Qual Info Flashcards
Cognitive Errors
-Related to the way the brain functions, processes, and files info, forms memories or makes judgements, and the difficulty of complete mathematical understanding
-9 Types categorized into Belief Perserverance Biases (5) and Info Processing errors (4)
Emotional Biases
Related to emotional, motivational, and social influences, or to human needs
Belief Perserverance Biases
-A cognitive error category
-Holding on to previous irrational and illogical beliefs
1) Conservatism
2) Confirmation
3) Representativeness
4) Illuision of control
5) Hindsight
Information Processing Errors
-A cognitive error category
-Misusing and the irrational/wrongful processing of info in financial decisions
1) Anchoring and adjustment
2) Mental Accounting
3) Framing
4) Availability
Cognitive Dissonance
-Closely related to various aspects of Belief Perserverance Bias
-A type of mental discomfort which occurs when new info conflicts with previously held beliefs or information
Conservatism Bias
-Belief Perserverance Bias
-Occurs when individuals fail to update perceptions to reflect new info. People assign more weight to previous beliefs and smaller weight to new info
Confirmation Bias
-Belief Perserverance Bias
-People notice what confirms their beliefs and ignore (or discount) info that contradicts/could change their beliefs
Representative Bias
-Belief Perserverance Bias
-Occurs when people classify new info based on previous experiences
-Ppl attempt a best fir into a existing classification
Base-Rate Neglect
-Part of representative bias, which is a belief perseverance bias
-Investors overreact to new info on a company without considering the underlying base probability of an event
-e.g. investors discover info leading them to believe comp is in growth phase when other evidence suggests a low prob of any comp being a growth comp
Sample-Size Neglect
-Part of representative bias, which is a belief perseverance bias
-Investors draw a conclusion that the entire population is similar to a very small sample
Illusion of Control Bias
-Belief Perserverance Bias
-Occurs when FMPs believe they have more control over a situation than they actually have
Anchoring and Adjustment Bias
-Info Processing Error
-Describes how people base their initial forecast on some past experience (anchor) and adjust that estiamte as new info presents itself, but initial anchor dominates the final prediction
Mental Accounting Bias
-Info Processing Error
-When investors assign different levels of importance to different “pots” of money
Framing Bias
-Info Processing Error
-Exhibit this when they answer the same question differently depending on how it is asked
Availability Bias
-Info Processing Error
-Occurs when people overestimate the probability of event occuring based on “availability” of their memory of the event (i.e. how easily the event comes to mind)
Emotional Biases
-May be harder to control bc they originate from unconscious influences rather than conscious calculation (as in cognitive errors)
1) Loss Aversion Bias
2) Overconfidence Bias
3) Self-control bias
4)status quo bias
5) Endowment bias
6) Regret-aversion bias
Loss Aversion Bias
-Emotional Bias
-Occurs when investors make decisions designed to avoid losses rather than to seek gains
Overconfidence Bias
-Emotional Bias
-Occurs when people overestimate their knowledge, abilities, or access to info and consequently have too much faith in their intuition, reasoning, or judgement
Self-Control Bias
-Emotional Bias
-Occurs when FMPs fail to support their long-term goals with short-term behavior
Status Quo Bias
-Emotional Bias
-Results primarily from inertia rather than conscious choice. Change is often uncomfortable for people and if no problem is apparent they will prefer not to make changes
Endowment Bias
-Emotional Bias
-People attach more value to the assets they own/inherit than assets they dont own
Regret Aversion Bias
-Emotional Bias
-Investors resist situations that require a decision for fear of a negative outcome
5-Way Model (BB&K)
-Classifies indvs based on level of confidence (y-axis) and method of action (x-axis)
Adventurer
-5 Way BBK Model (Confident, impetuous)
-Confident in decisions and willing to take changes, makes him reluctant to accept advice
Celebrity
-5 Way BBK Model (anxious, impetuous)
-Center of attention who holds some opinions but also knows his limitations
Individualist
-5 way BBK model (confident, careful)
-independent and confident by nature
Guardian
-5 Way BBK Model (anxious, careful)
-Cautious and concerned about future, meaning other types may become more guardian like as they age
Straight Arrow
-5 Way BBK Model (center)
-sensible and secure, willing to accept risk commensurate with a normal return
