AIS Cheatsheet — Formulas, Decision Tables, Checklists & Glossary

Use this as your high-yield AIS review. Pair it with the Syllabus for coverage and Practice for speed.

AIS in one picture (process beats trivia)

    flowchart TD
	  A["Client facts (objectives + constraints)"] --> B["Risk profile (tolerance + capacity)"]
	  B --> C["Allocation policy (targets + ranges)"]
	  C --> D["Implementation (securities / funds / solutions)"]
	  D --> E["Risk controls (diversify / rebalance / hedge)"]
	  E --> F["Monitor + evaluate + report"]
	  F --> A

Official exam snapshot (CSI)

Official exam weightings (AIS)

Sources: https://www.csi.ca/en/learning/courses/ais/curriculum and https://www.csi.ca/en/learning/courses/ais/exam-credits

Client constraints (the fastest way to eliminate wrong answers)

In AIS, many wrong answers fail because they violate a constraint. Train this reflex:

• Time horizon (when the money is needed)
• Liquidity (what cash must be available and when)
• Risk capacity (ability to absorb drawdowns)
• Risk tolerance (willingness to accept volatility)
• Tax context (taxable vs registered, withholding frictions, distribution types)
• Unique/legal constraints (concentration limits, ethical screens, employer rules)

One-sentence IPS summary (exam-friendly)

Write this mentally from each question stem:

• Objective: growth / income / preservation + timeline
• Constraints: liquidity + risk capacity + tax + any unique limits

Then ask: does the answer fit and is it defensible?

Risk profile + behavioural finance (high-yield)

Separate these three

• Risk tolerance (willingness)
• Risk capacity (ability)
• Risk required (needs)

If required return exceeds capacity, the “best” answer is often: reset expectations (goal/horizon/savings).

Biases → best advisor response

Questionnaire limitation (what to remember)

Questionnaires are inputs, not answers. Validate with: behaviour, constraints, and scenario questions.

Asset allocation essentials (must know)

Strategic vs tactical (one-liners)

• Strategic: long-term policy weights aligned to IPS
• Tactical: temporary deviations around policy ranges

Expected portfolio return

\[ E[R_p]=\sum_{i=1}^{n} w_i E[R_i] \]

What it tells you: The portfolio’s expected return is the weighted average of the expected returns of its components.

Symbols (what they mean):

• \(E[R_p]\): expected return of the portfolio.
• \(w_i\): portfolio weight of asset \(i\) (fraction of the portfolio’s value allocated to asset \(i\)).
• \(E[R_i]\): expected return of asset \(i\).
• \(n\): number of assets.

How to use it (exam pattern):

1. Convert weights to decimals (e.g., 30% → 0.30).
2. Multiply each \(w_i\) by \(E[R_i]\).
3. Sum the products.

Common pitfalls:

• Mixing percent and decimal returns (e.g., using 8 instead of 0.08).
• Forgetting that “cash” (or a money market position) is also an “asset” if it’s part of the allocation.
• Assuming \(E[R]\) is guaranteed—this is an expectation, not a promise.

Weights sum to 1:

\[ \sum_{i=1}^{n} w_i = 1 \]

What it tells you: Your allocation uses 100% of the portfolio value (everything is accounted for across holdings).

How to apply it:

• If your weights don’t sum to 1, you’re missing something (often cash, unallocated funds, or a rounding error).

Common pitfalls:

• Treating leveraged/short portfolios like long-only allocations. In leveraged portfolios, gross exposure can exceed 100%; in long-only retail contexts, weights typically sum to 1.

Two-asset portfolio variance (diversification math)

\[ \sigma_p^2 = w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2 \]

What it tells you: Portfolio risk (variance) depends on individual volatilities and how the assets move together (correlation).

Symbols (what they mean):

• \(\sigma_p^2\): portfolio variance (risk squared).
• \(\sigma_1,\sigma_2\): standard deviations (volatility) of assets 1 and 2.
• \(\rho_{12}\): correlation between the two assets (from -1 to +1).
• \(w_1,w_2\): portfolio weights.

