Monitoring & Rebalancing Posted by: deriv108 (IP Logged) Date: April 11, 2011 09:29PM This is a reading about C*. IPS => Asset Allocation => Execution => Monitor Portfolio => Rebalacing. What to monitor? Client’s Circumstance, LT Capital Market Expectation and Portfolio Holdins. How to Rebalacing? B&H, Constant-mix(CM), CPPI. For Constant-mix, we need to choose proper Corridor width. 1, Common Factors leading to SAA Changes: - Client(wealth, RRTTLLU) - Capital Market factor(bull/bear mkt, r-policy, yc, i, qual spread, asset risk) 2, Why rebalancing? maintain desired exposure to systemetic risk; provide discipline. 3, Dynamic Rebalancing: B&H, CM and CPPI. - CM can use PPR(Corridor) or Calendar Rebalancing. - CPPI uses floor value(F) in $stock=m*(TA-F). 4, Corridor width will show in the exam, I think. - objective, risk aversion, liquidity or volatility goes up, it’s narrower. - correlation with other assets increases, it’s wider. - price change has no effect. 4.1, CFAI’s Corridor width factors: - transaction cost, risk tolerance, correlation with rest of portfolio(+); - asset class volatility, volatility of rest of portfolio(-). 5, CM vs CPPI: - CM’s payoff curve is concave, no downside protection, weak upside potential, and outperform in flat and oscillating mkt. - CPPI is just opposite. B&H is in the middle. 6, One more C: CM’s relative risk is constant. CM: V0/TA0=p; (V1+x)/TA1=p, x is how much to buy/sell. CM: $stock=p*TA B&H: $stock=TA-Cash CPPI: $stock=m*(TA-F) PS. A corridor width set at ±p% of the target allocation(wi) is equivalent to the corridor width of wi±(wi*p%). Book6, P98 1, CM strategy is contrarian and supplies liquidity. 2, Constant Relative Risk Tolerance: “That is, with a constant-mix strategy, the amount of money invested in risky assets increases with increasing wealth, implying increasing risk tolerance. Because the amount of money held in risky assets increases to maintain a constant ratio of risky assets to wealth, risk tolerance increases proportionately with wealth (constant relative risk tolerance or constant relative risk aversion).”
lease rate = r-ln(f/s)*1/t
lease rate = r-ln(f/s)x1/t multiplied by 1/t not exp
alimesoda! wow i remember that name. git r done!
Re: Neumonics Thread Posted by: Aimee (IP Logged) Date: June 2, 2010 12:20AM Someone gave this one earlier for forecasting traps: OCRAPS Overconfidence Confirming evidence Recallability Anchoring Prudence Status quo
Tax_Drag = 1 - Gain_AT/Gain_BT FVIF(it)=[1+r*(1-t)]^n FVIF(cgt)=(1-tcg)*(1+r)^n + tcg*B FVIF(wt)=[(1+r)*(1-tw)]^n FVIF(tda)=(1-tn)*(1+r)^n FVIF(tea)=(1+r)^n FVIF(no skipping)=[(1-t)*(1+r)^n1]*[(1-t)*(1+r)^n2] FVIF(skipping)=(1-te)*(1+r)^N, N=n1+n2 FVIF(cgt)=(1-tcg)*(1+r)^n + tcg + (1-B)*tcg FVIF(all taxes)=(1-tx)*(1+rx)^n + tx + (1-B)*tcg Return After Realized Taxes: rx=r*[1-pi*ti-pd*td-pcg*tcg] Effective Capital Gan Tax rate: tx=tcg*(1-pi-pd-pcg)/(1-pi*ti-pd*td-pcg*tcg) (1+Rae)^n=FV/PV r*(1-Tae)=Rae Tae=? T(exempt)=Ts; T(credit)=max(Tr, Ts); T(deduction)=Ts+Tr(1-Ts) — RV(tax-free gift)=FV(tax-free gift)/FV(bequest)=? RV(taxable gift)=FV(taxable gift)/FV(bequest)=? RV(taxable gift, donor pays gift taxes)=?, item=(tg*te) RV(charitable donation)=FV(charitable gift)/FV(bequest)=?? – The return and investment time horizon affect the tax drag.
Deriv, do you sleep bro?