Passive Preservers
-BIT (Conservative style, passive)
-Not sophisticated investors with focus on financial security and wealth preservation
-Primarily emotional biases
Friendly Followers
-BIT (Moderate style, Passive)
-May be difficult to advise bc their cognitive biases give them confidence that encourages them to accept greater risk than their regret aversion will actually allow
Independent Individualists
-BIT (Growth style, Active)
-Most likely to be contrarian, resist following a financial plan, and are comfortable investing and taking risks
-Primarily cognitive biases
Active Accumulators
-BIT (Aggressive style, Active)
-Likely to have concentrated positions and high port turnover rates
-Primarily emotional biases
Bayes Formula
P(A|B) = [P(B|A) * P(A)]/[P(B)
Financial Crises Types
-Type 1 - A permanent, one-time decline with resumption of the trend rate after initial shock
-Type 2 - No persistent one-time decline but continuing a lower trend rate
-Type 3 - Both a permanent, one-time decline and continuation at a lower trend rate after initial shock
Value of Stock Market, GDP
Ve = GDP * (E/GDP) * (P/E) + Div Yield (for total return of stock market)
-Key insight is that corp earnings as a % of GDP and PE multiple cannot continually rise over the long-term
-Only way value of stock mrkt can increase over the long term is through long term GDP growth
Real Long Term Trend GDP Growth
=Labor input growth + Labor productivity growth
Business Cycles
-Result from short to medium term cycles that cause oscillations around longer term trend growth rate of economy
-Initial recovery -> Early Expansion -> Late Expansion -> Slowdown -> Contraction -> repeat
Initial Recovery
-After contraction, before early expansion (a few months)
-Economic features: After low point, output gap is large, inflation is decelerating, stimulative policies remain in place, economy starts to grow
-Captial Market Features: ST and LT govt bond yields likely to be bottoming but may still decrease, stock mrkt may begin to rise quickly as recession fears subside, riskier small cap stocks, HY bonds, and EM secs will do well
Early Expansion
-After initial recovery, before late expansion
-Economic Features
–output gap remains negative, but unemployment starts to fall
–consumers start to borrow to spend (housing and consumer durable demand increases)
–businesses step up production (profits begin to expand rapidly)
–central banks remove stimulus
-Capital Market features
–short rate begin to increase (long rates remain stable/increase slightly)
–Flattening yield curve
–stock price trend upwards
Late Expansion
-After early expansion, before slowdown
-Economic Features
–Positive output gap and danger of inflation (capacity pressures boost investment spending)
–low unemployment, strong profits, rising wages and prices (inflation)
–debt coverage ratios may deteriorate as business borrows to fund growth
–Monetary policy becomes more restrictive
-Capital Market Features
–private sector borrowing causes rates to rise
–yield curve continues to flatten as short rates rise faster than long rates
–stocks are volatile as investors watch for deceleration
–inflation hedges (e.g. commodities) may begin to OP cyclical assets
Slowdown
-After late expansion, before contraction
-Economic Features
–Fewer viable investment projects and overleveraging cause slowing growth (business confidence wavers)
–inflation continues to rise as business pricing attempt to outpace rising input costs
–Economy is vulnerable to shocks
-Capital market features:
–LT bonds may top but ST rates continue to rise/may peak (yield curve may invert)
–credit spread widens, depressing bond prices for lower credit issues
–stocks may fall (utilities and quality stocks likely to OP)
Contraction
–After slowdown, before initial recovery
-Economic Features
–Firms cut investment spending, then decrease production (unemployment can rise quickly)
–Profits drop sharply with credit mrkts tightening, accounting transgressions discovered, and bankruptcies
-Capital Market features
–ST and LT rates begin to fall (yield curve steepens)
–credit spreads widen, remains wide until trough
–early phase stock mrkt declining while late phase stock mrkt begins to rise
Taylor Rule
i* = r,neutral + pi,e + 0.5(y^,e - y^, trend) + 0.5(pi,e - pi,target)
i: target Policy nominal rate, r,neutral: real policy rate targeted with trend growth and target inflation, (y^,e - y^, trend): expected and trend real GDP growth rates
-When the interest rate given is nominal, do not need to add expected inflation:
i = r,neutral + 0.5(y^,e - y^, trend) + 0.5(pi,e - pi,target)
