AIS Cheat Sheet — Formulas, Decision Tables, Checklists and Glossary

Use this as your high-yield AIS review. Pair it with the Guide Home, the Study Plan, the FAQ, the Official Resources, and exact AIS practice on MasteryExamPrep.

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

Pressure map

AIS route check

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