IBBC CAPITAL ACADEMY / 2027
Formula and reasoning reference
Independent IBBC Capital draft content for self-study. Not affiliated with or endorsed by CFA Institute. New lessons await subject-matter review. No CFA designation or official PSM credit is awarded.
Use each formula with its assumptions and worked example; these are references for available drafts, not a complete formula book for three levels.
What a return actually measures
HPR = (P₁ − P₀ + D)/P₀; 1 + r_nominal = (1 + r_real)(1 + π)
Read assumptions and practice →Returns across time, costs and leverage
R_geo = [∏(1 + Rₜ)]^(1/n) − 1; r_log = ln(1 + R); R_real = (1 + R)/(1 + π) − 1
Read assumptions and practice →Who controls the cash flow?
TWR = ∏(1 + R_subperiod) − 1; Σ CFₜ/(1 + IRR)^t = 0; index = Σ prices/divisor
Read assumptions and practice →One valuation date and no-arbitrage cash flows
PV = Σ CFₜ/(1+sₜ)^t; r = D₁/P + g; f₁,₁ = (1+s₂)²/(1+s₁) − 1; F_X = S(1+r_d)^T/(1+r_f)^T
Read assumptions and practice →Read the shape of a return sample
s² = Σ(Rᵢ−R̄)²/(n−1); ρ = Cov(A,B)/(σAσB); downside deviation = √[Σ min(0,Rᵢ−τ)²/n]
Read assumptions and practice →Probabilities, conditional risk and updating evidence
E[R] = ΣpR; Var(R) = E[Var(R|S)] + Var(E[R|S]); P(H|E) = P(E|H)P(H)/P(E)
Read assumptions and practice →Estimate carefully and test a stated claim
SE(x̄) = s/√n; t = (x̄−μ₀)/SE; CI = x̄ ± t*SE; power = 1−β
Read assumptions and practice →From two assets to an efficient allocation
σp² = w²σA²+(1−w)²σB²+2w(1−w)Cov(A,B); wA,min = (σB²−Cov)/(σA²+σB²−2Cov); y* = (μP−rf)/(AσP²)
Read assumptions and practice →Simulate without inventing certainty
P₁ = P₀ exp[(μ−σ²/2)Δt + σ√Δt Z]; simulation error ∝ 1/√N; nearest-rank quantile = sorted[ceil(pN)]
Read assumptions and practice →A regression is an explanation with assumptions
b = Σ(x−x̄)(y−ȳ)/Σ(x−x̄)²; a = ȳ−bx̄; R² = 1−SSE/SST; β = Cov(Ri,Rm)/Var(Rm)
Read assumptions and practice →From a dataset to a defensible model
precision = TP/(TP+FP); recall = TP/(TP+FN); evaluation must respect information availability
Read assumptions and practice →Costs, competition and a firm’s production decision
Profit = (P−AVC)Q−FC; break-even Q = FC/(P−unit VC); HHI = Σ market share²
Read assumptions and practice →Business activity and the credit cycle
Growth = current/prior − 1; ratio growth = (1+numerator growth)/(1+denominator growth) − 1
Read assumptions and practice →Fiscal choices, deficits and debt dynamics
Spending multiplier = 1/(1−c) under simplified assumptions; bₜ = [(1+i)/(1+g)]bₜ₋₁ − primary surplus/GDPₜ
Read assumptions and practice →Monetary transmission and credible policy
Ex-ante real rate = (1+nominal rate)/(1+expected inflation)−1; approximate real rate ≈ nominal−expected inflation
Read assumptions and practice →Turn geopolitical narratives into testable scenarios
Scenario-weighted cash flow = Σ probability × cash flow; scenario probabilities must be justified assumptions
Read assumptions and practice →Trade, opportunity cost and the distribution of gains
Opportunity cost of X = forgone Y / additional X; tariff-inclusive price = world price × (1+tariff) under full pass-through
Read assumptions and practice →Currency quotes, real exchange rates and capital flows
Foreign appreciation = S₁/S₀−1; domestic value change = S₀/S₁−1; real FX index q = S×Pforeign/Pdomestic
Read assumptions and practice →Cross-rates, forward points and covered parity
Cross-rate: cancel currency units; reciprocal bid=1/ask; F=S(1+rd)^T/(1+rf)^T; forward=spot+points×point scale
Read assumptions and practice →Ownership, legal form and the issuer
Economic ownership = shares held/total shares under equal cash rights; voting share = votes controlled/total votes
Read assumptions and practice →Claims, stakeholders and financially relevant risks
Simple debt payoff = min(asset proceeds, debt due); equity payoff = max(asset proceeds−prior claims, 0)
Read assumptions and practice →Governance that changes incentives and oversight
