CFA Level3 Flashcards
Geometric Smoothing
Determines foundation distributions partly by Beginning MV X distribution % and partly as previous distribution increased for inflation, this creates a less volatile distribution %
Output gap
Below trend line growth and associated with a declining rate of inflation
Taylor Rule
Forecast the next change in ST rates
R target = policy neutral ST rate + 0.5 (expected inflation - target inflation) + 0.5 (expected GDP - trend GDP growth)
Cobb Douglas (CD) Production Function
Change Y/Y = Change A/A + a(Change k/k) + (1-a)Change L /L
Y = real output
A = total factor productivity
a = output elasticity
Solow Residual
Estimating TFP
Change in A = Change in Y - a(K) - (1-a)(L)
Total Factor Productivity (TFP)
labor + capital + technology
Measures the ability of an economy to produce more real output for the same inputs of labor and capital
Fed Model
S&P earnings yield (E/P) / 10 year treasury yield
Yardeni Model
Fair EY = E1 / P0 = Yb - d(LTEG)
Tobin’s Q
asset market value / asset replacement cost
MV of debt + MV of equity / asset replacement cost
Grinold-Kroner Model
Expected income return + expected nominal earnings growth + repricing return
(D1/P0 - change S) + (i + g) + change in P/E
Macaulay Duration
PV weighted average of when cash flows are to be received; less than maturity for a coupon bond
Modified Duration
Macaulay divided by (1 + discount rate)
Effective Duration
Takes into account embedded options
Key rate duration
Price sensitivity to specific points on the yield curve
Components of Fixed Income return
- Yield income (coupon / price)
- Rolldown return (projected ending / beg price) - 1
- Manager predicted price change based on D,C, and spread change
- Projected credit losses
- Projected foreign currency G/L
Duration Gap
BPVa - BPVl
Rules for Immunizing a single liability
- Initial PVA >= PVL
- Portfolio Macaulay duration Da = Dl
- Minimize portfolio convexity (min dispersion of asset cash flows around the liability and reduce risk to curve reshaping)
Money Duration (BPV)
BPV = MD * V * .0001
MD = Modified Duration
V =
Adjusting the Duration Gap
Target - Current / Instrument
Total Return Mandates (3)
Do not seek to fund future liabilities but may target an absolute rate of return
- Pure Indexing
- Enhanced Indexing
- Active Management
Collar
Long and short position in an out of the money call and put
Enhanced Indexing
Matching index duration but allowing deviations in other exposures
Key Rate Duration
Controls both interest rate and yield curve risk
Matrix / Evaluated Pricing
Price of similar, traded bonds is captured and used to calculate YTM
Modified Duration
Minimize tracking error due to parallel shifts in the yield curve
Change in value = -MD Change in rates
Key rate duration
Minimize tracking error due to nonparallel changes in the yield curve
Multiple key rates for single points in the yield curve = -D* change in rates
Advantages of a Laddered Bond Portfolio
- Natural liquidity
- Broadest diversification of cash flow across time and yield curve
- Diversification between price and reinvestment risk
- More convexity than the bullet, benefit from large parallel shifts
- Falls in middle of non parallel shifts
Strategies for an unchanged (Upward Sloping) Yield Curve (5)
- Buy and Hold
- Riding the yield curve
- Selling Convexity
- Carry Trades
Buy and Hold
Higher return by shifting to higher duration, buying duration risk to enhance portfolio yield under the assumption rates will remain stable
Selling Convexity
In a stable rate environment, increase portfolio returns by reducing the portfolio convexity below the benchmark
- Sell calls and sell puts
- Buy callable bonds and MBS (negative convexity)
Carry Trade
Buying a security at a higher yield and financing the purchase by borrowing at a lower interest rate
- Do best in stable markets can be very risky in highly volatile markets
Interest Rate Parity
Higher yield currency will trade at a forward discount to the lower yield currency
Crowding Risk
Mass effort to unwind a trade
Strategies for Changes in Level, Slope, or Shape of the Yield Curve
- Adjusting duration
- Increasing convexity
- Bullet, laddered and barbell strategies
Rolldown price
Price in 12 months + yield / spot interest rate
Holding Period Return
(Projected Price + coupon) / beginning price
G Spread
Interpolated spread when government maturities do not exist
I Spread
Computed and used the same way as the G-Spread but is based on the swap fixed rate
OAS
Option Adjusted Spread
does not reflect the impact of options on expected return
Benchmarks
SAMURAI
- Specified in advance
- Appropriate for the managers investment approach
- Measurable
- Unambiguous
- Reflective of the managers current investment opinions
- Accountable
- Investable
Roy’s Safety-first criterion
Rp - RL / standard deviation of portfolio
Myopic Loss Aversion
Macro issue when a large number of investors under-allocate to stocks, keeping their prices low and biasing upward their return
Conservatism
Cognitive Error
Initially rational view is formed but then retained without further consideration as new information comes in
Sharpe Ratio
Annualized Return - annualized risk free rate / Annualized standard deviation
Contagion
During crisis periods of market decline, correlations between markets move upwards towards +1 and benefits of diversification are not present
Tool used to track = Conditional Correlation matrices (Correlation for normal and for crisis)
