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CFAI Flashcards > Portfolio Management > Flashcards

Portfolio Management Flashcards

1
Q

Value at Risk (VaR)

A

Minimum loss that would be expected a certain percentage of time over a certain period of time

5% VaR = 1.65 standard deviations
1% VaR = 2.33 standard deviations
16% VaR = 1 standard deviation

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2
Q

Scenario Analysis

A

Compared to Sensitivity analysis (single risk factor), provides an estimate of the impact on portfolio value of a set of changes in magnitude in multiple risk factors

Computes value of an investment under a finite set of scenarios (e.g. best case, worst case, most likely case) and performance of portfolio under conditions of market stress

used when distribution of risk is discrete and can accommodate for correlated variables

E.g., stress tests or reverse stress tests

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3
Q

Sensitivity Analysis

A

Focuses on the impact on value of a given small change in one risk factor

Complementary to VaR in understanding portfolio risk

Used to estimate how gains and losses in the portfolio change with changes in the underlying risk factors

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4
Q

Statistical Factor Models

A

Advantages:

  1. Makes minimal assumptions

Disadvantages:

  1. Interpretation is generally more difficult than interpretation of macroeconomic or fundamental factor models
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5
Q

Elements of a VaR Statement

A

VaR statement contain elements of:

  1. Minimum loss
  2. Defined time period (frequency of losses)
  3. Stated probability of risk (tied to normal distribution confidence levels e.g. 5% VaR = 95% confidence level)
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6
Q

Define Sharpe Ratio and how to calculate it

A

Sharpe ratio provides a measure of how much the investor is receiving in excess of a risk less state

used to compare the portfolio return in excess of a risk less rate with the volatility of the portfolio return

Unaffected by the addition of cash or leverage in a portfolio

SR = Rp - RFR / STD(Rp)

RP = portfolio return
STF(Rp) = Standard deviation of portfolio return
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7
Q

Information ratio

A

Can be thought of a way to measure consistency of active return, which is what investors prefer

It IS impacted by leverage and cash

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8
Q

What is the formula for calculating variance of portfolio return?

A

(Weight Asset A)^2 * (variance of asset A) + (Weight Asset B)^2*(variance of asset B) + 2(WB)(WA)(CovAB)

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9
Q

How many trading days are there in a year?

A

250 trading days

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10
Q

List out the weaknesses of the Parametric method for calculating VaR

A

Estimates are only as good as the inputs
Length of look back period will affect the parameter estimates
Limited usefulness when normality cannot be reasonably assumed

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11
Q

What are strengths and weaknesses of using historical simulation to estimate the VaR?

A

Strengths:

You don’t need to assume a distribution
Method can be used to estimate VaR of a portfolio that includes options (i.e. need not worry about normality)

Weakness:
Using a highly volatile (stable) look back period can yield overestimate (underestimate) of VaR

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12
Q

What are the characteristics of estimating VaR using Monte Carlo simulation?

A

First and important key step is assuming a probability distribution of and correlations between each risk factor
Similar to historical simulation, VaR estimated from sorted outcomes
**Monte Carlo and parametric methods should yield identical results if the distribution and parameters are the same

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13
Q

Advantages of VaR

A

Concept is easy to explain
Allows the risk of different portfolios and asset classes to be compared
Can be used for performance evaluation
Used in optimal allocation of capital (i.e. risk budgeting)
Verified via backtesting
Widely accepted amongst global banking regulators

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14
Q

What are the limitations of VaR?

A

Estimation requires many choices
Assumptions of normality lead to underestimation of downside (Tail) risk
Does not account for liquidity risk or changing correlations
Focuses only on downside risk

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15
Q

What is an ETF?

A

Tracks an Index and trades on a secondary market
Market Makers are known as Authorized Participants (AP) who are authorized to create new or redeem existing shares
ETF manager/sponsor will define the list of securities that are needed to create new shares or creation unit

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16
Q

What are the advantages of ETF?

A

Lower cost - The in-kind creation/redemption eliminates transaction cost
Tax Efficiency - creation/redemption is not a taxable event; ETF sponsor may specify low basis stock as part of the redemption basket
Market Prices in line with NAV - APs can arbitrage any price discrepancy

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17
Q

What is an arbitrage gap?

A

Difference between price of ETF share and the NAVPS. APs can profit from price discrepancy by creating (redeeming) shares if the arbitrage gap is less (more) than the difference between price of ETF and NAV.

Arbitrage gap varies with transaction costs and service fees payable to ETF manager and the timing difference between when ETF trades and when underlying securities trade (due to time zone diff for foreign securities)

illiquid (liquid) securities have higher (lower) transaction costs and hence higher (lower) arbitrage gaps

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18
Q

What is Tracking Error?