-if the target rate calculated is greater than the current target rate, econ could grow too fast which would cause tightening of output gap. This is unsustainable and would lead to higher inflation and weaker growth
General Business Cycle Effect on Yield Curve
-Yield curve steepens as business cycle bottoms
-Flattens during expansions
-Becomes flat to inverted toward the peak as rates rise
-Re-steepens during contraction
Current Account
Reflects exports and imports of goods and services, investment income flows, and unliteral transfers
-Because financial market reacts more quickly to changes than real markets, changes to current account are reflected quickly in the capital account vis ST rates, exchange rates, and financial asset prices
-ST changes in current account are less likely to result in exchange rate changes
-Larger, persistent imbalances must be financed by adjustments to private or public savings
Capital Account
Reflects foreign direct investment (FDI), involving productive asset purchases and sales, and portfolio investments (PI), involving financial asset transactions
Balance of Payments Equation and Takeaways
(X - M) = (S - I) + (T - G)
-(X-M) = net exports, representing the current account
-(S - I) = Domestic savings - Domestic investment
-(T - G) = Taxes - govt spending
-for a floating rate exchange regime to be in EQ (every buyer has a corresponding seller), current account surplus (positive X-M term), where there are net buyers of a currency. This must be offset by a deficit of the capital account (i.e. investment overseas), where there are net sellers of the currency. This capital required to invest oversees comes from domestic savings (S) in excess of domestic investment (I) or a govt budget surplus where taxes raised (T) are higher than govt spending (G)
Conditions of YTM Being Earned
1) Cash flow of bond are received in full and on time
2) Bond is held to maturity
3) Cash flows are reinvested at YTM
-Generally effects of conditions 2 and 3 offset eachother. If horizon is less than port duration , condition 2 will dominate and investor underperforms YTM when rates rise. If horizon is more than port duration, 3 will dominate and investor underperforms YTM when rates fall
Building Block Approach
-Breaks the expected return for fixed income security into 4 components:
1) ST nominal default risk free rate
2) Term premium
3) Credit premium
4) Liquidity premium
Grinold Kroner Model
-Extends gordon growth model to consider effects of share repos and changes in valuation levels through forecast horizon
-E(R,e) = (D/P) + (%Delta(E) - %Delta(S)) + %Delta(P/E) + Expected Inflation
-D/P = Div yield, %Delta(E) = Nominal earnings growth rate, %Delta(S) = Expected change in shares outstanding
Components of Grinold Kroner Model
Model: E(R,e) = (D/P) + (%Delta(E) - %Delta(S)) + %Delta(P/E) + Inflation Expectation
-%Delta(P/E) = growth rate of PE ratio, the “repricing return”
-Income Component of Expected Return = D/P - %Delta(S)
-Expected Capital Gains = %Delta(E) + %Delta(P/E)
-Est. Rate of change in EPS= %Delta(E) - %Delta(S)
Singer-Terhaar Method
-EQ Approach
RP,i,sig = P,i,GM * Sig,i * (RP,GM / Sig,GM)
RP,i,Sig = Risk premium of mrkt “i” assuming 100% integration with global mrkts
-P,i,GM = Correl coefficient between i and global mrkt
-(RP,GM / Sig,GM) = Sharpe ratio of global mrkt port
Singer-Terhaar Method, Risk Premium in Perfectly Segmented Markets
RP,i,s = Sig,i * Sharpe Ratio,i
Singer-Terhaar Method, Risk Premium when Degree of Intergration (row) is A value between 0 and 100%
RP,i = (row)RP,i,G + (1-row)(RP,i,s)
Expected Real Estate Return, Cap Rate
E(R,RE) = Cap Rate + g,NOI - %Change(Cap Rate)
Cap rate = NOI / Prop Value
Dornbusch Overshooting Mechanism
-Assuming perfect cap mobility, assumes that cap flowing into a higher returning domestic economy will instantly strengthen the currency up to the point where, looking forward, currency is expected to weaken by the return advantage of domestic economy
E(%Delta(S,d/f)) = (r,d - r,f) + (Term,d - Term,f) + (Credit,d - Credit,f) + (ERP,d - ERP,f) + (LIQ,d - LIQ,f)
Unsmoothing Appraisal-Based Returns
R,t = (1 - lambda)r,t + (lambda)R,t-1
Lamda = parameter of model taking value between 0 (unsmoothed original data) and 1 (smoothed original data)
-R,t = current observed (smoothed) return
r,t = unobservable true return
Estimated Variance of True Return Series, Unsmoothing Appraisal-Based Returns
var(r) = [(1 + lamda) / (1 - lamda)]* var(R)
Lamda = parameter of model taking value between 0 (unsmoothed original data) and 1 (smoothed original data)
var(r) = est. variance of true return series
var(R) = observed variance of smoothed returns
-since lambda is b/t 0 and 1, true variance is always higher than reported smoothed variance
Marginal Contribution to Total Risk (MCTR)
=Asset Beta * Port. Std. Dev.