Governance review: conflict → affected claim → mechanism → evidence of operation → remaining risk
Read assumptions and practice →Working capital is a timing problem
CCC=DIO+DSO−DPO; current ratio=CA/CL; quick=(cash+marketable securities+receivables)/CL
Read assumptions and practice →Allocate capital using incremental cash flows
NPV=ΣCFₜ/(1+r)^t; IRR solves NPV=0; ROIC=NOPAT/average invested capital
Read assumptions and practice →Capital structure, required returns and financing trade-offs
WACC=wE×rE+wD×rD×(1−Tc); no-tax MM: rE=rU+(rU−rD)D/E; simple perpetual tax shield=Tc×D
Read assumptions and practice →A business model connects customers to cash
Unit contribution=price−variable cost; break-even units=fixed cost/contribution; toy undiscounted lifetime contribution=monthly contribution/churn
Read assumptions and practice →From filings to a defensible financial conclusion
Assets = liabilities + equity; ending equity = beginning equity + profit + OCI + owner contributions − distributions
Read assumptions and practice →Earnings: recognition, normalization and dilution
Basic EPS=(profit−preference dividends)/weighted shares; if-converted EPS=(ordinary profit+after-tax interest)/(weighted shares+conversion shares); margin=profit/revenue
Read assumptions and practice →Reading assets, obligations and equity
Current ratio=current assets/current liabilities; quick ratio=(cash+marketable securities+receivables)/current liabilities; common size=item/total assets
Read assumptions and practice →Reconstructing operating cash flow
Collections=Revenue−ΔAR; purchases=COGS+Δinventory; supplier payments=purchases−ΔAP; simple US GAAP CFO=NI+D&A−ΔAR−Δinventory+ΔAP
Read assumptions and practice →Cash generation, reinvestment and coverage
For stated US GAAP bridge: FCFF=CFO+interest(1−T)−capex; FCFE=CFO−capex+net borrowing; CFO margin=CFO/revenue
Read assumptions and practice →Inventory costs, write-downs and hidden margin effects
Goods available=beginning inventory+purchases; COGS=available cost−ending inventory; FIFO inventory=LIFO inventory+reserve
Read assumptions and practice →Long-lived assets: investment versus reported expense
Ending PPE=beginning PPE+additions−depreciation−impairment−carrying value disposed+other movements; disposal gain=proceeds−carrying value
Read assumptions and practice →Leases, retirement promises and equity compensation
Lease liability end=beginning+interest+new leases−payments±remeasurements; simplified pension deficit=benefit obligation−plan assets
Read assumptions and practice →Current and deferred tax: timing is not permanence
Tax expense=current tax+deferred tax expense; ETR=tax expense/pretax profit; simple DTL=taxable temporary difference×applicable rate
Read assumptions and practice →Reporting quality: evidence before accusation
Illustrative accrual screen=(net income−CFO)/average assets; growth=(ending−beginning)/beginning
Read assumptions and practice →Ratios as a connected financial diagnosis
ROE=NI/average equity=NI/sales×sales/average assets×average assets/average equity; CCC=DSO+DIO−DPO
Read assumptions and practice →Build and challenge a three-statement forecast
Revenue=units×price; growth=(1+volume growth)(1+price growth)−1; simple CFO=NI+D&A−Δoperating WC
Read assumptions and practice →Share classes, cash rights and residual risk
HPR=(P1−P0+D)/P0
Read assumptions and practice →Voting, jurisdictions and cross-border ownership
Voting proportion=controlled votes/total votes
Read assumptions and practice →Raising equity and executing trades
Quoted spread=ask−bid; proportional spread=(ask−bid)/midpoint
Read assumptions and practice →Distributions, growth and equity return attribution
1+Rhome=(1+Rlocal)(1+RFX)
Read assumptions and practice →Equity value, price and model selection
Equity=operating enterprise value−debt−other prior claims+excess cash
Read assumptions and practice →Discounted distributions and sustainable growth
V0=D1/(r−g), r>g; sustainable g=retention×ROE