Realized Tax Rate(ti,td,tcg): t(realized)=(pi*ti+pd*td+pcg*tcg) Realized Tax Rate(100% tax): p(realized) = (pi*1+pd*1+pcg*1) — All go to IRS!! Effective tcg = tcg*[1-p(realized)]/[1-t(realized)] < tcg where [1-t(realized)] is the proportion of unrealized gain. I’ve tried to understand the logic behind this effective tcg, but no luck. Unless someone can give an intuitive explanation, effective tcg is on my cheatsheet.
one correction: FVIF(cgt)=(1-tcg)*(1+r)^n + tcg - (1-B)*tcg FVIF(eff cgt)=(1-tx)*(1+rx)^n + tx - (1-B)*tcg
Broad Topical Overview Posted by: GetSetGo (IP Logged) Date: March 27, 2009 04:14PM Broad Topical Overview ( This will help us see where we have holes and drill down / discuss them. I didn’t include Ethics topics in the below list. There will be many areas where some of us can add additional levels of detail). 1. Behavioural Finance (Understand the definitions of behaviours and Identify the behaviour in a case) 2. PWM - Prepare or Critique an IPS, Return caliculations. Ability to identify risk tolerance. Pick appropriate portfolio 3. Institutional Investors: Prepare or Critique an IPS, Return caliculations. Be able to compare different Institutional investors goals and objectives. Pick appropriate portfolio. Affect of pension plan on WACC. 4. Capital Market expectations - Forming CME, Limitations to Econ Data, Econ Forecasting models, Forecasting exchange rates. 5. Econ - Big picture economic relationships (stocks, bonds, real estate, inflation, growth, currencies), BRICS, Stock market valuation models. 6. Asset Allocation - SAA vs TAA, Corner portfolios, Black litterman, Asset-only, ALM (institutional investors for whom this applies), International issues in Asset Allocation. 7. Bonds - Benchmarking, Active vs Passive investing, Duration, Key-Rate duration, Immunization and Cash Flow Matching, Reasons to trade bonds, Analyzing spreads, Use of leverage, credit risk management, hedging techniques, MBS, International bond portfolio management. 8. Equity - Active/Passive, Returns based vs Style based, Active management - performance attribution, Corp governance, Issues with International Equity Indices, 9. Alternates - Comparision of different classes of alternate investments (return, risk, liquidity, diversification - how it affects portfolio charecterstics when added, benchmarks, benchmark biases), Compensation structures for alternate managers, Hedge fund style charecterstics, commodity swaps vs interest rate swaps, commodity futures (pricing, arbitrage and basis risk) 10. Risk Management - Market risk, credit risk, Risk management process, Financial and non financial risks, risk-return tradeoffs and currency impacts of adding internationalassets to a portfolio, VAR measures - disadvantages, other risk mesurement tools. 11. Derivatives - Forwards, Futures, Options, Swaps (Value, Payoffs). Adjusting portfolio for TAA. 12. Monitoring & rebalancing - Market microstructure, order types, trade costs, Calculating implementation shortfall WVAP, trading tactic types, algorthimic trading, Calender and percentage rebalancing methods, Corridor width determination, Dynamic rebalancing ( CPPI, Buy-hold, constant mix). 13. Perf Evaluation - Perf attribution, risk adjusted measures, breaking down return into components. 14. GIPS - identification of errors or omissions, … This is not a comprehensive list, but a start to look at the big picture and see where we have holes in preparing. Cheers 
------------ Only copy&paste the good old post, which could be hard to locate next time.
I’m still in SS17, hopefully it’ll be done by tomorrow. You guys may finish the readings, so those formual are already in your minds. Now Let’s List Formulas by Study Session. To Keep it Simple, At Most One Formula for Each Reading…The formulas are the ones that are most likely tested or need to be memorized.