How to interpret it fast:

• \(\rho_{12}=+1\): no diversification benefit (they move together).
• \(\rho_{12}=0\): some diversification benefit.
• \(\rho_{12}<0\): strong diversification benefit (they tend to offset each other).

Exam takeaway: Lower correlation usually reduces portfolio volatility, but correlations can rise in stressed markets.

Rule: lower correlation → better diversification, but correlations can rise during stress.

Rebalancing quick math

1. Current weight: \(w_i = \frac{V_i}{\sum V}\)
2. Compare to target/range
3. Trade back to target (or within band), then document

What the formula means: \(w_i\) is “how much of my portfolio is in asset \(i\).”

Symbols (what they mean):

• \(V_i\): current value of asset \(i\).
• \(\sum V\): total portfolio value (sum of all positions, including cash if it’s part of the portfolio).

How rebalancing is tested:

• You’ll be asked to identify drift (current weights vs target weights) and choose trades that restore the allocation to policy.

Returns + compounding (core formulas)

Holding period return:

\[ HPR = \frac{P_1 - P_0 + D}{P_0} \]

What it tells you: Total return over a period = price change plus cash distributions, relative to the starting price.

Symbols (what they mean):

• \(P_0\): starting price.
• \(P_1\): ending price.
• \(D\): distributions received during the period (dividends/interest).

How to use it (exam pattern):

• If a question includes dividends/distributions, include \(D\) in the numerator.

Quick check: If \(P_1>P_0\) and \(D>0\), return should be positive.

Real return (inflation-adjusted):

\[ 1+r_{real} = \frac{1+r_{nom}}{1+\pi} \]

What it tells you: Real return is the return after adjusting for inflation (purchasing power).

Symbols (what they mean):

• \(r_{nom}\): nominal return (what the account statement shows).
• \(\pi\): inflation rate.
• \(r_{real}\): real return (purchasing-power return).

Exam shortcut: For small rates, \(r_{real} \approx r_{nom}-\pi\) (an approximation, not exact).

Future value with compounding:

\[ FV = PV(1+r)^n \]

What it tells you: How a present amount grows with compounding over \(n\) periods at rate \(r\).

Symbols (what they mean):

• \(PV\): present value (starting amount).
• \(FV\): future value (ending amount).
• \(r\): periodic rate (per year if \(n\) is years; per month if \(n\) is months).
• \(n\): number of compounding periods.

Common pitfalls:

• Using an annual \(r\) with monthly \(n\) (period mismatch).
• Forgetting that fees/taxes reduce the effective compounding rate (see fee drag below).

Risk + performance metrics (high yield)

Beta:

\[ \beta_i = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)} \]

What it tells you: \(\beta\) measures how sensitive an asset is to market movements (systematic risk).

Symbols (what they mean):

• \(R_i\): return of the asset.
• \(R_m\): return of the market (benchmark).
• \(\text{Cov}(R_i,R_m)\): covariance between asset and market returns.
• \(\text{Var}(R_m)\): variance of the market returns.

Interpretation (exam-friendly):

• \(\beta\approx 1\): moves roughly like the market.
• \(\beta>1\): amplifies market moves (higher systematic risk).
• \(0<\beta<1\): less sensitive than the market.
• \(\beta<0\): tends to move opposite the market (rare, but possible).

CAPM:

\[ E[R_i] = R_f + \beta_i\,(E[R_m]-R_f) \]

What it tells you: A simple model for a “fair” expected return given market risk exposure. It’s often used as a required return or a rough cost of equity.

Symbols (what they mean):

• \(R_f\): risk-free rate.
• \(E[R_m]-R_f\): market risk premium.
• \(\beta_i\): asset’s market sensitivity.

How it shows up on exams:

• Identify what return is “reasonable” for a given beta relative to a market premium.
• Compare two assets: higher beta → higher required return (all else equal).

Sharpe ratio:

\[ Sharpe = \frac{E[R_p]-R_f}{\sigma_p} \]

What it tells you: Risk-adjusted performance: excess return per unit of total volatility.