Read assumptions and practice →Comparable multiples without denominator traps
Price indication=comparable P/E×consistent EPS
Read assumptions and practice →Forecast financial drivers before assigning value
Revenue=units×price; growth=(1+volume growth)(1+price growth)−1
Read assumptions and practice →Industry economics and competitive durability
HHI=Σ market-share percentages squared; specify scale
Read assumptions and practice →Company analysis from history to scenarios
ROE=net margin×asset turnover×equity multiplier
Read assumptions and practice →Research reports that can be challenged
Scenario return=(target price−current price+distribution)/current price
Read assumptions and practice →Required returns and factor exposures
E(Ri)=Rf+βi[E(Rm)−Rf]; Ri=α+βRm+ε
Read assumptions and practice →Bond contracts and protective promises
Coupon payment=face×annual coupon rate/payments per year
Read assumptions and practice →Bond cash-flow shapes and embedded choices
Floating coupon=notional×(reference+quoted spread)×accrual fraction
Read assumptions and practice →Bond markets, indexes and trade liquidity
Market-value index weight=security market value/eligible total
Read assumptions and practice →Corporate funding and collateralized repos
Repo cash=collateral value×(1−haircut)
Read assumptions and practice →Government borrowers and market issuance
Issue proceeds=face amount×price per unit of face
Read assumptions and practice →Discount bonds and reconcile settlement prices
Full price=Σ CFt/(1+y/m)^(mt); full=clean+accrued
Read assumptions and practice →Compare yields and spreads on the same basis
EAR=(1+nominal yield/m)^m−1; current yield=annual coupon/price
Read assumptions and practice →Floating-note margins and money-market quotes
Investment yield=(F−P)/P×year-days/days; discount yield=(F−P)/F×year-days/days
Read assumptions and practice →Spot, par and forward curves
(1+z2)²=(1+z1)(1+f1,1); par coupon=(1−DFn)/ΣDFt
Read assumptions and practice →Bond horizons, reinvestment and Macaulay duration
DMac=Σ[t×PV(CFt)]/price
Read assumptions and practice →Modified duration, money sensitivity and basis points
ΔP/P≈−DmodΔy; PVBP≈Dmod×market value×10⁻⁴
Read assumptions and practice →Convexity and aggregate bond exposures
ΔP/P≈−DΔy+½C(Δy)²; Dportfolio=ΣwiDi
Read assumptions and practice →Effective, key-rate and empirical duration
Deff=(P−−P+)/(2P0Δcurve)
Read assumptions and practice →Default losses and changing credit spreads
EL=PD×LGD×EAD; LGD=1−recovery rate
Read assumptions and practice →Sovereign capacity, willingness and local constraints
Debt/GDP=consistent public debt/nominal GDP
Read assumptions and practice →Corporate credit: cash coverage and claim priority
Interest coverage=EBIT/interest; leverage=debt/normalized EBITDA
Read assumptions and practice →Securitization parties and risk transfer
Senior loss=max(pool loss−subordinate protection,0), within tranche notional
Read assumptions and practice →ABS structures, enhancements and collateral behavior
Overcollateralization=asset balance−note balance; specify ratio denominator
Read assumptions and practice →Mortgage cash flows and prepayment asymmetry
Ending mortgage balance=beginning−scheduled principal−prepayments−write-offs
Read assumptions and practice →Derivative exposures and trading arrangements
Notional=contract multiplier×underlying price
Read assumptions and practice →Commitments, contingent rights and payoff signs
Long call payoff=max(ST−K,0); long put payoff=max(K−ST,0)
Read assumptions and practice →Using derivatives without confusing a hedge with safety
Hedged currency proceeds=matched foreign amount×contracted forward rate
Read assumptions and practice →Replication and financing carry
F0(T)=S0(1+r)^T for a no-income asset under stated assumptions
Read assumptions and practice →Forward prices at inception and values later
Long forward value=DF(t,T)×[Ft(T)−K]
Read assumptions and practice →Futures prices and daily cash settlement
