Have tried to be accurate to the best of my knowledge. Your feedback/suggestions would be appreciated. All the best
A.** General Tips/Silly mistakes/Common errors**
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Although the exam is for 4 hrs spanning 100 questions , time will be a constraint as numerical questions are calculation intensive
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Be very familiar with the use of the calculator esp when to comes to calculating e,LN, combination , power , PV etc
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Set the decimal to 9
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Focus on Products and VaR as they weigh 60%
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Skip question immediately if u are stuck [We wouldn’t like our paper to finish at Q no. 84 when there could be possible sitters in the last bunch of 16]
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Many questions have multiple lines. Read the last line to directly get to the question and then read the para [understanding would be better]
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See the answer options before solving [in many of them if you can guess the direction viz sell/buy – long/short-gain/loss- bond price movement –up/down -2 options can be eliminated]
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Expect 20% of the questions to be really tough. The key is to identify them and leave them in the first .
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Expect that u may not remember all the formulae [everyone goes thru it is natural]
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Keep a tab of time . You should have solved around 25-30 questions/hr .
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Shade the correct option. [sometimes in a stressed situation we subconsciously shade the wrong one]
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Inputting of data in the correct form is critical [continuos compounding if the risk free rate is 5% , use .05 not 5 . In duration for 5 basis points use .0005 etc]
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Read the question carefully- they may have double negative or may ask which of these is FALSE/INCORRECT ?
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Pay special attention to calculation of variance/SD/volatility. Often it requires squaring or square rooting.
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Do not expect to master all concepts.
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Revisit/Reconfirm the conceptual subjective questions. They can be really tricky.
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Although people feel that 70% is required for passing , my belief is that 60-65% should be good enough [pass rate is 50% and expecting 50% of them to score more than 70% does’nt appear to be probable]
B.** Handy Material**
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6 pager schweser’s quick sheet – at the end of practice exam book of schweser
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Formulae at the end of Schwser notes
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Final Review Guidebook [akin to Secret Sauce of CFA]
C.** High level of testability**
[For the sake of brevity , am mentoning only the formulae/concept name without elaborating and not writing the actual one unless an issue needs highlight-Source- BT]
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VaR – [note that VaR is different if they are talking of confidence level or significance level]
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Portfolio volatility [remember to square root]
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CAPM- the mother of all equations
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Mean, Variance (SD)
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Sample mean [Std error, critical t-value]
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Distribution [Bernouli, Binomial, Poisson, Normal]
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Monte Carlo Simulation
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Volatility –EWMA, GAARCH (1,1)
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Linear Hedges [almost certain to be tested]
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Interest rates
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Cost of Carry
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Options [Binomial, BSM]
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Bond Price –Fwd rates
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Expected /Unexpected Loss
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D.** Key formulae/concepts – High testability**
**i)**Foundations for FRM
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VaR
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Basis Risk
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Expected Return of a portfolio
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Variance of a two asset portfolio
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Correlation [-ve is good fo diversification]
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Assumptions of CAPM [total 10]
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Multi factor model
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Sharpe- can be applied to all portfolios/Treynor –when diversified portfolio/Jensen-when comparing portfolio with same beta/Information Ratio/Sortino –when MAR is not given assume risk free rate as the MAR
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ERM-what it means ?
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Debt overhang
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Fin Disasters- LTCM/Metallgesellchaft
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GARP code of conduct [ members cannot outsource or delegate to others
ii) Quantitative Analysis
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Expected value
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Var(X)= E(X-u) squared
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Var (X+Y)= Var(X) + Var(Y) if x, y are independent random variables otherwise add a term ie 2 x Cov(X,Y)
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Leptokurtic- More Peaked-Fat Tails –Kurtosis > 3
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Z= Observation- Pop mean/SD - Very imp formula
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T-distribution-when constructing confidence interval based on small samples [< 30] from population of unknown variance
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Ch—square test- For hypothesis tests concerning the variance of a normally distributed population
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Std error= SD of the sample avg/sq root of n . n= no of observations
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Central Limit Theorm
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Confidence Intervaal – Point estimate +,- (reliabilityfactor x std error )
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Commonly used reliability factors– 90%-1.65 , 95%- 1.96 , 99%- 2.58
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Type –I-rejecting the null ypothesis when it is true-significance level- alpha =P(Type 1 error) -, Type –II error=Power of test = 1- p
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Linear Regression-Equation is linear in parameters. May or may not be in linear in variables
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R squared/Adjusted R squared
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Effects of heteroskedasticity – coefficient estimates are not affected
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Assumptions of Multiple Regresion -6 – error term is normally distributed, EV of error terms=0, variance for error terms is constant , error terms uncorrelated with each other
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Multicollinearity-2 or more of the independent variables are correlated
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F-test= how well the set of independent variables as a group explains the variation in dependent variables = ESS/k/ SSR/n-k-1
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Learn to read the ANOVA table
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Binomial- EV=np , Variance=npq
