CFA Portfolio Management Notes: Risk, Return, CAPM and the IPS [Level 1]

Portfolio Management is where the CFA Level 1 syllabus stops valuing single securities and starts judging combinations of them. CFA Institute weights the topic at 8-12% of the 2026 Level 1 exam, roughly 14 to 22 of the 180 questions, and these CFA portfolio management notes cover every formula and judgment the topic tests: portfolio return and variance, correlation, the Sharpe ratio, CAPM, and the investment policy statement (IPS).

The math is the lightest in the Level 1 investment topics, and that is exactly the trap: most questions test judgment, not calculation. This note sits in our CFA notes hub with the other nine topics, and it builds on the return ideas from Quantitative Methods.

Work through it in order: learn the four core formulas, do the three worked examples with a calculator in hand, then finish with the exam traps section.

CFA Portfolio Management Notes: The Big Picture

CFA portfolio management notes in one line: a portfolio blends assets so correlation, not individual volatility, drives risk. You will compute portfolio return as the weighted average of asset returns, portfolio variance with the covariance term, then judge results with the Sharpe ratio, the Treynor ratio, Jensen alpha and CAPM.

Three ideas organize the whole topic. First, portfolio return is simple: a weighted average. Portfolio risk is not simple, because assets move together, and the covariance term decides how much risk diversification removes. Second, only systematic risk earns a reward. Risk that diversification eliminates earns no premium. Third, the portfolio exists for a client. The IPS records what the client needs, what the client can tolerate and what constraints bind the manager, and every decision is tested against it.

The exam follows the same order. Early questions ask for a return or a standard deviation. Middle questions ask which measure, or which line, fits a described portfolio. Late questions move to the IPS, where you decide a client risk tolerance and spot the constraint the case facts hide in plain sight.

Return and Risk: The Building Blocks

The holding period return measures what one asset earned over one period, income included:

Holding period return = (Ending value – Beginning value + Income) / Beginning value

For example, you buy a share for $50. One year later it trades at $54 and it paid a $2 dividend on the way. The return is ($54 – $50 + $2) / $50 = $6 / $50 = 12.00%.

Means need care. A fund returns +20% in year 1 and -10% in year 2. Its arithmetic mean is (20% – 10%) / 2 = 5.00%, while its geometric mean is (1.20 x 0.90)^1/2 – 1 = 3.92%. That geometric figure is the compound growth the investor actually earned, so it is the right measure for reporting past multi-period performance. By contrast, the arithmetic mean is the better single-period forecast input. Our CFA Quantitative Methods notes cover the related money-weighted and time-weighted returns.

Risk splits into two types, and the split drives everything that follows:

Risk type	Comes from	Diversifiable?	Rewarded?	Measured by
Systematic risk	Interest rates, recessions, inflation, politics: factors that hit the whole market	No	Yes, it earns a risk premium	Beta
Unsystematic risk	One company or one industry: a factory fire, a lost contract, a failed drug trial	Yes	No premium	Part of total standard deviation

In short, total risk is the standard deviation of returns. As a portfolio adds holdings, unsystematic risk washes out and the standard deviation falls toward the systematic floor, which is why a well diversified portfolio of 30 or more stocks carries mostly market risk.

Portfolio Risk and Correlation in CFA Portfolio Management Notes

Portfolio expected return is the weighted average of the asset returns. Nothing more. Suppose a portfolio holds 60% in Asset A with an expected return of 12% and 40% in Asset B with an expected return of 8%:

Portfolio return = (0.60 x 12%) + (0.40 x 8%) = 7.20% + 3.20% = 10.40%

Portfolio variance is where candidates slip. For two assets, the formula has three terms, and the third term carries the covariance:

Portfolio variance = w_A²σ_A² + w_B²σ_B² + 2w_Aw_BCov_AB

Keep the same weights. Asset A has a standard deviation of 20% and Asset B has a standard deviation of 12%, and their correlation is 0.30. First, convert correlation to covariance: Cov_AB = 0.30 x 0.20 x 0.12 = 0.0072. Next, square the weights and the standard deviations: (0.60)² x (0.20)² = 0.0144, and (0.40)² x (0.12)² = 0.002304. Finally, add the covariance term: 2 x 0.60 x 0.40 x 0.0072 = 0.003456. Total variance = 0.0144 + 0.002304 + 0.003456 = 0.02016, so the portfolio standard deviation is the square root of 0.02016, which is 14.20%.