Unhedged Return in Foreign Asset
R (FC) + R (FX)
Hedged Return in a Foreign Asset
R (FC) - R (FX) + R (DC)
Decision Risk
Investors investing in securities they do not really understand and then exiting the strategy at an inopportune time and at a high cost, higher for PE because it is an illiquid asset
- Ability to exit lowers decision risk
Information Ratio
Active risk / Active return
IR = IC X IB (1/2)
IC = Information Coefficient
IB = investor Breadth
Joint Probability
Prob 1 + Prob 2 - (Prob 1 X Prob 2)
Advantages of Monte Carlo Simulation
- Focuses the client and manager on most important risk, outliving the assets. instead of short term volatility
- Visually displays for the client the prospects of outliving assets
- Can incorporate path dependency issues such as how changes in inflation affect both distributions and MC
- Can incorporate taxes and other factors in addition to return
Event Risk
Company or situation specific and would be important if it causes bonds to decline relative to the stock of the company
Market Liquidity Risk
Significant for distressed debt investors, illiquid securities that most investors avoid
Market Risk (Distressed Investing)
Long company’s bonds and short the stick is designed to remove market (systematic) risk
J Factor Risk
The effect of the judge on the results of any bankruptcy proceedings, may rule in favor of debt or equity which will impact returns
Treynor Measure
Excess return over the risk free rate per unit of systematic risk
R portfolio - rfr / Beta
M^2
Compares the risk adjusted portfolio return to the market return
Rf + (Rp - Rf)/std dev p) *stand dev market
Information Ratio
Excess return for standard deviation of excess risk
Active Return / Active risk
(Rp - Rb) / standard dev (Rp - Rb)
Jensen’s Alpha
Rp - (Rf + Bp(Rm - Rf))
Utility Value
Um = E(Rm) - .005(a)(variance)
Components of Implementation Shortfall (4)
- Commissions
- Delay in execution [BP - DP] X # shares later executed
- Realized Profit / Loss [ EP - DP] X # of shares at EP
- Missed Trade [CP - DP] X shares canceled
Fundamental Law of Active Management
IR = IC * Sq root of IB
Information ratio = Information coefficient (Depth of knowledge about individual securities) X number of investment decisions (IB)
Investor Breadth (IB)
Number of independent decisions an investor makes
Ex: Buy ten energy stocks, IB = 1
Information Coefficient (IC)
Investor’s forecast against actual outcomes
Skillful managers will have higher ICs
Decentralized Risk Governance
Places responsibility for execution within each unit of the organization
- Benefit: putting risk management in the hands of those closest to each part of the organization
Centralized Risk System (ERM)
Enterprise Risk Management System
Places execution within one central unit of the organization
Financial Risks (3)
- Market Risk
- Credit Risk
- Liquidity Risk
Non-Financial Risks (6)
- Operational Risk
- Settlement Risk (Herstatt Risk)
- Model Risk
- Sovereign Risk
- Regulatory Risk
- Tax, Accounting and Legal Contract Risk
Analytical VAR
- based on concept of one-tailed confidence intervals
VAR = (Rp - (z)(standard dev))*Value of portfolio
5% = 1.65 standard deviation below mean
1% = 2.33 standard deviation below mean
ROMAD
Rp / Max drawdown
Sortino Ratio
Rp - MAR / standard dev return < MAR
MAR = minimum acceptable return
Beta
Covariance (i,m) / Variance (m)
Adjusting Portfolio Beta
(Bt - Bp)/Bf *(Vp/Pf(multiplier))
Basis Risk
Item hedged in numerator, not perfect match for hedging vehicle in denominator
Effective Beta
% change in value of the portfolio / % change in index
Pre-investing
Buying contracts in anticipation of cash that will be received
Bull Spread
Provides limited upside if underlying rises (bull) with limited downside
- Purchase a call with low exercise price Xl and subsidize with selling a call with a higher exercise price X
Bear Spread
Limited upside if underlying declines (bear) with limited downside
Sell a call with a low strike price and buy a call with a high strike price
Butterfly Spread with Calls
Purchase or sale of 4 different call options of three different types
- Buy 1 call with low exercise price XL
- Buy 1 call with higher exercise price XH
- Write 2 calls with an exercise price in-between Xm
Straddle
Purchase a call option and a put option with same exercise price and expiration
Collar
Protective Put and Covered Call
- Goal is for the owner of the underlying security to buy a protective put and then sell a call t pay for the put premium
- Upside and downside are limited
- Good strategy for locking in value of a portfolio at a minimal cost
Interest Rate Call Option Payout
Payoff = NP (Max(0, LIBOR - strike price)(D/360)
Delta
Change in price of the option / Change in price of the underlying
Range from 0 (OTM) to 1 (ATM)
Delta Hedge Position
= - delta X number of options
G spread
Similar to benchmark spread, but uses interpolated YTM of the two closest bracketing on the run government bonds
I spread
Compare interpolated YTM of the two closes bracketed swap fixed rates
OAS
Best estimate of spread for bonds with options
Grinold - Kroner Model
Forecasting return
R = Div1/P0 + i + g - Change shares - change P/E
Active Weight
= current allocation - benchmark
Alpha / Beta Separation Strategy
Gain systematic risk exposure by allocating funds to (low cost) passive index strategies, while adding to alpha via market-neutral long/short managers