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Bernouli –EV=p , Variance =pq
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Poisson- EV= lambda =Variance
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Poisson= lambda ^x. e^-lambda/factorial of x
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MCS-GBM-equation
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EWMA/GAARCH (1,1)- Almost certain to be tested [see the gamma and long term variance in GAARCH]
iii) Financial Markets and Products
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Initial margin, maintenance margin
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Basis risk= spot price of asset being hedged – future priceof contract used in hedge
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Min variance hedge ration= SD of spot x correlation/SD of future
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No of contract= Beta of portfoilio x Portfolio value/Value of futures contract
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Value of future contract = future price x contract multiplier
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Change a portfoloio beta= [Target beta – existing beta] x Portfolio Value/Value of underlying
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Continuos compounding rate
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Theoritical price of bond- discount cash flows
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R fwd= R2T2 – R1T1/T2-T1
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FRA- remember to discount the net cash flow
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Estimated change = - Duration effect + Convexity effect [Note the opposite sign]
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Term theories- Expectations/Mkt segmentation/Liquidity preference
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Fwd price = Spot x e ^rT . In case of dividends replace rT by r – q)T
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Interest Rate Parity= F=S x e ^ ( rd- rf) T
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Backwardation/Contago - diff from normal backwardation/normal contago- In the later the comparison is between expected spot and fwd price
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Dirty price= Clean price + Accrued Income
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CTD Bond= which minimizes Quoted Bond Price - (Settlement Price x Conversion Factor )
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Actual fwd rate = Fwd rate implied by futures – 0.5 x T1 x T2 X alpha ^2
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Duration based hedge = N= - P x Dp/F x Df
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Comparative advantage in interest rate swap
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Valuing a currency swap
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6 factors impact the value of an option – current stock price , strike price, time to expiration , short term rosk free interest rate , present value of dividend , expected volatility
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Effect of each factor on value of call- increase/decrease
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PUT CALL PARITY c + Xe^ -rT =S +p
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Covered call – stock + short call- income strategy , Protective put – long stock + long put – insurance strategy
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Pay of various strategy- Bull /Bear/ButterflyCalender/Diagonal/Box
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Combination strategies- Straddle –bet on volatility/Strangle/Strap-Bet on volatility but bullish /Strip- Bet on volatility but bearish/Collar
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Variance of the basis = SD spot^2 + SD future^2 - 2 x SD spot x SD future x correlation
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Hedge effectiveness = 1 – Variance of the basis/SD spot ^2
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Lease rate in commodities.
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Crack Spread
iv) Valuation and Risk Models
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Discount factor
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Computing fwd rate
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If YTM > Coupon rate – Discount Bond
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DV01
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Modified duration / Convexity
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Duration of portfolio= weighted avg of duration [imp= weight of market value not pa rvalue]
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Negative convexity- in callable bonds when yields fall
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Binomial tree- [almost ceratin to appear]
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U=size of up move = e^SD X square root of T [note T is square root]
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D= 1/U
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Probability of up move = e^rt-D/U – D
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BSM assumptions-6- volatility is constant and known , underlying asset has no cash flow, options are European etc
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C= S x N(d1) - K x e^ -rt x N(d2) [ in dividend paying stock substitute S e^ - qt
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Continuosly compounded return = LN[Price today/Price last period]
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Greeks- Delta= change in call option value/change in stock price – highest at the money
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Vega ( volatility ), Theta ( time ), Rho- Risk free rate , Gamma- Rate of change of delta
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Stess testing
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Rating agency- Investment grade- S &P- BBB- Moodys- Baa
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Expected Loss = Exposure x LGD x PD
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Unexpected Loss= AE x [PD x SD of LGD^2 + LGD^2 xSD of PD^2]^0.5
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VaR (X%) J days = VAR (X%) 1 day/ J^0.5
E.** One Liners- Quickies**
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Stock returns are normally distributed, prices are lognormally
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A standard normal distribution is defined by 0 parameters
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No of iterations required to increase the accuracy by x is x^2
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A larges loss is not necessarily a risk mgmt failure
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Portfolio Possibility Curve [GMV is not the most efficient portfolio ie one having highest Shape ratio]
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Spot rates= zero rates
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American options can be exercised early [never optimal to exercise a call in a non dividend paying stock]
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Modified duration is less than Macaulay Duration
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Significance level= probability of making a Type 1 error
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Power of test= probability of making a Type II error
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Correlation coefficient = [R^2]^0.5
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Alpha + beta = persistence factor in GAARCH (1,1) model
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Settlement price= Quoted Futures Price
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Calender spread- profit if price stays in narrow range
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Expected shortfall= conditional VaR
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Futures arezero growth instruments
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Strenghthening of basis if unexpected-unfavourable for long hedge
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Risk Mgnt cannot create value in perfect financial markets
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To Hedge take opposite position