How Correlation Changes the Answer

Compare that with the naive answer: the weighted average of the two standard deviations is (0.60 x 20%) + (0.40 x 12%) = 16.80%. True portfolio risk, 14.20%, is 2.60 percentage points lower even at a positive 0.30 correlation. That gap is the diversification benefit, and it grows as correlation falls:

Correlation between A and B	Portfolio variance	Portfolio standard deviation
+1.00	0.028224	16.80%
+0.30	0.020160	14.20%
0.00	0.016704	12.92%
-0.50	0.010944	10.46%

Two exam rules follow. First, adding assets reduces risk only when the new assets do not move in lockstep with the old ones; 30 bank stocks diversify far less than 30 stocks across industries. Second, as holdings grow, average covariance matters far more than each asset variance, because the variance terms wash out. The bond side of a portfolio behaves the same way, and our CFA Fixed Income notes show where that bond risk comes from, starting with duration.

The Efficient Frontier, the CAL and the CML

Plot every possible portfolio by expected return against standard deviation: the top edge of the cloud is the efficient frontier, the highest return for each level of risk. Its leftmost point is the global minimum-variance portfolio. For that reason, investors choose only the upper half of the minimum-variance frontier, because every lower-half portfolio has a twin above it with the same risk and a higher return.

Add a risk-free asset and the best line from the risk-free rate is tangent to the frontier: the capital allocation line (CAL). In equilibrium the tangency portfolio is the market portfolio, the line becomes the capital market line (CML), and two-fund separation holds: every investor holds the same market portfolio and adjusts risk only by lending or borrowing at the risk-free rate.

The CML prices total risk, and only efficient portfolios sit on it. A single stock never belongs on it, because a single stock is not an efficient portfolio. Individual assets are priced by the security market line instead. In practice, confusing those two lines is the most tested distinction in this topic.

Sharpe, Treynor and Jensen in CFA Portfolio Management Notes

Three ratios dominate performance evaluation, and the exam tests whether you pick the one that matches the risk in the denominator. One fund, three answers. A fund earned 12.0% last year. The risk-free rate was 3.0%, the fund standard deviation was 15%, its beta was 1.2, and the market returned 10.0%.

Measure	Formula	Worked result	Use it when
Sharpe ratio	(Return – Risk-free rate) / Standard deviation	(12.0 – 3.0) / 15 = 0.60	The fund is the investor’s whole portfolio, so total risk is what matters
Treynor ratio	(Return – Risk-free rate) / Beta	(12.0 – 3.0) / 1.2 = 7.50%	The fund is one holding inside a diversified portfolio
Jensen alpha	Actual return – CAPM required return	12.0 – [3.0 + 1.2 x (10.0 – 3.0)] = 12.0 – 11.4 = +0.60%	You want the value the manager added over a passive benchmark of the same risk

Together, the three results tell one story: Jensen alpha is positive, so the manager added value on a risk-adjusted basis, and a Sharpe ratio of 0.60 means 0.60 units of excess return per unit of total risk. A related measure, M-squared, restates the Sharpe result as a return percentage at the market level of risk; the exam asks about it in words more often than in numbers.

However, one caution covers Treynor and Jensen: both depend on beta, and beta is an estimate that shifts with the sample period and the benchmark chosen, so a ranking of two funds can flip when the risk measure changes.

CAPM and the Security Market Line in CFA Portfolio Management Notes

The capital asset pricing model turns the systematic risk idea into a required return:

Required return = Risk-free rate + Beta x (Market return – Risk-free rate)

The bracketed term is the equity risk premium. Take a risk-free rate of 2.5% and an equity risk premium of 5.5%. A defensive stock with a beta of 0.8 requires 2.5% + (0.8 x 5.5%) = 2.5% + 4.4% = 6.90%. An aggressive stock with a beta of 1.4 requires 2.5% + (1.4 x 5.5%) = 2.5% + 7.7% = 10.20%. Same market, same risk-free rate: the stock with more systematic risk must promise more return, and the difference comes only from beta.

When you graph the model, you get the security market line (SML): required return against beta. Every asset, efficient or not, belongs on it in equilibrium. An asset above the line offers more return than its beta requires, so it is undervalued; below the line, overvalued. Contrast the CML: total risk on the axis, efficient portfolios only. The SML uses beta and holds everything.

CAPM output does real work elsewhere: the required return becomes the cost of equity in the dividend discount model and in WACC, which is why our CFA Equity Valuation notes start from a CAPM calculation.

The Portfolio Management Process and the IPS

The process has three steps. Planning means understanding the client and writing the IPS. Execution means setting the strategic asset allocation, selecting securities, and trading. Feedback means monitoring, rebalancing when allocations drift, and evaluating performance. The exam presents the steps out of order in case questions; anchor on the IPS.

The IPS states the client objectives first: the return requirement and the risk tolerance. Risk tolerance itself has two parts. Ability to take risk is objective: wealth relative to spending needs, a long horizon, stable income and low liabilities all raise it. Willingness is psychological: it comes from client attitudes and past behavior. When ability and willingness disagree, the advisor uses the lower of the two, and documents the conversation. A wealthy client who panics and sells in every drawdown gets a conservative portfolio, because willingness is the binding limit.