------------------------------ Benchmarks Posted by: Ako (IP Logged) Date: May 27, 2010 05:02PM Money weight return>Time weighted prior to strong performance Money weight return< time weighted prior to weak performance. Time weighted return does not take into account cashflow, which is generally out of mgmt control. GIPS prefers Time weighted. Portfolio return=market return+style return+active return P=market return+(benchmark return-market return)+(portfolio return-benchmark return) Active return is composed of a set of under weight and over weight position in benchmark Properties of a Valid Benchmark S-specified in advance (everyone knows in advance what the benchmark is. Benchmark based on Relative manager performance is not considered to be Specified in advance) A-Appropriate-should be consistent with managers investment style and area of expertise. Using a broad market index for a value investor is not appropriate. M-measurable-return calcs are easy to calculate. U-Unambigious-weight and identity of securities are known. O-Owned meaning that there is accountability R-Reflective on current investment opinion, that is the manager has knowledge of the securities and factor exposures of the benchmark I-Investable-you can passively invest in securites. Not possible with an absolute or relative benchmark. Should have low turnover. Test of a Benchmark Quality Systematic Biases-Beta of manager and benchmark close to 1 plus low correlation between (B-M) and (P-B) and strong correlation between style and (B-M) Tracking error-volatility of (P-B) should be less than (P-M) Risk characteristics-manager should have exposure at times great and less than benchmark but not consistently in one direction. Turnover-benchmark should have low turnover so that it is INVESTABLE(see above) Positive active positive-manager should hold a net positive active position (weight in portfolio-weight in benchmark) Performance Attribution EQUITY Macro Attribution Beginning Value Plus A a cash contributions-Cash inflows R Risk free-BV+ Net cashflows invested at RF rate A Asset Class return-incremental return based on passive investment in asset class using asset class weights B Benchmark-increm, return based on passive investment in benchmark using benchmark weights I Investment manager-increm. return based on active investment managers return using benchmark weights A Active Allocation-reconciling factor Micro Attribution Attributable to Portfolio manager skill (security weight in portfolio- security weight in benchmark)*(return in benchmark-TOTAL Benchmark) Attributable to Security analyst skill security weight in benchmark*(portfolio return – benchmark return) Asset/selection interaction (security weight in portfolio- security weight in benchmark)*(return in portfolio-return in benchmark) FIXED INCOME Total return = External interest rate effects + mgmt effects External Effects=expected and unexpected interest rate effects Expected is the implied forward rate Unexpected is difference between actual and implied forward rate from above Mgmt effects Interest rate effect Indicates how well mgmt predicted interest rate changes due to Duration-parallel shifts Convexity-parallel shifts Yield Curve changes-twist Sector Quality Measures ability to select right issuing sectors and quality group Security Selection Measures how the return of a specific security within a specific sector relates to avg performance of sector Trading activity Captures the effects of sale and purchase When examining return look at mgmt effect separately and determine where the majority of the return was coming from. Compare that with manager style to see if both are consistent. Risk Based Performance Measures-NON NORMAL RETURNS INVALIDATE ALL THESE MEASURES Beta Based Measures ExPost Alpha=Return on account – RF- estimated Beta during EVALUATION PERIOD *(Return on market- RF) Treynor Method= (Average Return over evaluation period – Average RF return)/estimated Beta during EVALUATION PERIOD Volatility Based Measure Ex Post Sharpe= (Average Return over evaluation period – Average RF return)/ estimated Standard Deviation over evaluation period M2-measures what the account would have returned if it had taken the same total risk as the market Information ratio=(Average portfolio Return over evaluation period – Average Benchmark return over same period)/ estimated tracking risk over evaluation period It is possible for Volatility based measure to indicate poor performance relative to Beta based measure. This may be the result of the manager taking large nonsystematic/Unique/idiosyncratic risk relative to systematic. Critics have attacked these risk based methods based on their reliance on single variable CAPM, Market proxy used, benchmarks used (for example it is difficult to passively invest a broad market index or custom based index and the costs associated with creating and managing them are ignore) and stability of the parameters.