Daily futures P&L=contracts×multiplier×price change
Read assumptions and practice →Swaps as payment-stream exchanges
Pay-fixed net coupon=N×(floating−fixed)×accrual; value=PV(received)−PV(paid)
Read assumptions and practice →Option exercise value, time and sensitivities
Call intrinsic=max(S−K,0); put intrinsic=max(K−S,0)
Read assumptions and practice →Replicate European options with put–call parity
c−p=S−PV(dividends)−PV(K)=DF×(F−K)
Read assumptions and practice →One-step binomial replication
q=[(1+r)−d]/(u−d); V0=[qVu+(1−q)Vd]/(1+r)
Read assumptions and practice →Alternative ownership, access and incentives
Uncalled commitment=total commitment−capital called, adjusted for agreement terms
Read assumptions and practice →Alternative returns after timing and fees
Net ending NAV=gross assets−management fee−incentive fee−other costs
Read assumptions and practice →Private equity and private debt over a fund life
Equity multiple=exit equity plus distributions/paid-in equity, with consistent flow definitions
Read assumptions and practice →Property income and infrastructure contracts
Direct-capitalization value=stabilized NOI/cap rate
Read assumptions and practice →Land, productive resources and commodity carry
Productive-land cash surplus=output×sale price−specified operating cash costs
Read assumptions and practice →Hedge-fund strategies and concealed exposures
Gross=(long+absolute short)/NAV; net=(long−absolute short)/NAV
Read assumptions and practice →Digital assets, custody and economic claims
Recovery gain required=1/(1−loss fraction)−1
Read assumptions and practice →Diversification, utility and efficient risky portfolios
σp²=w1²σ1²+w2²σ2²+2w1w2ρ12σ1σ2; U≈E(R)−½Aσ²
Read assumptions and practice →Capital allocation, beta and performance ratios
Sharpe=(Rp−Rf)/σp; Treynor=(Rp−Rf)/βp; α=Rp−[Rf+βp(Rm−Rf)]
Read assumptions and practice →Investment management as a continuing process
Funding ratio=plan assets/present value of benefit obligations
Read assumptions and practice →Write an IPS that governs real allocation choices
Liquidity-reserve ratio=known near-term net cash need/investable assets
Read assumptions and practice →Recognize bias and design a decision process
Prospective return uses current opportunity cost; historical loss uses original cost
Read assumptions and practice →Risk governance, budgets and response choices
Monetary VaR=portfolio value×stated relative VaR; not a maximum-loss bound
Read assumptions and practice →Ethical judgment when incentives create pressure
Decision record: facts → affected parties → duties → feasible actions → review
Read assumptions and practice →Navigate the ethical code and conduct framework
Analyze facts → duties → assessment → corrective procedure; never infer a performance guarantee from credentials
Read assumptions and practice →Professionalism: law, independence and competence
Professional response: identify stricter duty; protect independence; verify claims; maintain role competence
Read assumptions and practice →Material information and orderly capital markets
Decision dimensions: materiality, public dissemination, possession, trading/inducement and controls
Read assumptions and practice →Client duties across suitability and allocation
Proportional allocation=available units×eligible requested units/total eligible requests
Read assumptions and practice →Employer loyalty, outside pay and supervision
Outside-pay response: identify conflict → written consent → fair processes → supervisory monitoring
Read assumptions and practice →Reasonable research, clear costs and retained evidence
Research chain: sources → methods → reasonable basis → clear communication → retained record
Read assumptions and practice →Conflicts, personal dealing and referral economics
Conflict response: avoid or disclose effectively; prioritize client/employer trades; disclose referral arrangements
Read assumptions and practice →Program integrity and accurate credential references