The Five IPS Constraints

Constraints come next, and the curriculum groups them as tax, liquidity, time horizon, legal and regulatory, and unique circumstances:

Constraint	What it captures	Typical case clue
Liquidity	Cash the client must withdraw, and when	A house purchase or tuition payment due within a year
Time horizon	Length of each stage until money is needed	A 30-year-old saving for retirement has a long, often multi-stage, horizon
Tax	Tax status of the client and of each account	Tax-exempt institutions care about pre-tax return; taxable clients do not
Legal and regulatory	Laws and rules that bind the portfolio	Trust law, pension regulation, insider restrictions on employer stock
Unique circumstances	Anything personal that the other four miss	A client who refuses tobacco stocks, or holds a concentrated family business

Finally, behavioral biases explain why the IPS exists in writing. Clients anchor on purchase prices, herd into whatever has risen, and keep losing positions to avoid admitting a loss. The exam names biases such as loss aversion, status quo bias and mental accounting in case vignettes; the answer is almost always to return to the IPS allocation rather than chase the bias. Our CFA Ethics notes complete the picture, because suitability is a Standard, not a suggestion.

Exam Traps in CFA Portfolio Management Notes

• Computing portfolio risk as a weighted average of standard deviations. That shortcut is exact only when correlation is +1. Every other case needs the full variance formula with the covariance term.
• Judging a single fund with the Sharpe ratio when the fund is one holding among many. Inside a diversified portfolio, systematic risk is the risk that survives, so Treynor or Jensen is the right tool.
• Taking the higher of ability and willingness for risk tolerance. The rule is the lower of the two.
• Plotting an individual stock on the CML. The CML holds efficient portfolios only and prices total risk. Individual assets belong on the SML, priced by beta.
• Saying unsystematic risk earns a premium. It does not. Diversification removes it at no cost, so the market pays nothing for it.
• Adding a covariance term to portfolio return. Return is a plain weighted average. Covariance enters the risk calculation only.
• Reporting past performance with the arithmetic mean. Multi-period past performance is geometric. The arithmetic mean overstates what the investor actually compounded.

One-Page Revision Box: CFA Portfolio Management Notes

• Holding period return = (End – Start + Income) / Start. Example: $50 to $54 plus $2 income = 12.00%.
• Portfolio return = weighted average of asset returns. Example: 0.60 x 12% + 0.40 x 8% = 10.40%.
• Portfolio variance = w_A²σ_A² + w_B²σ_B² + 2w_Aw_Bρ_ABσ_Aσ_B. Example: variance 0.02016, standard deviation 14.20% at correlation 0.30.
• Sharpe = excess return / total standard deviation. Treynor = excess return / beta. Jensen = actual return minus CAPM required return.
• CAPM: required return = risk-free rate + beta x equity risk premium. Beta 0.8 at a 2.5% risk-free rate and 5.5% premium = 6.90%.
• CML: total risk, efficient portfolios only. SML: beta, all assets. Risk tolerance = lower of ability and willingness. IPS constraints: tax, liquidity, time horizon, legal, unique.

Frequently Asked Questions

How heavily is Portfolio Management weighted in CFA Level 1?

CFA Institute weights Portfolio Management at 8-12% of the 2026 Level 1 exam, roughly 14 to 22 of the 180 questions. Its formulas also feed Equity Valuation and the IPS cases, so the effective value beats the weight alone.

What is the difference between the CML and the SML?

The capital market line plots expected return against total risk (standard deviation) and contains only efficient portfolios. The security market line plots required return against beta and contains every asset, efficient or not. If a question mentions a single stock, the answer almost always involves the SML.

When do I use the Sharpe ratio instead of the Treynor ratio?

Use the Sharpe ratio when the portfolio being judged is the investor’s entire holding, because total risk is what that investor bears. Use the Treynor ratio when the fund is one part of a larger diversified portfolio, because only its systematic risk, measured by beta, adds to the investor’s overall risk.

Why does correlation matter more than the number of holdings?

Because the benefit comes from assets not moving together. Fifty stocks with an average correlation of 0.90 cut risk far less than twenty stocks at 0.20. In the formula, that is the covariance term at work: the two-asset example in this note falls from 16.80% to 10.46% as correlation drops from +1.00 to -0.50.

What belongs in an investment policy statement?

Two objectives, the return requirement and the risk tolerance, plus five constraints: tax considerations, liquidity needs, time horizon, legal and regulatory factors, and unique circumstances. The IPS is written in the planning step, drives the asset allocation in execution, and is the reference point for the feedback step when markets or client circumstances change.