# Investments Elective Course Guide: [Your programme, term and section] > A course guide for the second-year MBA elective in investments: the investment process and policy, return > measurement, mean-variance portfolio theory and asset allocation, the CAPM, index and multi-factor models, market > efficiency, fixed income, derivatives in portfolios, performance evaluation and active management. It builds on the > core finance course, in particular mba/mba-capm-wacc-card and mba/mba-corporate-finance-guide, and links to them > instead of repeating them. It is for second-year students choosing and planning the elective, students aiming at > asset management, wealth management, sales and trading or endowment roles, and study groups. It gives the > competencies the course builds, the prerequisites, a 13-session roadmap linked to the concept cards, a key concepts > map, an original mini-case on a fictional hospital foundation (Tallow Creek Medical Center) with exhibits, discussion > questions and a teaching note, a grading rubric, an exam plan, the struggles most students hit, a reading list and a > self-test with an answer key. Source basis: the primary works of investment theory from Markowitz (1952) to Fama and > French (2015), written up in original words. Session order and grading are typical of leading international > programmes; your syllabus decides. Replace every [bracketed] value and every row marked *Example*. This is a learning > aid, not investment advice. ## Document control | Field | Value | |---|---| | Programme, term and section | [Programme name, term, section] | | Learner | [Your name] | | Faculty and teaching assistants | [Names, office hours] | | Learning team | [Names] | | Data sources used in the course | [Factor library, market data terminal, course files] | | Grading weights | [Problem sets 25%, cases 25%, participation 15%, final 35%] | | Reviewed by | [Study partner or mentor] | | Version | [0.1] | | Last updated | YYYY-MM-DD | ## Contents - [What the course is for](#what-the-course-is-for) - [Prerequisites](#prerequisites) - [The course in one page](#the-course-in-one-page) - [Session roadmap](#session-roadmap) - [Key concepts map](#key-concepts-map) - [Mini-case: Tallow Creek Medical Center Foundation](#mini-case-tallow-creek-medical-center-foundation) - [Teaching note](#teaching-note) - [Typical assignments and how they are graded](#typical-assignments-and-how-they-are-graded) - [Exam preparation plan](#exam-preparation-plan) - [Common struggles](#common-struggles) - [Reading list](#reading-list) - [Self-test questions](#self-test-questions) - [My notes and next steps](#my-notes-and-next-steps) - [Sources and further reading](#sources-and-further-reading) - [Answer key](#answer-key) - [Revision history](#revision-history) ## What the course is for The core finance course looks at investment from the company's side: which projects to fund and at what cost of capital. The investments elective looks from the investor's side: how to combine assets into a portfolio, how to price risk, how to tell skill from luck and exposure, and how to run an investment programme for an owner with goals and constraints. Three questions organise it: **what should the portfolio hold** (asset allocation and security selection), **what return should be expected for the risk** (asset pricing models), and **did the manager add value** (performance evaluation). One idea runs through all three: return is earned by bearing risk that cannot be diversified away, and anything else must be explained before it is paid for. The competencies the course builds, mapped to the competency list used across this library (see mba/mba-core-curriculum-map). The AACSB Global Standards for Business Education, ratified by AACSB members on 20 April 2026, leave each school to define its own learning goals, so check your programme's list (as of October 2026, see aacsb.edu): | Competency area | What you should be able to do by the end of the course | |---|---| | Analytical and quantitative reasoning | Build an efficient frontier, run and read a factor regression, price a bond and compute its duration, evaluate a manager with risk-adjusted measures | | Ethical decision making | Recognise conflicts of interest in fees and advice, misleading performance presentation, and duties to the beneficiaries of a fund | | Communication | Write an investment committee memo that states the recommendation, the expected return and risk, and the main uncertainty on the first page | | Leadership and teamwork | Split a case model in a learning team, check each other's inputs, and defend a recommendation against a sceptical committee | | Global perspective | Handle currency, home bias and regional factor data; compare investor types across countries | | Technology, data and AI | Clean return data, document sources and dates, use spreadsheet matrix functions and regression tools, and check AI-generated formulas by hand | ## Prerequisites | Skill | Check yourself | Where to fix it | |---|---|---| | Time value of money and bond basics | Price a 5-year bond with a 4% annual coupon at a 5% yield | mba/pre-mba-finance-primer, mba/mba-corporate-finance-guide | | CAPM, beta and diversification | Explain why only systematic risk is priced | mba/mba-capm-wacc-card | | Statistics: variance, covariance, correlation | Compute the volatility of a two-asset portfolio by hand | mba/pre-mba-quant-refresher, academic/stats-correlation | | Regression | Read a coefficient, its standard error, t-statistic and R-squared | mba/mba-regression-for-managers-card, academic/stats-linear-regression | | Option payoffs | Draw the payoff of a protective put | mba/mba-options-real-options-card | | Spreadsheet matrix work | Use `MMULT`, `MINVERSE`, `TRANSPOSE`, `LINEST` and Solver | mba/pre-mba-excel-modeling-drills | ## The course in one page **Measuring returns.** Holding-period return $(P_1 - P_0 + D)/P_0$. Arithmetic means estimate next period's expected return; geometric means describe compound growth, and for volatile assets the geometric mean is lower, approximately $\bar{r}_g \approx \bar{r}_a - \tfrac{1}{2}\sigma^2$. Real return $(1 + r)/(1 + \pi) - 1$. **Portfolio theory.** Portfolio variance $\mathbf{w}^\top \Sigma \mathbf{w}$; the efficient frontier, the tangency portfolio with the highest Sharpe ratio, two-fund separation, and the complete portfolio $y^* = (\mu_T - r_f) / (A \sigma_T^2)$ (Markowitz 1952; Tobin 1958; mba/mba-portfolio-theory-card). **Asset pricing.** CAPM $E[R_i] = r_f + \beta_i (E[R_m] - r_f)$ (Sharpe 1964; Lintner 1965); single-index model (Sharpe 1963); APT (Ross 1976); Fama-French three- and five-factor models and momentum (Fama and French 1993, 2015; Carhart 1997; mba/mba-factor-models-card). **Market efficiency.** Prices reflect available information in weak, semi-strong or strong form (Fama 1970). Anomalies such as momentum (Jegadeesh and Titman 1993) challenge the simplest versions; the debate is whether they are risk premiums or behavioural mispricing. **Fixed income.** Price is the present value of coupons and principal at the yield; modified duration $D^* = D / (1 + y)$ gives $\Delta P / P \approx -D^* \Delta y$, with convexity as the second-order correction (Macaulay 1938; mba/mba-fixed-income-card). **Derivatives in portfolios.** Futures and swaps change exposure cheaply; options reshape the return distribution (mba/mba-derivatives-risk-guide). **Performance evaluation.** Sharpe ratio $(R_p - r_f)/\sigma_p$ (Sharpe 1966), Treynor ratio $(R_p - r_f)/\beta_p$ (Treynor 1965), Jensen's alpha $R_p - [r_f + \beta_p (R_m - r_f)]$ (Jensen 1968), appraisal ratio $\alpha / \sigma_\varepsilon$ (Treynor and Black 1973) and information ratio $(R_p - R_b) / TE$, active return per unit of tracking error (mba/mba-performance-evaluation-card). ## Session roadmap | Session | Topic | Card to read | Case or exercise | Deliverable | |---|---|---|---|---| | 1 *(Example)* | The investment process: owners, objectives, constraints, the investment policy statement; return measurement | mba/pre-mba-finance-primer, finance/investment-policy-statement-institutional | Draft an IPS for a fictional foundation | IPS outline | | 2 *(Example)* | Risk, return and diversification | mba/mba-capm-wacc-card (idea section), mba/mba-portfolio-theory-card | Two-asset frontier in Excel | Problem set 1 | | 3 *(Example)* | Mean-variance optimisation, the efficient frontier and the tangency portfolio | mba/mba-portfolio-theory-card | Three-asset frontier with MMULT, MINVERSE and Solver | Problem set 2 | | 4 *(Example)* | Strategic asset allocation, estimation error, Black-Litterman, rebalancing | mba/mba-portfolio-theory-card, finance/strategic-asset-allocation-study | This guide: Tallow Creek mini-case | Team case memo | | 5 *(Example)* | CAPM, the single-index model and beta estimation | mba/mba-capm-wacc-card, mba/mba-factor-models-card | Beta and index-model regressions | Problem set 3 | | 6 *(Example)* | APT and multi-factor models; factor investing | mba/mba-factor-models-card | Factor regressions on downloaded data | Problem set 4 | | 7 *(Example)* | Market efficiency, anomalies and behavioural finance | This guide (course in one page) | Event-study or anomaly replication exercise | Short paper | | 8 *(Example)* | Bond pricing, yields, duration and convexity | mba/mba-fixed-income-card | Bond portfolio immunisation exercise | Problem set 5 | | 9 *(Example)* | Term structure, credit risk and fixed-income portfolio management | mba/mba-fixed-income-card, finance/bond-credit-analysis | Credit spread analysis | Team case memo | | 10 *(Example)* | Derivatives in portfolios: futures overlays, swaps, protective puts | mba/mba-derivatives-risk-guide, mba/mba-forwards-futures-swaps-card | Hedging an equity sleeve with futures | Problem set 6 | | 11 *(Example)* | Performance evaluation, attribution and presentation standards | mba/mba-performance-evaluation-card, finance/performance-attribution-report | Manager evaluation exercise | Manager memo | | 12 *(Example)* | Active management, fees and alternative investments | mba/mba-factor-models-card, finance/manager-due-diligence-report, mba/mba-private-equity-guide | Hedge fund or private equity allocation case | Class discussion prep | | 13 *(Example)* | Portfolio risk management and review | mba/mba-value-at-risk-card, mba/mba-exam-prep | Integrative case under time | Final exam | ## Key concepts map | Concept | One-line meaning | Card | |---|---|---| | Arithmetic and geometric returns | Expected one-period return versus compound growth | This guide, mba/mba-formula-sheet | | Efficient frontier, GMV, tangency portfolio | Best risk-return combinations of risky assets | mba/mba-portfolio-theory-card | | Capital allocation line, two-fund separation | Every investor holds the same risky mix, in different amounts | mba/mba-portfolio-theory-card | | Risk aversion and the complete portfolio | How much risk an owner should hold | mba/mba-portfolio-theory-card | | CAPM, security market line, beta | Only market risk is priced | mba/mba-capm-wacc-card | | Single-index model, APT | Few common factors drive co-movement | mba/mba-factor-models-card | | Fama-French and Carhart factors | Size, value, profitability, investment, momentum | mba/mba-factor-models-card | | Alpha, appraisal ratio, information ratio | Return beyond priced exposures, per unit of active risk | mba/mba-factor-models-card, mba/mba-performance-evaluation-card | | Duration, convexity, immunisation | Interest-rate sensitivity of bonds and liabilities | mba/mba-fixed-income-card | | Futures, swaps, options in portfolios | Changing exposure without trading the underlying | mba/mba-derivatives-risk-guide, mba/mba-forwards-futures-swaps-card | | Sharpe, Treynor, Jensen measures | Risk-adjusted performance | mba/mba-performance-evaluation-card | | Value at risk and expected shortfall | Downside risk measures for limits and reporting | mba/mba-value-at-risk-card | ## Mini-case: Tallow Creek Medical Center Foundation **Situation.** The Tallow Creek Medical Center Foundation raises and invests money for a regional hospital. Its long-term pool stands at USD 240m. Each year the foundation pays the hospital 4.5% of the pool's value for patient programmes, equipment and nursing scholarships, and the board wants to keep that spending stable in real terms forever. For a decade the pool has followed a simple policy: 60% global equity and 40% investment-grade bonds, rebalanced annually. Grace Adeyemi, a retired actuary who now chairs the investment committee, has asked the committee's newest member, Tomás Varga, a second-year MBA student volunteering on the committee, to prepare the analysis for the next meeting. She has three concerns. First, the consultant's capital market assumptions (Exhibit 1) suggest that the current policy will not earn enough to maintain real spending. Second, the consultant has proposed two alternatives: Proposal A adds real assets (infrastructure and real estate funds) for diversification, and Proposal