Absolute Contribution to total Risk (ACTR)
=Asset weight * MCTR
Ratio of Excess return to MCTR
=(Expected return - risk free rate) / MCTR
-Asset allocation optimal when this ratio is the same for all assets
Liability-Relative Asset Allocation
-An asset allocation process with the presence of a clients liabilities within the investment horizon. includes Surplus optimization approach, 2-portfolio Approach, and Integrated Asset-Liability Approach
Surplus Optimization Approach
-Liability-Relative Asset Allocation approach
-Uses the traditional MVO approach based on the volatility of the surplus volatility as the measure of risk, Characteristics: Simple, linear correlation, all levels of risk, any funding ratio, single period
2-Portfolio Approach (Hedging/Return-Seeking Portfolio Approach)
-Liability-Relative Asset Allocation approach
-Partitions assets into 2 groups: A hedging port managed so that its assets are expected to produce a good hedge to cover req CFs from liabilities, and a return-seeking port that can be treated as an asset only port
-Characteristics: Simple, linear/nonlinear correlation, conservative levels of risk, positive funding ratio for basic approach, single period (S-LN-CPS)
Integrated Asset0Liablity Approach
-Liability-Relative Asset Allocation approach
-The most comprehensive of the 3 Liability-Relative Asset Allocation approaches, where decisions regarding the composition of liabilities are made in conjunction with their asset allocation
-Characteristics: complex, linear/nonlinear correlation, all levels of risk, any funding ratio, multiple periods
Portfolio Returns and Taxes
r,at = p,d(r,pt)(1-t,d) + p,cg(r,pt)(1-t,cg)
r,at: expected after-tax return, r,pt: expected pre-tax return, p,d: proportion of r,pt attributed to dividend income, p,cg: proportion of r,pt attributed to capital gains
stdDev,at = stdDev,pt(1-t)
–> means expected after tax return std dev is smaller than pre-tax return std dev
Put-Call Parity
S,0 + p,0 = c,0 + [X / {(1+r)^T}]
S,0: price of underlying security; p,0 and c,0 are prices of put and call options, both with strike price ‘X’ and expiration ‘T’; [X / {(1+r)^T}]: the PV of a risk free 0 coup bond paying X at option expiration
Put-Call Forward Parity
Basic Long Option Payoffs
Call Option: MAX[S,T - X, 0] - c,0
Put Option: MAX[X - S,T, 0] - p,0
Covered Call Factoids
-A combo of long underlying security position and a short call position
-Investment objectives: Yield enhancement (writting slightly OTM calls in a static mrkt), Reducing overweight position (selling ITM call in static mrkt increases effective sale price), or target price realization
Covered Call Equations
-Value of Covered Calls @ Expiration: S,T - MAX[S,T - X, 0]
-P&L: S,T - MAX[S,T - X, 0] + c,0 - S,0
-Max Profit: X - S,0 + c,0
-Max Loss: S,0 - C,0
Breakeven: S,0 - c,0
Covered Call Payoff Graph
-Max gain occurs when stock price appreciates to the strike price
-Max loss occurs when stock price falls to 0
Protective Put Factoids
-A combo of a long underlying security position and a long put position
-Basically a form of insurance with objective of protective against investment loss. Can think of put premium as cost of insurance
-Major risk is they have a finite term and have to be rolled over periodically (expensive)
Protective Put Equations
-Value of Protective Puts @ Expiration: S,T + MAX[X - S,T, 0]
-P&L: S,T + MAX[X - S,T, 0] - S,0 - p,0
-Max Profit: Theoretically unlimited
-Max Loss: S,0 - X + p,0
-Breakeven: S,0 + p,0
Protective Put Payoff Graph
-Max gain unlimited as gains on underlying long stock are unbound above
-Max loss occurs when stock price falls to exercise price
Delta, Calls and Puts
-Delta = Change(option price)/Change (underlying)
-Long Call Delta: Always positive, between [0,1]. Long ATM call option will have delta = 0.5
-Long Put Delta: Always negative, between [-1,0]. Long ATM put option will have delta = -0.5
Bull Spreads
-Objective is to benefit from rising prices with a lower cost than a simple long position or a call option
-Both call and put bull spreads you are long the lower strike option and short the higher strike option
Call Bull (Debit) Spread Factoids
-Buying a lower strike price call option (X,L) and selling a higher strike price call option (X,H) with the same expiration date
-As the higher strike call (which you are short on) is less expensive than lower strike call (which you are long on), call bull spread requires a cash outflow (debit spread)
-Risk is that underlying must rise above lower strike price to offset initial costs
Put Bull (Credit) Spread Factoids
-Buying a lower strike put option and selling a higher strike put option with the same expiration date
-As the higher strike price (short on) is more expensive, put bull spread generates an initial cash inflow (credit spread)
