Portfolio Management Flashcards
Linear regression requires the analyst to plot combinations of the asset’s return and the market return, and then
drawing a line through the points such that it minimises the sum of squared deviations from the line.
A stock plotted below the Security Market Line:
Is overpriced
limitation of the Treynor ratio
It does not work for negative beta assets
Smart Beta strategies focus on factors such as
value, momentum or dividend characteristics. Compared to traditional, passive funds they tend to have higher turnover and higher management fees
money market mutual fund and bond mutual fund,
> the maturity is as short as overnight and rarely longer than 90 days.
bonds with maturities as short as one year and as long as 30 years.
The core portfolio and the satellite portfolio
> does form the majority of assets, and is managed on a passive basis.
The aim is to earn the long term systematic risk premium in a tax efficient manner.
> aims to generate high active return, with no regard for the benchmark.
To add to a portfolio
> Sharpe ratio of the new asset to be greater than the Sharpe ratio of the existing portfolio multiplied by the correlation of the new asset and existing portfolio
> add a new asset to our portfolio with a negative expected return, if that asset significantly reduces portfolio risk
beta
βp = Cov(Rp,Rm)/σm2
(Rp – Rf) × (σm/σp) + Rf – Rm
(Rp – Rf) × (σm/σp) + Rf – Rm
A multi-boutique asset manager firm is best described as a(
holding company which owns several asset management firms with specialized investment strategies
Historical Return and Risk
Risk-return trade-off
1 + E(R) = (1 + rrF) x [1 + E(π)] x [1 + E(RP)]
Expected return = Real risk-free interest rate x Inflation rate x Risk premium
Financial assets
* Defined by risk and return characteristics
Return
* Periodic income
- E.g. cash dividends or interest payments
* Capital gain/loss
HPR:
Capital gain Dividend yield
Risk-return trade-ofF
- Positive relationship between expected risk and returns
- Higher return only possible with higher risk investments
- E.g. small caps have higher risk and return than large cap stocks
- Risk premium
- Excess return over nominal risk-free interest rate
- Equity return > Bond returns > T-bill returns
- Market prices reward higher risk with higher returns
- Characteristic of a risk-averse investor
Other investment characteristics
* Evaluating investments using mean and variance
- Assumes returns are normally distributed
- Assumes markets are operationally and informationally efficient
Investment Characteristics of Assets
Skewness
Refers to extent to which a distribution is not symmetrical.
Positively skewed
Mean > Median > Mode
Negatively skewed
Mean < Median < Mode
- 68% of observations within ± 1σ of mean
- 95% of observations within ± 2σ of mean
- 99% of observations within ± 3σ of mean
Kurtosis
* Measure that tells us when a distribution is more or less peaked than a normal
distribution
* Kurtosis increases an asset’s risk
- Not captured in a mean-variance framework
- Use value-at-risk
Leptokurtic (Fat-tail) distribution
Platykurtic (Thin-tail) distribution
Mesokurtic (Normal) distribution
Market characteristics
* Cost of trading
- Brokerage commission
- Bid-ask spread
* Difference between buying and selling price
* Affected by liquidity
- Price impact
* How price moves in response to an order in the market
* Extent of price impact determined by liquidity
* Liquidity
- More of an issue in emerging markets rather than developed markets
- More of an issue in corporate bond markets
* Especially lower credit quality bonds
Risk Aversion and Portfolio Selection
Utility theory and indifference curves
Utility theory and indifference curves
* Risk averse investor
- Utility derived from guaranteed income is greater than alternative
* Utility
- Measure of relative satisfaction that investor derives from different portfolios
- Can quantify rankings of investment choices using risk and return
* Assume investors are risk averse
Utility of an investment (U)=E(R) -0.5Asigma^2
Conclusions:
* Utility is unbounded on both sides
- Highly positive or highly negative
* Higher return contributes to higher utility
* Higher variance reduces utility
- Reduction in utility gets amplified by risk aversion coefficient
* Utility can be increased with higher return or lower risk
* Utility does not indicate or measure satisfaction
- Investors prefer investments with higher utility
Risk Aversion and Portfolio Selection
Indifference curves
- Plots combinations of risk-return pairs that an investor would
accept to maintain a given level of utility - Curve connects points of equal satisfaction (utility)
- The steeper the curve, the greater the risk aversion
Application of utility theory to portfolio selection
- Risk-free asset and risky asset
- Risk-free asset has zero risk and return, Rf
- Risky asset has risk of
σi (>0) and expected return E(Ri)- E(Ri) > Rf
E(Rp) = rf + wi(Ri-Rf)
Expected Risk
(1−w )σ
Capital allocation line (E(r) vs standard deviation
Represents portfolio available to an investor
ER = rf +sigma p (E(r) - rf)/ sigma i
Sharpe - (E(r) - rf)/ sigma i
Portfolio of many risky assets
sigma^2P = AVG sigma^2 / N + (N-1)/N* AVG COV
First term
- As N becomes larger, contribution of one’s asset variance becomes
negligible