B raises equity to increase expected return (Exhibit 2). Third, the equity sleeve includes Manager K, an active small-cap manager whose track record the consultant calls "outstanding"; the consultant proposes raising its allocation to 15% of the pool (Exhibit 3). The hospital adds a constraint. It plans a new outpatient wing, and the foundation has pledged USD 30m toward it, payable in about 24 months. The chief financial officer of the hospital wants that money to be there regardless of markets (Exhibit 4). Several committee members, mindful of the year the pool fell sharply, would prefer to reduce risk. Others argue that a perpetual foundation can afford to ride out volatility and should hold more equity. The history matters to the committee. In the worst year of the last decade the pool lost about a sixth of its value, and the board cut the hospital grant for the following year, which delayed a nurse residency programme. The board then adopted a rule that spending would be based on the pool's value at the start of each year, which makes the grant move with markets. Hospital managers have asked whether the rule could be smoothed. The consultant's assumptions are the only forecasts the committee has; nobody on the committee has checked them against a second source, and Grace wants the memo to say how much the conclusions depend on them. She also reminds Tomás that the committee is a fiduciary for the hospital's patients, not for any manager or consultant. Tomás has a week. Grace has asked him for a two-page memo that answers four questions: what return the pool needs, which allocation the committee should adopt and why, what to do about Manager K, and how to handle the pledge. **Exhibit 1. Capital market assumptions (consultant, *Example*, 10-year horizon, nominal USD).** | Asset class | Expected return | Volatility | Correlation with equity | with bonds | with real assets | |---|---|---|---|---|---| | Global equity | 7.5% | 16% | 1.0 | 0.2 | 0.6 | | Investment-grade bonds | 4.5% | 6% | 0.2 | 1.0 | 0.3 | | Real assets | 6.0% | 12% | 0.6 | 0.3 | 1.0 | | Cash (risk-free) | 3.5% | 0% | | | | **Exhibit 2. Policy options (*Example*).** | Option | Equity | Bonds | Real assets | USD m (equity / bonds / real) | |---|---|---|---|---| | Current policy | 60% | 40% | 0% | 144.0 / 96.0 / 0.0 | | Proposal A | 50% | 30% | 20% | 120.0 / 72.0 / 48.0 | | Proposal B | 70% | 20% | 10% | 168.0 / 48.0 / 24.0 | **Exhibit 3. Manager K, 60 months, annualised, gross of fees (*Example*).** | Measure | CAPM regression | Three-factor regression | |---|---|---| | Alpha | 3.1% (t = 2.2) | 0.3% (t = 0.3) | | Market loading | 1.05 | 0.98 | | SMB loading | | 0.45 | | HML loading | | 0.38 | | Management fee | 0.80% a year | | | Fee of a small-cap value index fund | 0.25% a year | | **Exhibit 4. Spending and liquidity (*Example*).** | Item | Value | |---|---| | Spending rate | 4.5% of pool value a year (USD 10.8m in year 1) | | Long-run inflation assumption | 2.5% a year | | Investment and administration costs | 0.35% a year | | Pledge to the outpatient wing | USD 30.0m in about 24 months (12.50% of the pool today) | **Discussion questions.** 1. What nominal return does the pool need to maintain real spending after costs? Use the multiplicative form and compare it with the simple sum. 2. Compute expected return, volatility and Sharpe ratio for each option in Exhibit 2. Which is efficient relative to the others? Does any option meet the required return in expectation, and in compound (geometric) terms? 3. What is the probability, under a normal approximation, that the annualised return over 10 years falls short of the requirement for each option? What does that imply for the spending rule? 4. Evaluate Manager K. Is the CAPM alpha evidence of skill? What would you recommend about the proposed 15% allocation? 5. How should the foundation handle the USD 30m pledge, and how does that interact with the allocation decision? 6. Draft the first paragraph of Tomás's memo. ## Teaching note **Question 1: required return.** $(1.045)(1.025)(1.0035) - 1 = 7.49\%$ (7.4874%); Excel `=(1+4.5%)*(1+2.5%)*(1+0.35%)-1`. The simple sum, 7.35%, understates it by about 0.14 of a point. This is a compound (geometric) requirement: the pool must grow at 7.49% a year on average to keep real spending and real value constant. **Question 2: the options.