Independent education must use original material and accurate, permitted credential descriptions
Read assumptions and practice →Integrated ethics cases and preventive procedures
Case analysis=evidence + duty + conduct assessment + tailored corrective and preventive action
Read assumptions and practice →Conditional exposures in a return model
yhat=b0+b1*M+b2*S
Read assumptions and practice →Fit is not forecast reliability
R²=1−SSE/SST; adjusted R²=1−(SSE/(n−k−1))/(SST/(n−1))
Read assumptions and practice →Diagnose the error before repairing inference
t=(b−b_null)/SE(b)
Read assumptions and practice →Indicators, odds and influential observations
p=1/(1+exp(−z)); odds=p/(1−p)
Read assumptions and practice →Forecast a persistent series honestly
xhat(t+2)=a+b*(a+b*x_t); long-run mean=a/(1−b)
Read assumptions and practice →Learn signals without leaking the answer
precision=TP/(TP+FP); recall=TP/(TP+FN)
Read assumptions and practice →Turn alternative data into an auditable project
usable rows=raw−duplicates−additional unusable rows
Read assumptions and practice →Read an FX quote before hedging
F=S*(1+r_dom)/(1+r_for)
Read assumptions and practice →Separate growth accounting from an equity forecast
gY≈gTFP+alpha*gK+(1−alpha)*gL
Read assumptions and practice →Follow ownership through the financial statements
Equity-method close=opening+share of profit−share of dividends; full goodwill=consideration+FV(NCI)−FV(net assets)
Read assumptions and practice →Separate pension economics and share dilution
Net interest=(opening obligation−opening assets)*discount rate
Read assumptions and practice →Translate currency without inventing operating growth
Simplified CTA=net assets at closing rate−historical equity translation
Read assumptions and practice →Analyze a bank through capital and asset quality
CET1 ratio=CET1 capital/RWA; NPL ratio=NPL/gross loans
Read assumptions and practice →Challenge earnings with cash and disclosure evidence
Simplified accrual ratio=(net income−CFO)/average assets
Read assumptions and practice →Connect margins, turnover and financing
ROE=net profit margin*asset turnover*equity multiplier
Read assumptions and practice →A repurchase changes arithmetic before it creates value
EPS after cash repurchase=unchanged earnings/(initial shares−repurchased shares)
Read assumptions and practice →Make a governance concern financially explicit
PV cost=sum(cost_t/(1+r)^t)
Read assumptions and practice →Estimate a project-specific cost of capital
betaE=betaA*[1+(1−T)D/E]; WACC=wE*kE+wD*kD*(1−T)
Read assumptions and practice →Price the synergy before paying for it
Acquirer NPV=synergy−(offer−standalone target value)
Read assumptions and practice →Choose a valuation model for the claim
Equity value=FCFE1/(ke−g), ke>g
Read assumptions and practice →Link dividends, retention and mature growth
V0=D0*(1+g)/(ke−g); sustainable g=b*ROE
Read assumptions and practice →Build free cash flow from operating economics
FCFF=EBIT*(1−T)+D&A−capex−deltaNWC; FCFE=FCFF−interest*(1−T)+net borrowing
Read assumptions and practice →Match a multiple to its denominator
EV=equity value+debt−cash; EV/EBITDA=EV/EBITDA
Read assumptions and practice →Charge equity capital before calling earnings residual
RI_t=NI_t−ke*B_(t−1); V0=B0+sum(RI_t/(1+ke)^t)
Read assumptions and practice →Value the private business before ownership adjustments
Equity value=normalized EBITDA*EV multiple−net debt
Read assumptions and practice →Extract a forward rate from spot discounting
(1+s2)^2=(1+s1)*(1+f1,1)
Read assumptions and practice →Reprice cash flows without arbitrage
P=sum(CF_t*d_t)
Read assumptions and practice →Identify who owns the embedded option
Callable=straight−issuer call; putable=straight+holder put
Read assumptions and practice →Separate expected credit loss and market compensation
EL=EAD*PD*LGD; LGD=1−recovery
Read assumptions and practice →Read the CDS protection and its remaining risks
