting.
Portfolio
Optimal Portfolio
What happens when the efficient frontier portfolios are combined with a risk free asset?
Name of the new line produced?
A combination of a portfolio on the efficient frontier and risk free asset Rf produces a new capital allocation line.
Choosing the portfolio to create a CAL tangential to the efficient frontier produces a new optimal set of portfolios which dominate the efficient frontier.
The final line produced is the Capital Market Line (CML).
Note the risk free asset has expected return Rf and σf = 0.
Note the point to the right of P represents borrowing at the risk free rate to leverage investment in the portfolio.
Portfolio
Optimal Portfolio
How does a risk investor finally choose a portfolio with a combination of optimal portfolio and risk free asset?
The point on the highest indifference curve (for the relevant risk aversion level) tangential to the new CAL is chosen.
This will be a better result than the equivalent portfolio without the risk free asset, on the efficient frontier.
Portfolio
Capital Market Theory
What is the CML
What portfolio do individual investors choose?
Capital Market Line
This is the line representing possible return/variance pairings achievable with a weighting between a portfolio on the efficient frontier and the risk free asset.
All investors will invest in the same portfolio, since it is the most efficient, but achieve their desired level of risk by selecting the appropriate weighting of the risk free asset.
Portfolio
Capital Markets Theory
Market Portfolio
Proportion of each asset held
Represented by point M on the chart. All investors should hold this portfolio. In equilibrium all risky assets will be held in the portfolio, since all investors should be holding the same portfolio.
All assets in portfolio M should be held in proportion to their market value (assuming efficient markets).
Portfolio
Capital Markets Theory
What is the effect of a risk-free rate spread on the Markowitz efficient frontier?
(i.e. you can invest at the risk free rate but must borrow at a slightly higher rate)
There are two tangential points on the efficient frontier. To the left you can reduce investment in the portfolio F and invest at the risk free weight, to the right you can borrow at the higher rate to leverage portfolio K.
The area on the efficient frontier between portfolios F and K is also on the overall Markowitz efficient frontier.
Portfolio
Risk
Systematic and unsystematic risk
Which has a value reflected in higher returns?
Total risk is the standard deviation of security returns.
Systematic risk is the risk inherent in the market which cannot be diversified away. Factors include global GDP growth.
Unsystematic risk is the risk which can be diversified away and reflects factors unique to the industry or security.
Systematic risk is reflected in the price since it can’t be diversified away, unsystematic risk is not rewarded.
Portfolio
Return-Generating Models
Definition
Three types
A return-generating model is a model or formula which estimates the expected return of a security based on certain parameters (eg market model, CAPM).
- Macroeconomic factor models include factors such as surprises in GDP, rates and inflation.
- Fundamental factor models include factors like market cap, PE ratio, financial leverage, earnings growth rate.
- Statistical factor models select factors which best explain historical return covariances (factor analysis) or variances (principal-components).
Portfolio
Beta
Description of beta
Formula
Beta reflects a securitys covariance with the market portfolio (Covi,M), which is an absolute measure.
Beta is infact the standardised version of this covariance:
since Covi,j = pi,j * σi,j
ß = Covi,M / CovM,M = Covi,M / σM2
Portfolio
CAPM
CAPM assumptions
- All investors are Markowitz efficient, want to target points on the efficient frontier depedent on their risk-return utility function
- Markets are frictionless (no transaction costs)
- All investors have the same one-period time horizon (eg one year)
- All have homogenous expectations (identical probability distributions for returns)
- Investments infinitely divisible
- All investors are price takers (trades can’t affect security prices)
Portfolio
CAPM
Formula
Market risk premium
Security risk premium
E(Rstock) = Rf + [E(RM) - Rf] * ßstock
Market risk premium = E(RM) - Rf
Security risk premium = [E(RM) - Rf] * ßstock
Portfolio
CAPM
Security Market Line (SML)
Similar to the Capital Asset Line, however this is the relationship between return and beta, and is obviously linear.
Where the CAL represents expected returns on efficient portfolios, the SML examines expected returns on individual assets based on their level of systematic risk (beta).
The slope of the SML is the market risk premium.
Portfolio
CAPM
Alpha
Alpha is when there is a difference between the expected and required return (per CAPM and the SML). It reflects additional return expected above the CAPM expectation.
Portfolio
CAPM
What is the beta of a portfolio?
Simply the weighted average of betas of the components of the portfolio.
Portfolio
CAPM
Treynor Ratio
Sharpe Ratio
The Treynor Ratio measures the excess return on an investment which has no diversifiable risk:
(RP - Rf) / ßP
The Sharpe Ratio measures the excess return per unit of risk
(RP - Rf) / σP
Sharpe is more relevant if the portfolio is not fully diversified, but Treynor is more relevant if it is since then only systematic risk matters.
Portfolio
CAPM
Jensen’s Alpha
This is the excess of return over the expectation per the CAPM model:
alphaP = RP - [Rf + ß(Rm - Rf)]
Portfolio
CAPM
Security Characteristic Line
Similar to the Security Market Line (SML), the SCL graphs the relationship between excess market return and excess security return, using formula:
Ri - Rf = alphai - ßi(Rm - Rf)
So it intercepts y axis at alphai (since this is the excess security return when there is no excess market return) and rises with a slope of ß.
Portfolio Management
Are investors objectives expressed in terms of risks or returns.
Investors objectives are expressed in the terms of both risks and returns, since the investment decision is a trade off between the two.
An analysis of risk tolerance should precede any discussion of return objectives.