** With Exhibit 1 and portfolio variance $\mathbf{w}^\top \Sigma \mathbf{w}$ (`=SQRT(MMULT(TRANSPOSE(w),MMULT(Cov,w)))`): | *Example* option | Expected return | Volatility | Sharpe ratio | Approximate geometric return ($\mu - \sigma^2/2$) | One-year 5% worst case | Loss on USD 240m at that point | |---|---|---|---|---|---|---| | Current 60/40 | 6.30% | 10.35% | 0.2705 | 5.76% | -10.73% | USD 25.7m | | Proposal A 50/30/20 | 6.30% | 10.22% | 0.2740 | 5.78% | -10.51% | USD 25.2m | | Proposal B 70/20/10 | 6.75% | 12.28% | 0.2648 | 6.00% | -13.44% | USD 32.3m | Proposal A has the same expected return as the current policy with slightly lower volatility, so it dominates it under these assumptions; the gain is real but small (0.13 of a point of volatility). Proposal B raises expected return by 0.45 of a point at the cost of about 2 points more volatility and a lower Sharpe ratio. No option meets 7.49% even in expectation, and in compound terms the gap is 1.5 to 1.7 points a year. The one-year 5% worst case uses the normal quantile: `=NORM.INV(5%,mu,sigma)`. For reference, the unconstrained tangency portfolio under Exhibit 1 (33.9% equity, 51.9% bonds, 14.2% real assets, mba/mba-portfolio-theory-card) has a higher Sharpe ratio (0.2808) but an expected return of only 5.73%: the most efficient portfolio is not the one that meets this owner's goal, and the foundation cannot borrow to lever it. **Risk budget.** Under Proposal A equity contributes about 75.1% of portfolio variance, real assets 17.8% and bonds 7.1%; under the current policy equity contributes about 90.3%. Capital weights understate how concentrated the risk is. **Question 3: shortfall probability.** Using the geometric approximation and a 10-year annualised volatility of $\sigma / \sqrt{10}$, `=NORM.DIST(7.49%, mu - sigma^2/2, sigma/SQRT(10), TRUE)` gives about 70.1% for the current policy, 70.2% for Proposal A and 65.0% for Proposal B. Whatever it chooses, the foundation is more likely than not to fall short of 7.49% over a decade. Risk alone cannot close the gap. The committee has three levers: accept a lower spending rate (for example, smoothing spending on a multi-year average and reviewing the 4.5% rate), cut costs, or accept that the real value of the pool will probably erode. That is a governance decision for the board, informed by the numbers, not a choice the investment staff should make silently by adding risk. **Question 4: Manager K.** The CAPM alpha of 3.1% looks significant (t = 2.2), but under the three-factor model it falls to 0.3% with t = 0.3, and the SMB (0.45) and HML (0.38) loadings show a small-value tilt (mba/mba-factor-models-card). Net of the 0.80% fee the three-factor alpha is about -0.50% a year. A small-cap value index fund at 0.25% delivers the same exposure for 0.55 of a point less; on USD 36m (15% of the pool) the fee difference is about USD 0.20m a year (USD 0.288m versus USD 0.090m). Recommendation: do not raise the allocation on this evidence; decide whether the foundation wants a small-value tilt at all, and if it does, consider the low-cost route. Ask for holdings-based analysis and a longer record before any further decision. **Question 5: the pledge.** USD 30m due in 24 months is a known liability with a short horizon: it should not be exposed to equity risk. A one-year 5% worst case of about 10% on a 60/40 pool is a loss of about USD 3m on USD 30m. Set aside the pledge in high-quality bonds or bills with maturities that match the payment date (a duration-matched reserve, mba/mba-fixed-income-card). Under Proposal A the bond sleeve is USD 72.0m, so the reserve fits inside it, but the remaining long-term bonds then fall to USD 42.0m; the committee should look at the long-term allocation on the USD 210m that remains, not the whole pool. **Question 6: a strong opening paragraph.** It states the recommendation, the numbers and the decision the board must take, for example: "We recommend adopting Proposal A, which matches the current expected return of 6.3% with slightly lower risk and a more balanced risk budget, ring-fencing the USD 30m pledge in matched bonds, and not increasing the allocation to Manager K, whose excess return is explained by a small-value tilt available at lower cost. No allocation under the consultant's assumptions is likely to earn the 7.5% needed to sustain 4.5% real spending; we ask the board to review the spending rule." **What the case teaches.