It’s hard to find this…AF is so active! Here is my list of formulas for SS17. I post this for myself, so please don’t blame my notation. If it doesn’t make sense to you, please simply ignore it…they may look familiar to you if you use both Curriculum and Schweser notes. R(CF at the beginning):=V1/(V0+CF)-1 R(CF at the end):=(V1-CF)/V0-1 Jensen’s Alpha = Ri-E(Ri), E(Ri)=Rf+bi*(Rm-Rf) Treynor Measure = (Ri-Rf)/bi Sharpe Ratio = (Ri-Rf)/SDi M2 measure = Rf + (Sharpe Ratio for i)*SDm P=(P-B)+(B-M)+M =A+S+M =(active return) + (style index [benchmark] return) + (market return) By the way, ASM is a PC assembly language. Micro performance Attribution (psi): Rv = P-B = sum(wpj*Pj - wbj*Bj) = … = sum[(wpj-wbj)*(Bj-B) + (wpj-wbj)*(Pj-Bj) + wbj*(Pj-Bj)] = (pure sector allocation) + (alloc/selection interaction) + (within-sector selection) = psi Global Return Decomposition & Attribution: Rjd=pj+dj+cj, where cj=sj*(1+pj+dj) Rpd=sum(wj*pj+wj*dj+wj*cj) =sum[wj*Ij + wj*(pj-Ij) + wj*dj + wj*cj] ---- this is Decomposition. Assume Ijd = Ij + Cj for global index[benchmark] return in base currency(from curriculum!). Rpd = sum[wjb*Ijd + (wj-wjb)*Ij + wj*(pj-Ij) + wj*dj + (wj*cj-wjb*Cj)] That is, Global Performance Attribution. In plain language: Global Return in Domestic[Base] Currency = (benchmark return in base currency) + (market allocation) + (security selection: notice it’s wj – portfolio weight, NOT wjb – benchmark weight) + (yield) + (currency allocation). For two-period return to active management: R(A,2)=P-B =(1+Rp1)*(1+Rp2)-(1+Rb1)*(1+Rb2) =Ra1*(1+Rb2) + Ra2*(1+Rp1) Where Rp1=Ra1+Rb1, Rp2=Ra2+Rb2
a negative times a negative equals a positive
Higher standard deviation + Lower beta => Lower Diversification. — This is not a formula!!
For two-period return to active management: R(A,2)=P-B =(1+Rp1)*(1+Rp2)-(1+Rb1)*(1+Rb2) =Ra1*(1+Rb2) + Ra2*(1+Rp1) Where Rp1=Ra1+Rb1, Rp2=Ra2+Rb2 I just realised i have zero recollection of this one…is it in book 6
It’s not from CFAI Book…You can prove it by youself. The notation is from Schweser.
SS17, Reading 46: Evaluating Portfolio Performance. 1, Chain-linking[TWR], Linked IRR[MWR=f(size,timing)]; difference=f(CF, perf fluctuation). 2, Validity of Benchmark: SAMURAI - Specified in advance…and known to both the manager and the fund sponsor. - Appropriate…consistent with the manager’s investment style or area of expertise. - Measurable…calculate the benchmark’s return on a timely basis, for various time periods - Unambiguous…the names of securities and their weights are clearly noted. - Reflective of current investment opinions…have opinions and investment knowledge. - Accountable[Owned]…accountable for the constituents and performance. - Investable…available as a passive option. 3, Seven Types of Benchmarks: …Factor-model-based… - Market Model: zero-factor value, normal beta, normal portfolio. 4, Benchmark Quality: Beta, tracking error, risk, coverage, turnover, +ve active position. 5, Macro attribution inputs: - policy allocations, - benchmark portfolio return, - fund return, valuation, and external CF. 6, Macro attribution: ARABIA - net contribution, RFR - Asset Categories, Benchmark, Investment Managers, - Allocation Effects (a reconcilliation factor). 7, Micro Attribution(Rv=P-B): sector weighting/stock selection; fundamental factor model. 8, Fixed-income attribution. 9, Risk Adjusted Performance Appraisal Measures. 10, QC charts, Manager Continuation Policy[Type I Error(horn): keep manager with Rv<=0]
Short List of SD/Beta/*Risk: 1, Asset Beta: Ba=wd*Bd+we*Be 2, Total Asset Beta: B(a,T)=w(a,o)*B(a,o)+w(a,p)*B(a,p) 3, Market Volatility: [SD(t)]^2=theta*[SD(t-1)]^2 + (1-theta)*[e(t)]^2 4, Factor Model based market variance: SDi^2=f(beta(i,j), SDj, Cov) 5, Covariance of two markets: Cov(i,j)=f(no worry) 6, Beta(i)=Cov(i,M)/SDm^2 7, Variance of Foreign Asset Return in Dollar Terms: SD$^2=SDlc^2+SDs^2+2*SDlc*SDs*rho(lc,s) 8, Contribution of currency risk: SD$-SDlc 9, SDp^2=(w1*SD1)^2+(w2*SD2)^2+2*w1*w2*SD1*SD2*rho(1,2) 10, (total active risk)^2=(true active risk)^2+(misfit active risk)^2 11, Downside Deviation; Maximum Drawdown; 12, Annualized SD: SD(annual)=SD(daily)*sqrt(250) 13, Tracking Error, tracking risk, active risk. 14, Risk Budgeting[Allocation]: sector risk, selection risk.