A

Tracking difference between NAV and benchmark return (annualized standard deviation of the daily tracking difference)

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19
Q

What are the sources of tracking error?

A
  • ETF fees and expense
  • Sampling & Optimization
  • Depository receipts/other sector ETFs
  • Index changes
  • Reg & Tax requirements
  • Fund accounting practices
  • Asset manager operations
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20
Q

How to calculate the holding cost to the ETF investor?

A

Round-trip commission refers to the cost associated with buying and selling the ETF
Round-trip trading cost = round-trip commission fees + bid-ask spread
Total cost = round-trip trading cost + management fees (mgmt fees are relevant for long-term buy and hold investors)

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21
Q

What are the risks associated with ETFs?

A
  1. Counterparty risk
    Exchange traded notes (ETNs)
    Settlement risk
    Security lending
  2. Fund Closure - Hard close refers to full liquidation with negative tax consequences to the investor (ideally); Soft close refers to creation/redemption halts and slowly unwinds
  3. Expectation-related risk (10% gain is not the same as 10% loss)
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22
Q

Uses of an ETF in portfolio management

A
  1. Liquidity management
  2. Rebalancing
  3. Portfolio completion
  4. Transition management

Asset class exposure management

  1. Core exposure
  2. Tactical strategies
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23
Q

Active ETF strategies are most likely to be used for?

A

Mostly for fixed income rather than equity given the lower liquidity. These are suitable for long-term buy and hold investors as they seek to beat the benchmark and therefore tracking risk is expected to be higher for active ETFs than for passive ETFs

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24
Q

What is the arbitrage pricing theory (APT)?

A

Describes the equilibrium relationship between E(R) for well-diversified portfolio and their multiple sources of systematic risk (i.e. risk that cannot be diversified away)

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25
Q

What are the assumptions of APT?

A
  1. Unsystematic risk can be diversified away
  2. Returns are generated using a factor model (there is a lack of clarity on how to identify risk factors)
  3. No arbitrage opportunities exist (implies investors will take take large positions to exploit any perceived mispricing resulting in asset prices to adjust immediately)
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26
Q

APT formula

A

E(Rp) = Rf + (Sensitivity factor x factor risk premium)1…

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27
Q

what is the Macroeconomic Factor Model?

A

This model assumes asset returns are explained by surprises in macroeconomic risk factors (e.g. GP, interest rates, inflation). Factor surprises are defined as the difference between realized value and predicted value

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28
Q

what is the fundamental factor model?

A

This model assumes asset returns are explained by factors specific to the firm (e.g. P/E ratio, market cap, earnings growth rate). Factors are returns and not surprises (like macroeconomic factor model)

Factor sensitives are standardized (betas are like z-scores)

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29
Q

what are some differences between macro and fundamental factor models?

A
  • Macro models are time-series of surprises whereas fundamental models are cross-sectional asset returns
  • Macro model beta (factor sensitivity) is regression based whereas fundamental models is standardized (z-score)
  • Macro model factor returns are surprises in macro variables whereas fundamental models is computed from multiple regression
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30
Q

Define active return

A

Active return is the difference between the portfolio return and its benchmark

Rp-Rb

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31
Q

Define active risk/tracking risk

A

It is the standard deviation of active return. It can be calculated as:

Tracking error = sq.rt. [{summation(active return)^2}/n-1]

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32
Q

What does information ratio measure and how do you calculate it?

A

It measures active return per unit of active risk - i.e. a managers’s consistency in generating active returns. The higher the better.

It can be calculated as:

IR = (Avg Rp - Avg Rb) / active risk/tracking error

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33
Q

What are the sources of active return?

A

Active return = factor return + security selection return

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34
Q

what is the decomposition of active risk?

A

Active risk squared -> active factor risk + active specific risk; where:

  • Active factor risk is attributable to factor tilts
  • Active specific risk is attributable to stock selection

And active specific risk = [Summation (Wp - Wb)^2] * residual

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35
Q

Compare CAPM to Multifactor models

A

CAPM gives investor a choice between a risk-free asset and the market portfolio

Multifactor models:

  • better describe portfolio characteristics
  • provide better diversification/risk management possibilities
  • provide more efficient portfolios if asset returns are better described by multifactor models
36
Q

What is the difference between factor portfolio and tracking portfolio?

A

A factor portfolio has a factor sensitivity of 1 to a particular factor and zero to all other factors (i.e. a pure bet on a factor)
A tracking portfolio has a specific set of factor sensitivities often designed to replace the factor exposures of a benchmark index with the objective to outperform the benchmark using same factor exposures but different set of securities selection

37
Q

What is condition VaR?