-Risk is that if stock price falls below high strike price, investor will begin losing initial cash flow
Call Bull (Debit) Spread Equations
-Value @ Expiration: MAX[0, (S,T - X,L)] - MAX[0, (S,T - X,H)]
-Profit: MAX[0, (S,T - X,L)] - MAX[0, (S,T - X,H)] - (c,L - c,H)
-Max Profit: X,H - X,L - (c,L - c,H) when S,T > X,H
-Max Loss: (c,L - c,H), when S,T < X,L
-Breakeven Price: X,L + (c,L - C,H)
Call Bull (Debit) Spread P&L Graph
-Max profit occurs when S,T > X,H
-Max Loss occurs when S,T < X,L
Put Bull (Credit) Spread Equations
-Value @ Expiration: MAX[0, (X,L - S,T)] - MAX[0, (X,H - S,T)]
-Profit: MAX[0, (X,L - S,T)] - MAX[0, (X,H - S,T)] - (p,L - p,H)
-Max Profit: p,H - p,L, when S,T> X,H
-Max Loss: (X,H - X,L) - (p,H - p,L), when S,T < X,L
-Breakeven: X,H - (p,H - p,L)
Put Bull (Credit) Spread P&L Graph
-Max profit occurs when S,T > X,H
-Max Loss occurs when S,T < X,L
Bear Spread
-Objective is to benefit from falling prices at a lower cost than a simple short position/put option with same expiration date
-Both call and put spreads you are long the higher strike option and short the lower strike option
Call Bear (Credit) Spread Factoids
-Investor buys a higher strike call and sells a lower strike call with same expiration date
-As the higher strike call option is less expensive than lower strike call, results in an initial cash inflow (credit spread)
-Risk is that stock price rises above the lower strike price, causing him to loose initial credit spread
Put Bear (Debit) Spread Factoids
-Investor buys higher strike put option and writes lower strike put option with same expiration date
-As higher strike put option is more expensive, put bear spread generates initial cash outflow (debit spread)
-Risk is that if stock price does not fall below the high strike price, investor will lose initial cash outflow
Call Bear (Credit) Spread Equations
-Value @ Expiration: MAX[0, S,T - X,H] - MAX [0, S,T - X,L]
-P&L: MAX[0, S,T - X,H] - MAX [0, S,T - X,L] - (c,H - c,L)
-Max Profit: Net premium received, c,L - c,H, when S,T < X,L
-Max Loss: (X,H - X,L) - c,L + c,H, when S,T > X,H
-Breakeven: X,L + c,L - c,H
Call Bear (Credit) Spread P&L Graph
-Max Profit occurs when S,T < X,L
-Max Loss occurs when S,T > X,H
Put Bear (Debit) Spread Equations
-Value @ Expiration: MAX[0, X,H - S,T] - MAX[0, X,L - S,T]
-P&L: MAX[0, X,H - S,T] - MAX[0, X,L - S,T] - (p,H - p,L)
-Max Profit: (X,H - X,L) - (p,H - p,L), when S,T < X,L
-Max Loss: (p,H - p,L)
-Breakeven: X,H - (p,H - p,L)
Put Bear (Debit) Spread P&L Graph
-Max Profit occurs when S,T < X,L
-Max Loss occurs when S,T > X,H
Straddle
-Objective is to profit from a directional play on volatility, either for decreasing (short straddle) or increasing (long straddle). Both involving going long/short both put/call with same expiration on same asset
Long Straddle Factoids
-Profitable when volatility rises above market consensus
-Buy a put and a call with same strike prices and same expiration on same asset
Long Straddle Equations
-Value @ Expiration: MAX [0, S,T - X] + MAX[0, X - S,T]
-P&L: MAX [0, S,T - X] + MAX[0, X - S,T] - c,0 - p,0
-Max Profit: X - S,T - c,0 - p,0. Unlimited if S,T > X. Limited to X - c,0 - p,0 if S,T = 0
-Max Loss: c,0 + p,0, when S,T = X
-Breakeven: Upside breakeven (when S,T > X) = X + c,0 + p,o, downside breakeven (when S,T < X) = X - c,0 - p,0
Long Straddle P&L Graph
-Max Profit (Upside): Unlimited when S,T > X. Max Profit (downside) limited to X - c,0 - p,0 when S,T = 0
-Max Loss when S,T = X
Short Straddle Factoids
-Profitable when volatility declines and there is minimal movement in underlying asset
-Sell a put and a call with same strike prices, same expiration and on same asset
Short Straddle Equations
-Same as long straddle but with signs reversed
-Value @ Expiration: -MAX[0, S,T - X] - MAX [0, X - S,T]
-P&L: -MAX[0, S,T - X] - MAX [0, X - S,T] +c,0 + p,0
-Max Profit: c,0 + p,0 when S,T = X
-Max Loss: Unlimited when S,T > X, limited to X - c,0 - p,0 when S,T =0
-Breakeven: Upside Breakeven (when S,T > X) = X + c,0 + p,0, downside breakeven (when S,T < X = X - p,0 - c,0
Short Straddle P&L Graph
-Max Profit: When S,T = X
-Max Loss (Upside): Unlimited when S,T > X. Max Loss (downside) limited to X - c,0 - p,0 when S,T = 0
Collar Factoids
-Assumes investor owns underlying. Achieves downside protection by buying long put below current market price and reducing this cost of protection by writing covered call exercisable above current market price
-Risk is that it the short call limits upside participation
Collar Equations
-Value @ Expiration: S,T + MAX [0, X,L - S,T] - MAX[0, S,T - X,H]
-P&L: S,T + MAX [0, X,L - S,T] - MAX[0, S,T - X,H] - S,0 - p,0 + c,0
-Max Profit: X,H - S,0 - p,0 + c,0 when S,T >/= X,H