* Second term
- Approaches average covariance as N increases
* If all assets have same variance and same weighting
- Correlation is the main determining factor in portfolio risk
sigmaP = (sigma^2 / N + (N-1)/N* COV)^(1/2)
Portfolio Risk
Power of diversification
- Correlation is key in diversification of risk
- Lower correlations are associated with lower risk
- Challenge is to find assets with correlations much lower than +1
- Reasonable to assume historical risk is a proxy for future risk
- Risks do not change dramatically from period to the next
- Correlations
- Above 0.90 considered to be high
- Below 0.3 considered attractive for diversification
Avenues for diversification
- Diversify with asset classes
- Correlations among asset classes do not appear to be high
- Can also use industries and sectors
- E.g. energy stocks and healthcare stocks
- Can be costly for small portfolios
- Diversify with index funds
- Cheaper to use mutual funds and ETFs
- Diversification among countries
- Countries are different because of industry focus, economic policy
and political climate - Diversify by not owning your employer’s stock
- Evaluate each asset before adding to a portfolio
- There may already be sufficient exposure to asset class
- Buy insurance for risky portfolios
- Negative correlation with assets
- Reduces exposure to an extreme loss
- E.g. gold or buying a put option
Optimal risky portfolio – adding in risk-free asset
Optimal Risky Portfolio
where Efficient frontier of risky assets is tangent to CAL
Efficient Frontier and Investor’s Optimal Portfolio
Two-fund separation theorem
- Investors will hold a combination of risk-free assets and an optimal
portfolio of risky assets - Regardless of taste, risk preferences, and initial wealth
- Investor’s investment problem
- Investment decision
- Identify optimal portfolio based on return, risk, and correlations
- Ignore investor’s preferences
- Financing decision
- Using indifference curves, select portfolio on CAL
- Determines allocation to risk-free asset (lending) and optimal risky portfolio
Portfolio Planning
Definition
* Program developed in advance of constructing a portfolio that is expected
to satisfy client’s investment objectives
* Investment policy statement (IPS)
- Written document governing portfolio planning process which is often supported by a document outlining policy on sustainable investing IPS
* Starting point of portfolio management process
* Communicates a plan for achieving investment success
- Client achieving investment goals
- Comfortable with risks taken
* Fact finding discussion with client
* Construction of IPS
- Should be standard procedure
- May be required by law
Major components of an IPS
Introduction Describes the clients
Statement of purpose States the purpose of the IPS
Statement of duties
and responsibilities
Details duties and responsibilities of the client, custodian of client’s assets and
investment managers
Procedures Explains steps to take to keep IPS current and procedures to follow to respond to various contingencies
Investment objectives Explains client’s objectives in investing
Investment constraints Presents the factors that constrain the client in seeking to achieve the investment objectives
Investment guidelines Provides information about how policy should be executed and on specific types of asset excluded from investment
Evaluation and review Provides guidance on obtaining feedback on investment results
Appendices
Strategic asset allocation. Baseline allocation of portfolio asset to asset
classes
Rebalancing policy. Investor’s policy with respect to rebalancing asset class
Portfolio Planning
Risk objectives
- IPS should clearly state risk tolerance of client
- Quantitative risk objectives can be absolute or relative
- Absolute
- i.e. not to lose more than 5% of capital in a year
- Measure using variance or standard deviation
- Relative
- Relate risk to one or more objectives
- Measure using tracking risk or tracking error
- Standard deviation of difference between a portfolio’s returns and its benchmark returns
- Tolerance
- Function of client’s ability to accept (bear) risk and their willingness to take risk
- Items that impact on ability to take risk
- Time horizon, expected income, level of wealth relative to liabilities
- Willingness
- Based on personality
Portfolio Planning
Conflict between ability and willingness to take risk
- Ability to take risk – below average
- Willingness to take risk – above average
- Assess tolerance as below average
- Ability to take risk – above average
- Willingness to take risk – below average
- Counsel client as to implications, i.e. reduced return
- Use lower of two factors
- Document decisions made
Portfolio Planning
Return objectives
- Absolute or relative basis
- Absolute
- Client wants to achieve 8% return pa
- Relative
- Desire to outperform benchmark by 1%
- Institutional investors may set a return objective relative to a peer group or
universe of managers - Can be problematic if limited information is known about peer group
- Good benchmark should be investable
- Can be stated before or after fees
- Can be stated pre or post-tax
- Should be a required return to meet a certain objective
- Should be realistic and state if it is nominal or real
- Should be consistent with client’s risk objective