A

It is the expected loss, given that the loss is equal to or greater than VaR (assumes portfolio is already in a loss event)

Also referred to as expected tail loss or expected shortfall

Difficult to calculate under the parametric approach

38
Q

What is incremental VaR?

A

It is the change in VaR from a change in the portfolio allocation to a security

e.g., increase in the weight of a particular security in a portfolio

Difference between the minimum loss before the change in allocation and after the allocation

39
Q

What is marginal VaR?

A

Very similar to incremental VaR, it is a reasonable approximation of the sensitivity of VaR to a 1% change in the portfolio weight of a security

40
Q

What is ex ante tracking error (Relative VaR)

A

Measures the VaR of the difference between the return on the benchmark and return on portfolio

41
Q

Formula to calculate change in call price as a measure of option risk

A

change in call price =

delta (change in underlying) + 1/2gamma(change in underlying)^2+ vega(change in volatility)

42
Q

What is active share?

A

application of a risk measure specific to asset management, it’s difference between weight of a security in the portfolio and its weight in the benchmark

43
Q

What is surplus-at-risk?

A

A key risk measure used by pension funds known as surplus-at-risk, a VaR for plan assets minus liabilities.

44
Q

What is the formula for the inter-temporal rate of substitution?

A

marginal utility of consuming 1 unit in the future / marginal utility of current consumption of 1 unit

45
Q

What is break-even inflation?

A

It is the expected inflation + risk premium for inflation uncertainty.

If nominal yield on DF bond- real yield on DF bond is positive (negative) than you are better (worse) off with a T-bond than TIPS

46
Q

Define cyclical industries

A

Earnings of companies in cyclical industries tend to be more sensitive to business cycle

47
Q

Define defensive industries

A

Earnings of companies in defensive industries tend to remain relatively stable and immune to changes in business cycles

48
Q

What is Shiller’s real cyclically adjusted PE ratio (CAPE) say?

A

Uses inflation adjusted prices and 10-yr moving avg of real earnings to reduce volatility in the P/E multiple

used for long term assessment of portfolio value

49
Q

Describe the concept of diminishing marginal utility of wealth

A

Investors marginal utility of consumption declines as wealth increases and thus higher during periods of scarcity - i.e. during economic contractions

50
Q

Explain how sector rotation strategies work

A

Strategy seeks to understand the relationship between performance of diff. sectors and business cycle to forecast shifts in business cycle to rotate money out before shift in performance occurs

51
Q

What are the three factors that impact Information Ratio?

A
  1. Information Coefficient
  2. Transfer coefficient
  3. Breadth
52
Q

What is breadth?

A

The number of independent bets an investor makes each year

Equal to # of securities multiplied by the # of decisions per year IF

1) R(A) are cross-sectionally uncorrelated
2) active returns are uncorrelated over time

53
Q

Explain how managers think what the optimal weight of an asset should be

A

Optimal weight of an asset is positively related to the forecast active return of the asset and negatively related to the forecast volatility of the active return of the asset

in other words, higher the forecast for return on that asset, higher the optimal weight of that asset in portfolio

54
Q

What is the fundamental law of active management (full + basic)

A

Full fundamental law encompasses constraints in the portfolio (TC) that forces actual weights to not equal optimal weights

Therefore, the expected active portfolio return =

E(Ra) = (TC)*[IC*√(BR)* σA]
IR = (TC)*[IC*√(BR)]

Basic fundamental law has no constraints (i.e. TC =1) and is the same formula as above.

55
Q

Formula for Sharpe ratio maximizing optimal level of active risk for an unconstrained portfolio

A

st. dev[R(A)] = IR / SR(b) x st.dev[R(b)]

56
Q

What is the formula for calculating the Sharpe ratio of the portfolio given optimal level of active risk?

A

SR(P)² = SR(B)² + (TC)²(IR)²

57
Q

What is the ex-ante information coefficient?

A

Measures manager skill;

the EXPECTED correlation between active returns and forecast active returns

58
Q

What is the ex-post information coefficient?

A

Ex-post IC measures ACTUAL correlation between active returns and forecast active returns

59
Q

What are the three factors that impact Information Ratio?

A
  1. Information Coefficient
  2. Transfer coefficient
  3. Breadth Ratio
60
Q

What is the breadth ratio?

A

The number of independent bets

61
Q

Explain the fundamental law of active management

A

Optimal weight of an asset is positively related to the forecast active return of the asset and negatively related to the forecast volatility of the active return of the asset

in other words, higher the forecast for return on that asset, higher the optimal weight of that asset in portfolio

62
Q

What is the fundamental law of active management (full + basic)

A

Full fundamental law encompasses constraints in the portfolio (TC) that forces actual weights to not equal optimal weights

Therefore, the expected active portfolio return =

E(Ra) = (TC)*[IC*sqrt(BR)* st.dev of active portfolio]
IR = (TC)*[IC*sqrt(BR)]
63
Q

What is the optimal level of active risk?