-Minimum Profit (potentially a loss) X, L - S,0 - p,0 + c,0, when S,T </= X,L
-Breakeven Price: S,0 + p,0 - c,0 if there is a max loss (when X,L < S,0)
Collar P&L Graph
Calendar Spread
-Options strategy where investor sells and buys same type of option, but with different expiration dates to take advantage of time decay
Long Calendar Spread
-ST option is sold and LT option is purchased
–Investor expects to profit from time passage as ST option falls in value by more than LT option
-Profitable when markets are stable in sort term and longer-term implied volatility rises
Short Calendar Spread
-ST option is bought and LT option is sold
-Investor expects to profit from time passage as LT option falls in value by more than ST option
-Profitable when markets are volatile in ST with falling LT implied volatility
Volatility Smile
-Occurs when OTM puts and calls exhibit greater implied volatility than ATM options
-Can become a volatility skew in times of market stress as more ppl are interested in buying port protection in the form of puts, driving up prices and implied vol
Options Strategies Given Investment Objectives
Notional Size of Swap Required to Adjust Duration of Fixed Income Portfolio
N,s = [(MDUR,T - MDUR,P) / MDUR,S] * MV,P
MDUR,S = MD of receive-fixed Swap
Principal Invoice Amount, Futures
=(Future Settlement Price 100) x CF x Contract size
Profit/Loss From Delivering Deliverable Bond, Futures
=Principal Invoice Amount - Cost of purchasing bond
Basis Point Values (BPVs)
-Measures the absolute change in value of a portfolio for a 1 bp change in yields
BPV,P = MV,P x MDUR,p x 0.01%
of Futures Required to Change Portfolio Duration, BPV
N,f = [(BPV,T - BPV,p) /( BPV,f / CF)
Futures Price and CTD Bond, BPV
BPV,f = BPV,CTD / CF
-Fair futures prices are inversely related to the CF of the CTD bond
of Futures Required to Adjust Beta Exposure of Equity Portfolio
N,F = (S/F) * [(B,T - B,S) / B,F]
=(S/F) * (-B,S / B,F)
S = mrkt value of equity portfolio
F = value per futures contract (price x multiplier)
B,S = Equity portfolio beta
-When doing a 2-piece trade (i.e. buying one future, selling another), B,s = 0 for the buy side and B,T = 0 for the sell side. S = Target allocation, or what you are working with
VIX Term Structure
-Flat shape shows vol is expected to remain stable over near to LT
-Downward slope shows decreasing vol expectations over time, making prices higher for ST contracts (backwardation). If VIX is in backwardation and vol expectations are expected to remain constant, VIX prices will increase as contract approaches maturity
-Upward slope shows increasing vol expectations overtime, making prices lower for ST contracts (contango). If VIX is in contango and vol expectations are expected to remain unchanged, VIX prices will decrease overtime
Variance Swap
-Allows investors to take directional bets on implied vs realized vol to speculate/hedge portfolios
-The payoff at expiration of long variance swap will be positive when realized variance is greater than strike variance
-Only exchange cash at settlement
Notional Variance, Variance Swap
N,Variance = N,Vega / (2 x Strike Price)
-Ignore decimals/%’s, make all numbers whole numbers
Settlement Amount Paid to Long Swap Position, Variance Swap
Settlement Amt, T = N,Vega * [ (var - X^2) / (2 * Strike Price)
=N,variance * (Var - X^2)
–Ignore decimals/%’s, make all numbers whole numbers
Value of Variance Swap, T
-Ignore decimals/%’s, make all numbers whole numbers
Forward Premium/Discount, Currenices
F, FC/DC - S, FC/DC = S, FC/DC * {[(i,FC - i,DC) * (Act/360)] / [1 + (i,DC * (act / 360))]}
-If forward rate is higher than spot rate, base currency (domestic currency) is said to be trading at a forward premium and is expected to appreciate in the future
Forward Rate, Currencies
=S,FC/DC * {[1 + (i,FC x act/360)] / [1 + (i,DC x act/360)]}
Return on Global Assets, Domestic Currency
R,DC = [w1 * (1 + R,FC1)(1 + R,FX1) + w2 * (1 + R,FC2) (1 + R,FX2)] - 1
-Make sure return terms are stated with domestic currency in numerator
Variance of Domestic Return
Var(R,DC) = var(R,FC) + var(R,FX) + [2 * stdDev(R,FC) x stdDev(R,FX) x p(R,FC , R,FX)]
-make sure return terms are stated with domestic currency in numerator
Effective Duration
= [(PV-) - (PV+)] / [2(Delta(curve))(PV,0)]
Effective Convexity
=[(PV-) + (PV+) - 2(PV,0)] / [(Delta(curve)^2)(PV,0)]
-Bonds with greater convexity enjoy greater price increase when yields fall and smaller price decline when yields rise
-Bonds with longer maturity tend to have greater convexity than shorter maturity bonds
Components of Fixed Income Return
-E(r) = Coupon income + rolldown return + E((delta(P)) due to yield change and spread) + E(currency gains/losses)