Symbols (what they mean):

• \(E[R_p]-R_f\): excess return over the risk-free rate.
• \(\sigma_p\): standard deviation (volatility) of portfolio returns.

Interpretation:

• Higher Sharpe is generally better (more return per unit risk).
• Useful for comparing portfolios with different volatility profiles.

Common pitfalls:

• Using returns and volatility over different time horizons (monthly vs annual).
• Comparing Sharpe ratios when returns are not measured consistently (pre-fee vs net of fee).

Tracking error: volatility of active return \(R_p-R_b\).

Information ratio:

\[ IR = \frac{E[R_p - R_b]}{\sigma_{active}} \]

What it tells you: Active manager skill per unit of active risk (tracking error).

Symbols (what they mean):

• \(R_b\): benchmark return.
• \(E[R_p-R_b]\): expected active return (alpha vs benchmark).
• \(\sigma_{active}\): standard deviation of active returns (tracking error).

Interpretation:

• Higher IR suggests better consistency at generating active return relative to risk taken.

Time-weighted vs money-weighted returns (know the difference)

Time-weighted return (neutralizes external cash flows):

\[ TWR = \prod_{k=1}^{m} (1+r_k) - 1 \]

What it tells you: Performance of the investments independent of client deposits/withdrawals.

Symbols (what they mean):

• \(r_k\): return in subperiod \(k\) (between external cash flows).
• \(m\): number of subperiods.

How to use it:

1. Break the timeline at each cash flow.
2. Compute each subperiod return \(r_k\).
3. Multiply \((1+r_k)\) across periods, then subtract 1.

Exam cue: If the question is “how did the manager perform?” → time-weighted is usually the right tool.

Money-weighted return / IRR (cash-flow sensitive):

\[ 0 = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t} \]

What it tells you: The investor’s realized return considering timing and size of cash flows (deposits/withdrawals).

Symbols (what they mean):

• \(CF_t\): cash flow at time \(t\) (sign convention varies by calculator; be consistent).
• \(r\): internal rate of return (IRR) that makes NPV = 0.
• \(t\): time period index.

Exam cue: If the question is “what return did the investor experience given contributions/withdrawals?” → money-weighted/IRR.

Common pitfalls:

• Forgetting that money-weighted return can look “bad” even when investments did fine (e.g., investing right before a drawdown).

Rule: When cash flows are large or badly timed, MWR can differ materially from TWR.

Fundamental analysis (AIS level framing)

Top-down → bottom-up

1. Macro regime (growth/inflation/rates)
2. Industry structure (competition, cyclicality, regulation)
3. Company fundamentals (quality, profitability, leverage, cash flow)
4. Valuation (what you pay matters)

Common ratios (interpretation, not memorization)

Valuation shapes

Gordon growth (dividend discount):

\[ P_0 = \frac{D_1}{r-g} \]

What it tells you: A simplified intrinsic value for a dividend-paying stock when dividends are expected to grow at a constant rate forever.

Symbols (what they mean):

• \(P_0\): estimated current price (intrinsic value).
• \(D_1\): next period’s dividend.
• \(r\): required return (discount rate).
• \(g\): perpetual dividend growth rate.

How it’s tested:

• Recognize that if \(r\) falls or \(g\) rises, value increases (all else equal).
• Verify the model assumptions (stable business, stable growth).

Critical constraint: Must have \(r>g\). If \(r\le g\), the model breaks (infinite/negative values).

DCF skeleton:

\[ V_0 = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} + \frac{TV_n}{(1+r)^n} \]

What it tells you: Present value equals the discounted value of future cash flows plus a terminal value.

Symbols (what they mean):

• \(CF_t\): cash flow in period \(t\).
• \(r\): discount rate (required return).
• \(TV_n\): terminal value at time \(n\) (captures value beyond explicit forecast horizon).
• \(n\): number of forecast periods.

How it’s tested (AIS level):

• Identify the main value drivers: growth, margins/cash flows, and discount rate.
• Recognize that terminal value often dominates the valuation → assumptions matter.