Protection settlement=notional*(1−auction recovery)
Read assumptions and practice →Distinguish forward price and existing-contract value
Forward price F0=S0*(1+r)^T; existing long value=St−K/(1+r)^(T−t)
Read assumptions and practice →Replicate an option before assigning probabilities
q=(R−d)/(u−d); C=(q*Cu+(1−q)*Cd)/R; delta=(Cu−Cd)/(Su−Sd)
Read assumptions and practice →Disentangle commodity spot moves and roll effects
F=S*exp((r+storage−convenience yield)*T)
Read assumptions and practice →Separate property income from financing
Property value=stabilized NOI/capitalization rate
Read assumptions and practice →Bridge REIT accounting earnings and cash measures
Simplified FFO=NI+property depreciation−property-sale gain; AFFO proxy=FFO−maintenance capex
Read assumptions and practice →Look through a hedge fund’s net exposure
Net return=(long exposure*rLong−short exposure*rShort)/NAV
Read assumptions and practice →Translate a macro shock into cash flow and discounting
Value=next cash flow/(required return−growth)
Read assumptions and practice →Translate information coefficient into feasible active risk
IR≈IC*sqrt(independent breadth)*TC; expected active return=IR*active risk
Read assumptions and practice →Track ETF value and the cost of access
Premium=(market price−NAV)/NAV
Read assumptions and practice →Decompose a portfolio into factor exposures
Expected excess return=alpha+sum(beta_j*factor return_j)
Read assumptions and practice →Use a risk quantile without calling it a maximum loss
One-day normal VaR≈portfolio value*(z*sigma−mu)
Read assumptions and practice →Make a backtest investable in time
Simple one-period net return=gross−transaction cost drag−fee drag
Read assumptions and practice →Ethical judgment requires more than a legal minimum
Identify applicable obligations → examine facts → select and document compliant action
Read assumptions and practice →Apply the stricter relevant duty and preserve independence
Applicable stricter duty; independent judgment; documented dissociation when necessary
Read assumptions and practice →Recognize material information before touching a trade
Assess materiality and public availability separately; restrict use of material private facts
Read assumptions and practice →Match advice to a client before chasing yield
Suitability=client circumstances+mandate+portfolio context, not product return alone
Read assumptions and practice →Disclose outside compensation before it distorts duties
Identify compensation conflicts; written consent before acceptance; protect employer property
Read assumptions and practice →Build a reasonable basis and preserve the research trail
Reasonable basis → model and term validation → clear communication → retained support
Read assumptions and practice →Resolve incentives before relying on disclosure
Avoid feasible conflicts; disclose unavoidable incentives fully and fairly
Read assumptions and practice →Protect examination integrity and accurate status claims
Preserve exam confidentiality; describe status factually; no partial designation or return guarantees
Read assumptions and practice →Resolve overlapping ethical issues in one investment decision
Address every applicable duty; client priority+conflict control+reasonable basis+truthful communication
Read assumptions and practice →Forecast regimes before forecasting portfolios
E[Rp|scenario]=ΣwE[R|scenario]; planning mean=ΣpE[Rp|scenario]
Read assumptions and practice →Build return expectations from economic components
Bond return≈carry+roll−duration×Δy−credit loss; V≈NOI/cap; Rdom=(1+Rlocal)(1+Rfx)−1
Read assumptions and practice →Choose the objective before the asset mix
Economic net wealth=financial and relevant nonfinancial assets−liabilities; funding ratio=eligible assets/liability PV
Read assumptions and practice →Optimize a policy without worshipping the optimizer
E[Rp]=wᵀμ; σp²=wᵀΣw; feasible weights must satisfy liquidity and policy constraints