** The efficient frontier is necessary but not sufficient: the owner's liabilities and spending rule decide where to stand. Diversification gains between reasonable portfolios are small compared with the gap between expected returns and goals. Alpha must be measured against the exposures an investor could buy cheaply. Liquidity needs with a date should be matched, not invested. ```mermaid flowchart TD A["Owner goal: 4.5% real spending forever"] --> B["Required return 7.49%"] B --> C["Compare options on the frontier"] C --> D{"Any option meets 7.49%?"} D -->|No| E["Board decision: spending rule, costs, accept erosion"] D -->|Yes| F["Adopt and monitor"] C --> G["Proposal A dominates current policy"] A --> H["USD 30m pledge in 24 months"] H --> I["Matched bond reserve outside the long-term pool"] C --> J["Manager K: alpha explained by factors"] J --> K["Do not increase, consider low-cost factor fund"] ``` ## Typical assignments and how they are graded Typical assignments: weekly problem sets (frontier, factor regression, bond duration, hedging), two or three team case memos, an individual manager evaluation or stock pitch (finance/stock-pitch), class participation, and a final exam, often open-book with a spreadsheet. | Criterion | Excellent (4) | Adequate (2 to 3) | Weak (0 to 1) | |---|---|---|---| | Recommendation | Clear decision on page one, with the expected return, risk and main uncertainty | Decision present but buried or hedged | No decision, or a summary of facts | | Analysis | Correct models, inputs justified, numbers reconciled, Excel formulas traceable | Mostly correct, some inputs unexplained | Errors in variance, regression or discounting | | Assumptions and sensitivity | Inputs dated and sourced; key sensitivity shown (returns, correlations, window) | Some sensitivity | Point estimates treated as facts | | Owner's perspective | Goals, liabilities, liquidity, constraints and fees drive the recommendation | Mentioned but not used | Ignored | | Communication | Two pages, exhibits labelled, plain language | Long or cluttered | Hard to follow | ## Exam preparation plan | Week | Focus | Method | |---|---|---| | 9 | Portfolio theory and asset allocation | Rebuild the Tallow Creek frontier from blank cells; redo self-test in mba/mba-portfolio-theory-card | | 10 | Asset pricing and factor models | Run CAPM and three-factor regressions on one fund from scratch; explain each coefficient aloud | | 11 | Fixed income and derivatives | Bond price, duration and convexity drills; a futures hedge ratio; a protective put payoff | | 12 | Performance evaluation, mixed practice | Timed past-exam questions across topics; log misses in mba/mba-error-log | | 13 | Full mock exam | One timed paper under exam conditions, then review errors only (mba/mba-exam-prep) | ## Common struggles 1. **Matrix algebra in spreadsheets.** Practise `MMULT`, `MINVERSE` and `TRANSPOSE` on a 3 x 3 case until it is routine (mba/pre-mba-excel-modeling-drills). 2. **Units and annualisation.** Monthly versus annual, variance versus volatility, percent versus decimal. Write the unit next to every input cell. 3. **Treating inputs as facts.** Expected returns are estimates with large errors; always show sensitivity. 4. **Reading regressions.** Confusing statistical significance with economic size, and the LINEST reverse order. 5. **Bond conventions.** Coupon frequency, clean versus dirty prices, Macaulay versus modified duration. 6. **Forgetting the owner.** A technically optimal portfolio that ignores liabilities, liquidity or fees is wrong for the case. 7. **Arithmetic versus geometric returns.