A

σR(A) = TC IR*/SR(B) *σR(B)

This is the level of risk that will generate the highest Sharpe ratio

64
Q

What is the formula for the Sharpe ratio of the portfolio given optimal level of active risk?

A

SR(P)² = SR(B)² + (TC)²(IR)²

65
Q

How to determine variation of active return in a constrained portfolio?

A

A constrained portfolio will prevent a manager from being able to establish optimal level of active risk and thus highest sharpe ratio

Two components:

  1. Variation due to realized IC: TC² (manager skill)
  2. Variation due to constraint induced noise: 1-TC²
66
Q

What is the formula for calculating the total risk of the portfolio with optimal level of active risk?

A

σ²(p) = σ²(b) + σ²(a)

67
Q

What is the information coefficient of a market timer?

A 
IC = 2*(Nc / N) - 1 where:
Nc = # of correct bets
N = total # of bets

A market timer who is correct about the direction of the market or sector 50% of the time will have an IC=0

68
Q

What are the limitations of the fundamental law?

A

Ex-ante estimation errors of IR (IC & BR) often result in lower ex-post IR

Managers are overconfident in their ability to outperform the market (IC)

Manager’s bets are often correlated and not independent resulting in high √BR and thus high IR

69
Q

Define explicit trading cost

A

Trading cost that include brokerage, taxes, and fees (any cost where a receipt can be expected)

70
Q

Define slippage (delay cost)

A

Cost of an adverse price movement during the lag in executing a large trade (risk when breaking large orders)

71
Q

What are the limitations of effective spread?

A

Poor indicator when a large order is split (i.e. does no account for price impact cost)

Does not account for slippage when part of the order is not fulfilled

Does not account for opp cost when the unfilled portion of the order is canceled due to adverse price movement

72
Q

What is a limit order book?

A

Shows the available posted bid and ask prices with corresponding quantities that the dealer is willing to purchase or sell

73
Q

What is a standing limit order?

A

Provides liquidity to the market and trade at their post prices but at a risk of failure to complete the trade

74
Q

What is the effective spread and how do you calculate it?

A

uses the midquote price as the benchmark price.

2*(per-share eff. spread transaction cost)

per-share effective spread transaction cost =

(side) * (transaction price - midquote price)

side = +1 for buy orders -1 for sell orders

75
Q

What is VWAP?

A

Volume-weighted average price (aka interval VWAP) at which all the trades were executed during the time interval between the order being placed and executed

easy to interpret; evaluates the price at which an order is executed relative to other trades during the same time period

76
Q

How do you calculate VWAP transaction cost?

A

trade size x side x (trade VWAP - benchmark VWAP)

77
Q

What are the limitations of VWAP?

A

Not useful if the trade being evaluated is a significant part of the trading volume in the market

Does not capture the price impact cost

78
Q

Define implementation shortfall

A

Measures transaction costs as the different between the value of the actual portfolio and value of a hypothetical paper portfolio

Addresses the shortfalls of VWAP by measuring total cost of trading to include all 3 implicit cost types (slippage, opp cost, price impact)

79
Q

Define liquidity aggregation algorithm

A

Creates a super book displaying liquidity across all markets

80
Q

Define smart order routing algorithm

A

Send orders to the markets with the best prices and sizes

81
Q

What do electronic front runners do?

A

Use AI to sniff out large trades (or many small trades) on the same side and then use low latency to trade ahead of them

82
Q

What is the distinction between high frequency traders and low-latency traders?

A

High frequency traders make quick round-trip trades thousands of times during the day

Low-latency trades rely on speed in receiving news and trading on it

83
Q

What are advanced orders?

A

The limit prices change automatically based on some role - e.g. old orders get deleted and replaced by a new order)

84
Q

List the different types of electronic trading strategies

A

Hidden Orders
Leapfrog
Flickering quotes
Machine learning

All ways to avoid exposing orders to other e-traders looking to front run

85
Q

What are the types of electronic arbitrage?

A

Take liquidity on both sides (trade posted bid/ask in multiple markets simultaneously)

Offer liquidity on one side - market order + limit order

Offer liquidity on both sides - limit orders for both legs; lowers trading cost but more risky

86
Q

What is spoofing/layering?

A

Example of abusive trading practice/market manipulation where fake limits are created to fake market sentiment

87
Q

How do you calculate the effective spread?

A

2 x (execution bid - midquote)

CFAI Flashcards (10 decks)

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