Read assumptions and practice →Constraints, taxes and behavioral discipline
Cash reserve need=dated obligations+contingency allowance; modeled realization tax=gain×assumed tax rate
Read assumptions and practice →Design an equity mandate around a usable benchmark
Net expected return≈gross expected return−explicitly defined costs
Read assumptions and practice →Use bonds to finance commitments as well as returns
Dollar duration=PV×modified duration; horizon return≈carry+roll−D×Δy
Read assumptions and practice →Plan alternative investments around capital calls
Private weight=private NAV/(private NAV+public value); liquidity=available assets−calls−spending
Read assumptions and practice →Private-client policy on an economic balance sheet
Economic net wealth=financial capital+human capital−liabilities; real after-tax return=(1+Raftertax)/(1+inflation)−1
Read assumptions and practice →Institutional policy starts with the liability and sponsor
Funded ratio=plan assets/liability PV; deficit=liability PV−assets
Read assumptions and practice →Measure execution without hiding the unfilled order
ISbuy=ΣQfilled(Pexec−Pdecision)+fees+Qunfilled(Pclose−Pdecision); full effective spread=2×direction×(Pexec−mid)
Read assumptions and practice →A sovereign fund must connect fiscal and portfolio risk
Stressed liquidity=liquid assets×(1−loss)−withdrawals−other dated needs
Read assumptions and practice →Separate performance from the sources of performance
Rp=ΣwpRp,i; allocation=Σ(wp−wb)(Rb,i−Rb); selection=Σwb(Rp,i−Rb,i); interaction=Σ(wp−wb)(Rp,i−Rb,i)
Read assumptions and practice →Select managers using investment and operational evidence
Expected net alpha≈gross alpha−all incremental fees/costs; incentive fee=contract rate×eligible gain
Read assumptions and practice →Read a performance presentation before trusting its claim
Simplified composite return without flows=Σbeginning-asset weight×portfolio return
Read assumptions and practice →Choose option protection by payoff, cost and risk exposure
Collar expiry value=S+max(Kput−S,0)−max(S−Kcall,0); profit=expiry value−net initial cost
Read assumptions and practice →Resize portfolio exposures with explicit hedge arithmetic
Nβ=(βtarget−βcurrent)Vp/(βfVf); ND=(Dtarget−Dcurrent)Vp/(DfVf); DV01≈Dmodified×V×0.0001
Read assumptions and practice →Make the currency quote and hedge direction explicit
Rdom=(1+Rforeign)(Send/Sbegin)−1; short-foreign forward payoff=foreign notional×(F−Send)
Read assumptions and practice →Ethical reasoning before the compliance checkbox
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Professionalism when pressure conflicts with competence
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Protect market integrity without banning legitimate research
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Client duties across allocation, suitability and confidentiality
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Loyalty, outside compensation and supervisory controls
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Reasonable research and transparent model communication
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Avoid conflicts where possible and disclose the rest clearly
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Protect exam integrity and describe qualifications accurately
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Resolve a multi-duty committee incident
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Translate a manager code into operating controls
Identify facts → duties → affected parties → feasible action → evidence and follow-up
Read assumptions and practice →Index portfolios: choose the exposure before the vehicle
Fee=AUM×rate; active return=portfolio−benchmark; tracking error=SD(active return)
Read assumptions and practice →Active equity: turn a thesis into a falsifiable process
Illustrative net alpha=gross alpha−incremental costs
Read assumptions and practice →Build active portfolios within a risk budget