Exam habit: avoid “precision theatre.” Prefer answers that emphasize assumptions + sensitivity.

Technical analysis (use it ethically)

Know the language:

• trend, support/resistance, momentum, volume confirmation
• sentiment indicators (crowding)
• intermarket cues (rates/FX/commodities influencing risk assets)

Best-practice phrasing: probabilistic (“signals suggest…”) not certain (“will go up”).

Debt securities (selection and risk control)

Bond price:

\[ P = \sum_{t=1}^{n} \frac{C}{(1+y)^t} + \frac{F}{(1+y)^n} \]

What it tells you: A bond’s price is the present value of coupons plus the present value of principal.

Symbols (what they mean):

• \(P\): bond price.
• \(C\): coupon payment per period.
• \(F\): face (par) value repaid at maturity.
• \(y\): yield per period (must match the coupon period).
• \(n\): number of remaining periods.

Exam takeaway: If yields rise, discounting is heavier → price falls. If yields fall → price rises.

Duration approximation:

\[ \frac{\Delta P}{P} \approx -D_{mod}\,\Delta y \]

What it tells you: A quick approximation of percentage price change for a small yield change.

Symbols (what they mean):

• \(\Delta P/P\): approximate % change in price.
• \(D_{mod}\): modified duration (interest rate sensitivity).
• \(\Delta y\): change in yield (in decimal terms, e.g., 0.01 for 1%).

How to use it (exam pattern):

• If duration is 6 and yields rise by 0.50% (0.005), then \(\Delta P/P \approx -6\times 0.005 = -0.03\) → about -3%.

Limitations: Works best for small yield changes and non-callable bonds; convexity improves the estimate.

Convexity adjustment:

\[ \frac{\Delta P}{P} \approx -D_{mod}\,\Delta y + \frac{1}{2}Cvx(\Delta y)^2 \]

What it tells you: A more accurate estimate of price change by adding curvature (convexity).

Symbols (what they mean):

• \(Cvx\): convexity measure (captures the curvature of the price–yield relationship).
• The \((\Delta y)^2\) term means convexity matters more for larger yield moves.

Interpretation:

• For plain (non-callable) bonds, convexity is typically positive → helps on large rate moves.
• For callable bonds, effective convexity can be lower or negative → price gains may be capped as yields fall.

Ladder vs barbell vs bullet

Credit spread intuition

• spreads widen → market demands more compensation for credit risk
• spreads tighten → perceived risk falls / liquidity improves

Mutual fund selection (high yield checklist)

When the question asks “what should you consider?”, a safe answer usually mentions:

• mandate/style fit
• benchmark relevance
• fees + turnover (net return matters)
• risk profile and holdings concentration
• manager/process stability
• monitoring triggers (mandate/manager change, persistent underperformance)

Selection pitfalls

Alternatives (structure + liquidity + risk)

In AIS, alternatives are often tested via: liquidity terms, fees, and valuation reliability.

International investing + taxation (keep it simple)

Currency return decomposition (conceptual)

For a Canadian investor holding a foreign asset:

\[ 1+R_{CAD} \approx (1+R_{foreign})\,(1+R_{FX}) \]

What it tells you: Your CAD return combines the asset’s local return and the currency move.

Symbols (what they mean):

• \(R_{CAD}\): return measured in Canadian dollars.
• \(R_{foreign}\): return in the foreign market’s local currency.
• \(R_{FX}\): return from the currency move (foreign currency vs CAD).

How to interpret quickly:

• If the foreign asset is up and the foreign currency strengthens vs CAD, both effects boost \(R_{CAD}\).
• If the foreign asset is up but the foreign currency weakens, currency can offset gains.

Exam shortcut: For small rates, \(R_{CAD} \approx R_{foreign} + R_{FX}\) (approximation).

Withholding taxes (concept)

• International dividends/interest can face withholding tax.
• Treaties and credits may reduce double taxation, but rules change—verify using current official sources.

After-tax return skeleton:

\[ R_{after} = R_{pre} - \text{tax drag} - \text{fees} \]

What it tells you: Net outcomes are driven by pre-tax performance minus frictions.