-Coupon income = Coupon income + reinvestment interest relative to bonds price (if no reinvestment income, coup inc = Bonds annual current yield)
-Roll-Down Return = (B,1 - B,0) / B,0
-Rolling Yield = yield income + roll-down return
-E((delta(P)) due to yield change and spread) = (-D * Delta(Y)) + [0.5 x CX x (delta(Y)^2)]
Portfolio Return, Leverage
r,P = Leveraged return / Portfolio equity = {[r,i x (V,E + V,B)] - (r,B x V,B)} / V,E
=(return to Equity + return to borrowed) / Portfolio equity = [r,i(V,E) + V,B(r,i - r,B)] / V,E
=Return on equity capital + return on borrowed capital = r,i + (V,B / V,E)(r,i - r,B)
r,i: Asset return, V,E: Invested equity, V,B: Borrowed equity capital, r,B: Cost of borrowed capital
Futures Leverage
Leverage = (Notional Value - Margin) / Margin
Repo Rate
=(Selling price - Repurchase price) / Selling price
Repo Price
Principal (initial selling price) + interest = Principal x [1 + r,R(Term/360)]
r,R = repo rate
Rebate Rate, Securities Lending
=Collateral earnings rate - security lending rate
Liability Driven Investing (LDI) Strategy
-A form of Asset-liability mgmt (ALM) that takes the liabilities as given and builds the asset portfolio in accordance with the interest rate characteristics of the liabilities
Classification of Liabilities
-I: Traditional fixed rate bonds with no embedded options
II: Bonds with embedded options, term life insurance policy
III: Floating rate notes/inflation protected security
IV: property and casualty insurance payouts
Yield Curve Dynamics
-Changes in yield levels: Occur when yield curve changes by same number of bps at each maturity (AKA Parallel shift)
-Changes in yield curve slope: Can be quantified as the difference between yields for long maturities less yields for short maturities (when spread widens, curve is said to steepen and when it narrows, curve is said to flatten)
-Changes in yield curve shape (curvature) - Can be quantified by the Butterfly Spread
Butterfly Spread
-Can be used to quantify the yield curve shape (curvature)
-Butterfly Spread = 2YTM10 - (YTM2 + YTM30)
-Generally positive, increases as curve becomes more concave (humped) and would likely be negative for a convex (U-shaped) curve
Price Change in Bond
(AKA Price-Yield Return)
%Delta(V, Full price) = -MD,P x Delta(Y) + 0.5(C,P)(Delta(Y)^2)
-Use Effective Duration when available
-Use end of horizon measurements when available
Strategies to Increase Duration - Purchase Bullet
-Buy bond with duration greater than benchmark
-Excess return: Price appreciation as YTM declines
-Risks: Yields increase rather than decrease
Strategies to Increase Duration - Receive Fixed Swap
-Fixed rate receiver
-Excess return: Swap MTM gain as yield falls plus carry (fixed less floating rate) and less margin cost
-Risks: Higher floating rate/higher swap yield level
Strategies to Increase Duration - Long Futures
-Buy contract for forward delivery
-Excess return: Futures MTM gain less margin cost
-Risks: Yields increase/funding costs increase
Strategies for Yield Curve Changes General
-Bull scenarios generally denote falling rates while bear scenarios denote rising rates
-Duration neutral strategies apply when port mgmt has no view on which end of the curve may change more than the other (no net change in duration between long and short end)
-Steepening scenarios suggest long end will increase in yield relative to short end
-Flattening scenarios suggest long end will decrease in yield relative to short end
Strategies for Yield Curve Changes - Duration-Netural, Steepening
-Net 0 duration
-Excess return: Gain from slope increase
-Risks: Yield curve flattens
Strategies for Yield Curve Changes - Duration-Netural, Flattening
-Net 0 duration
-Excess return: Gain from slop decrease
-Risks: Yield curve steepens
Strategies for Yield Curve Changes - Bull Steepening
-Net long duration
-Excess Return: Gain from slop increase / lower yields
-Risks: Yield curve flattens or higher yields
Strategies for Yield Curve Changes - Bear Steepening
-Net short duration
-Excess return: Gain from slope increase / higher yields
-Risks: Yield curve flattens or lower yields
Strategies for Yield Curve Changes - Bull Flattening
-Net long duration
-Excess return: Gain from slope decrease / lower yields
-Risks: Yield curve steepens or higher yields
Strategies for Yield Curve Changes - Bear Flattening
-Net short duration
-Excess return: Gain from slope decrease / higher yields
-Risks: Yield curve steepens or lower yields
Credit Risk
-Identifies risk that a debt issuer will fail to make a promised interest/principal payment, and includes Default risk (probability that debt issuer will fail to make the payment) and Loss severity (amt of loss if default occurs)
Loss Given Default (LGD)
=EE * (1 - RR)
EE = expected exposure (bond value)
Expected Loss (EL)
=LGD * POD
Yield Spread