Active Share=0.5Σ|wp−wb|;IR=alpha/active risk;days=trade size/(participation×daily volume)
Read assumptions and practice →Hedge liabilities, not just bond-price volatility
PV=L/(1+y)^T; annual zero: Dmac=T, Dmod=T/(1+y); ΔPV≈−Dmod×PV×Δy
Read assumptions and practice →Translate a curve view into controlled rate exposure
ΔP/P≈−ΣKRD_iΔy_i; cash change=value×percentage change
Read assumptions and practice →Credit alpha must survive default and liquidity stress
Spread loss≈spread duration×Δspread;expected loss≈PD×LGD
Read assumptions and practice →Execution: balance urgency, impact and opportunity cost
IS=actual buy cost+fees−decision price×quantity;IS bp=IS/paper cost×10,000
Read assumptions and practice →An endowment must finance its illiquidity ambition
Net liquidity need=spending+calls−distributions;coverage=accessible liquid assets/stress need
Read assumptions and practice →Commitments, structures and honest private-fund metrics
DPI=D/PIC;RVPI=NAV/PIC;TVPI=DPI+RVPI
Read assumptions and practice →GP economics, alignment and an investment decision
Specified carry=20%×(realization−returned capital);LP total=realization−carry
Read assumptions and practice →Private equity across a company’s life
Post-money=pre-money+new capital;equity=EV−net debt;MOIC=exit equity/entry equity
Read assumptions and practice →Private debt: contract protection before headline yield
Leverage=debt/EBITDA;DSCR=CFADS/(interest+scheduled principal)
Read assumptions and practice →Special situations: value follows the legal waterfall
Junior recovery=max(0,min(junior claim,assets−senior claim))
Read assumptions and practice →Real assets: property cash flow before appraisal comfort
Simple value=stabilized NOI/cap rate;equity=value−debt
Read assumptions and practice →Infrastructure: finance the project through its life
DSCR=CFADS/debt service;project value=PV(contractual and justified residual cash flows)
Read assumptions and practice →Choose a wealth-service model by needs and conflicts
AUM fee=assets×fee rate;all-in cost=headline+product+custody+execution+other applicable costs
Read assumptions and practice →Family communication is an investment control
Allocation share=proposed amount/usable family capital;required approvals=stated voting threshold
Read assumptions and practice →Goals-based planning across a household lifetime
Goal PV=future spending/(1+after-tax planning return)^years
Read assumptions and practice →Investment planning must be evaluated after tax and spending
Tax=(sale−basis)×stipulated rate;net proceeds=sale−tax
Read assumptions and practice →Preserve purchasing power and the household income engine
Future cost=current cost×(1+inflation)^T;domestic liability=foreign amount×domestic-per-foreign FX
Read assumptions and practice →Complex families, founders and executives need one economic map
Economic net wealth=assets−liabilities−relevant contingent adjustments;concentration=related gross assets/total gross assets
Read assumptions and practice →Transfer wealth with purpose, liquidity and enforceable instructions
Illustrative gift FV=pool(1−gift tax)(1+r)^T;bequest FV=pool(1+r)^T(1−estate tax)
Read assumptions and practice →A model committee challenges an earnings forecast
ŷ = b₀ + Σbⱼxⱼ; adjusted R² = 1−(1−R²)(n−1)/(n−k−1)
Read assumptions and practice →Match a pension liability without confusing price risk
Decision → calculation/evidence → case-specific reason → limitation
Read assumptions and practice →Read a fund waterfall and the evidence behind a mark
Decision → calculation/evidence → case-specific reason → limitation
Read assumptions and practice →Separate spending needs from willingness to take risk
Decision → calculation/evidence → case-specific reason → limitation
Read assumptions and practice →Financial statements that balance: earnings, cash and valuation
CFO = NI + D&A − ΔAR − Δinventory + ΔAP; FCFF = CFO + interest(1−T) − capex; FCFE = CFO − capex + net borrowing
Read assumptions and practice →