What “tax drag” includes (conceptually):

• withholding tax on foreign income
• taxes on distributions and realized capital gains
• loss of deferral (turnover can accelerate taxation)

Exam takeaway: When two options have similar pre-tax returns, costs and taxes can decide the “best” answer.

Portfolio solutions fundamentals (how questions are framed)

Portfolio solutions are typically tested as governance and discipline questions:

• do costs and structure fit the client?
• is it consistent with risk profile and constraints?
• how will it be monitored and evaluated?
• what are the “dos and don’ts” (avoid performance chasing; document rationale)

Overlay management: adding a layer (e.g., hedging or risk control) on top of the core portfolio.

Protecting client investments (risk tools)

First-line risk controls (often the best answer)

• reduce concentration
• rebalance back to policy
• shorten duration / reduce credit risk when appropriate
• improve diversification across drivers

Hedging tools (conceptual)

• Options: define downside (cost)
• Futures: efficient broad hedges (basis risk)
• CFDs: leveraged exposure (counterparty + leverage risk)

If the client can’t understand it, it’s usually not the best answer.

Impediments to wealth accumulation (what to say)

• Fees and taxes compound silently.
• Inflation erodes purchasing power.
• Behavioural errors can dominate outcomes (panic selling, chasing).

Fee drag example:

\[ FV = PV(1+r-\text{fee})^n \]

What it tells you: Fees reduce the compounding rate; even “small” fees can materially reduce long-term wealth.

Symbols (what they mean):

• \(r\): gross (before-fee) return per period.
• \(\text{fee}\): fee rate per period (e.g., management fee as a %).
• \(n\): number of periods.

How it’s tested:

• Compare outcomes across products with different all-in costs.
• Recognize that higher-turnover/high-fee products face a larger “hurdle” to justify themselves.

Glossary (high-yield AIS terms)

• Active management: deviating from a benchmark to seek excess return.
• Alpha: return above what a risk model/benchmark would predict.
• Asset allocation: choosing weights across asset classes.
• Asset class: group of securities with similar risk/return drivers.
• Asset location: placing assets in accounts to optimize after-tax outcome.
• Benchmark: reference portfolio used to evaluate performance.
• Behavioural finance: study of systematic investor biases and non-rational behaviour.
• Beta: sensitivity of a return series to the market.
• Correlation (\(\rho\)): co-movement measure between returns.
• Covariance: scale-dependent co-movement between returns.
• Credit spread: yield difference between risky and risk-free debt.
• Currency risk: variability due to exchange rate changes.
• Diversification: spreading exposure to reduce unsystematic risk.
• Duration: interest-rate sensitivity measure for bonds.
• Fee drag: reduction in wealth due to ongoing fees.
• Fundamental analysis: valuing a security using economic/financial data.
• Gordon growth model: dividend-based valuation \(P_0=\frac{D_1}{r-g}\).
• Hedging: actions intended to reduce a specific risk exposure.
• Holding period return (HPR): total return over a period.
• IPS: Investment Policy Statement defining objectives, constraints, and rules.
• IRR / Money-weighted return: cash-flow-sensitive return measure.
• Liquidity: ability to trade without large price impact.
• Overlay management: adding a risk/exposure layer on top of a core portfolio.
• Rebalancing: trading to restore portfolio weights to targets/ranges.
• Risk capacity: financial ability to bear loss.
• Risk tolerance: willingness to bear volatility.
• Sharpe ratio: excess return per unit total risk.
• Style drift: manager deviates from stated mandate/style.
• Suitability: recommendation must fit objectives/constraints and risk profile.
• Technical analysis: price/volume-based analysis approach.
• Term structure: relationship between yields and maturities.
• Time-weighted return: return measure that neutralizes external cash flows.
• Tracking error: volatility of active return relative to benchmark.
• Withholding tax: tax withheld by a foreign country on income paid to non-residents.

Sources: https://www.csi.ca/en/learning/courses/ais/curriculum and https://www.csi.ca/en/learning/courses/ais/exam-credits