-Difference between bond YTM and similar-maturity govt bond
-Advantages: simple to calculate, widely understood
-Disadvantages: Maturity mismatch, curve slope bias, inconsistent over time
G-Spread
-Spread over interpolated govt bond
-Advantages: Transparent, maturity matching default risk free govt bond
-Disadvantages: Subject to changes in govt bond demand
I-Spread
Yield spread over swap rate of same maturity
-Advantages: Spread vs mrkt based (MRR) measure often used as hedge or for carry trade
-Disadvantages: Point estimate of term structure and not useful for option bonds
ASW (Asset Swap) Spread
-Spread over MRR of fixed bond coupon
-Advantages: Transparent, traded spread that converts current bond coupon to MRR plus a spread
-Disadvantages: Market-based spread rather than cash flow absed spread and now useful for option bonds
Z-Spread
-Constant yield spread over a govt (or swap) spot curve
-Advantages: Reflects term structure of govt or swap zero rates
-Disadvantages: More complex calculation and not useful for option bonds
CDS Basis Spread
-Difference between yield spread and CDS spread of same maturity
-Advantages: Transparent, interpolated CDS spread vs Z spread
-Disadvantages: Market based spread rather than cash flow based spread and not useful for option bonds
OAS Spread
-Yield spread using Z spread including bond option volatility
-Advantages: Allows comparison of option free risk bonds with option bonds
-Disadvantages: Complex calculation based on volatility and, with MBS, prepayment assumptions. Bonds with embedded options unlikely to earn OAS over time
Credit Strategy - Bottom Up Approach
-Portfolio management selects the best relative value securities from bonds in the same country, industry, or other category
-First segment the potential universe of credit issues into similar credit risks, then use credit relative value analysis to find most attractive in that credit segment . Then applies a weighting method.
Credit Relative Value Analysis
-Used in Bottom Up Approach
-Looks at the spread for similar securities with the idea that, all else equal, mgmt would prefer greater yield for the same risk. For non-similar securities, mgmt would determine whether excess return sufficiently compensates for the risk imparted by the nonsimilar factors
-E[Excess Spread] = Spread,0 - (EffSpread Dur x Delta(Spread)) - (POD x LGD)
Spread Curve
-Shows the spread of the fitted curve for each issuers securities of different maturity or duration. Higher spread curve indicates wider spread over benchmark and thus greater perceived risk
-Recent issues by well known issuers have narrower spreads compared to older issues by infrequent issuers. Spreads widen as issues age
Spread Duration and Weighting
-The % change in price for a given % change in yield spread
-W,MV, Sdc = W,MV,Index x [D,S,index / D,S,sector]
-Spread duration weighting structures the portfolio to provide the same % change in price from each position given a 1% change in spread
Credit Strategy - Top-Down Approach
-Mgmt first broadly defines appropriate sectors, then selects sectors expected to benefit from perceived macro trends, the over/underweights the sectors
Spread Sensitivity
-A secondary credit market measure of liquidity
-The % change in spread over a reference rate for a % change in outflows from mutual funds or credit market
CDS Price
P,CDS = (Fixed CDS Coupon - CDS Spread) x EffSpreadDur,CDS
-If spread is greater than fixed coupon, P,CDS < 0 and buyer pays seller
-Fixed coupon is determined the the Intl Swaps and Derivatives Association: IG issuers usually carry 1% fixed coupon and HY issuers carry 5%
Passively Managed Equity Portfolio - Replication Strategies
-Full replication should result in negligible tracking error but requires a large enough mandate size and liquid index constituents. This is preferred when the index has a relatively small number of constituents (less than 1k) and when the index is market cap weighted
-Stratified sampling is used when the benchmark index contains large number of securities / mandate size is small.
-Optimization is a middle ground
Active Return
R,A = nSUMi=1 [w,i - W,i)r,i]
w,i = portfolio weight of asset i
W,i = benchmark weight of asset i
R,A = SUM[(B,pk - B,bk)F,k + (a + e)
B,pk = Portfolio sensitivity to each reward factor k
B,bk = benchmark sensitivity to each reward factor k
F,k = rewarded factor return
a = return due to mgmt skill at security selection and timing
e = idiosyncratic return
Breadth of Expertise
E(R,A) = IC x RAD(BR)stdDev(R,A)(TC)
IC = expected information coefficient (correlation between forecast and actual active return)
BR = breadth (# of independent, uncorrelated mgmt decisions)
TC = transfer coefficient (the degree to which port insights translate to investment decisions)