** Use the arithmetic mean for one-period expectations and the geometric mean for compound growth and spending sustainability. ## Reading list - Core textbook choices (by name only): Bodie, Z., Kane, A., and Marcus, A. J., *Investments*; Elton, E. J., Gruber, M. J., Brown, S. J., and Goetzmann, W. N., *Modern Portfolio Theory and Investment Analysis*; Ang, A., *Asset Management: A Systematic Approach to Factor Investing*. - Fixed income: Fabozzi, F. J., *Bond Markets, Analysis, and Strategies*. - Active management: Grinold, R. C., and Kahn, R. N., *Active Portfolio Management*. - Endowment and foundation investing: Swensen, D. F., *Pioneering Portfolio Management*. - Market history: Dimson, E., Marsh, P., and Staunton, M., *Triumph of the Optimists*. - Open resource: OpenStax, *Principles of Finance* (CC BY-NC-SA 4.0). - Performance presentation (dated fact): as of October 2026, the current Global Investment Performance Standards (GIPS) are the 2020 edition published by CFA Institute (effective 1 January 2020), with separate sets for firms, asset owners and verifiers, plus guidance statements and Q&As (check gipsstandards.org for the current versions before you rely on them; finance/performance-composite-report). - Factor data (dated fact): as of October 2026 the Kenneth R. French Data Library publishes free three-factor, five-factor and momentum returns (check the current files on the library page). ## Self-test questions 1. A share bought at 100 pays a dividend of 3 and is sold at 110. What is the holding-period return? 2. A portfolio returned 7% nominal with inflation of 2.5%. What is the real return? 3. An asset gains 50% then loses 50%. What are the arithmetic and geometric mean returns? Which tells you how much money you have? 4. A fund returned 9% with volatility 15% and beta 1.2; the risk-free rate is 3%. Compute its Sharpe and Treynor ratios. 5. With a market return of 8%, what is the fund's Jensen alpha? What if the fund had returned 10.5%? 6. State the three forms of market efficiency and one piece of evidence that challenges the weak form. 7. Why does the tangency portfolio not necessarily suit an owner with a high required return and no ability to borrow? 8. What does a positive CAPM alpha and a zero three-factor alpha with a positive SMB loading tell you? 9. Why should a liability due in two years be matched with bonds rather than held in the long-term pool? 10. Interleaving: which measure would you use? (a) Ranking a fund that is the investor's whole portfolio. (b) Ranking a fund that is one of many in a diversified portfolio. (c) Judging an active manager against a benchmark. ## My notes and next steps | Item | My entry | |---|---| | Why I am taking this elective, and the career track it supports | [ ] | | Weakest prerequisite and the plan to fix it | [ ] | | Sessions I found hardest | [ ] | | Mistakes logged in mba/mba-error-log | [Date and short description] | | Next review date | YYYY-MM-DD | | Next elective or card | [mba/mba-derivatives-risk-guide / mba/mba-electives-roadmap] | ## Sources and further reading - Macaulay, F. R. (1938). *Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856*. National Bureau of Economic Research. - Markowitz, H. (1952). Portfolio selection. *The Journal of Finance*, 7(1), 77-91. - Tobin, J. (1958). Liquidity preference as behavior towards risk. *The Review of Economic Studies*, 25(2), 65-86. - Sharpe, W. F. (1963). A simplified model for portfolio analysis. *Management Science*, 9(2), 277-293. - Sharpe, W. F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. *The Journal of Finance*, 19(3), 425-442. - Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. *The Review of Economics and Statistics*, 47(1), 13-37. - Treynor, J. L. (1965). How to rate management of investment funds. *Harvard Business Review*, 43(1). - Sharpe, W. F. (1966). Mutual fund performance. *The Journal of Business*, 39(1, Part 2), 119-138. - Jensen, M. C. (1968). The performance of mutual funds in the period 1945-1964. *The Journal of Finance*, 23(2), 389-416. - Fama, E. F. (1970). Efficient capital markets: a review of theory and empirical work. *The Journal of Finance*, 25(2), 383-417. - Treynor, J. L., and Black, F. (1973). How to use security analysis to improve portfolio selection. *The Journal of Business*, 46(1), 66-86. - Ross, S. A. (1976). The arbitrage theory of capital asset pricing. *Journal of Economic Theory*, 13(3), 341-360. - Brinson, G. P., Hood, L. R., and Beebower, G. L. (1986). Determinants of portfolio performance. *Financial Analysts Journal*, 42(4), 39-44. - Black, F., and Litterman, R. (1992). Global portfolio optimization. *Financial Analysts Journal*, 48(5), 28-43. - Fama, E. F., and French, K. R. (1993). Common risk factors in the returns on stocks and bonds. *Journal of Financial Economics*, 33(1), 3-56. - Jegadeesh, N., and Titman, S. (1993). Returns to buying winners and selling losers: implications for stock market efficiency. *The Journal of Finance*, 48(1), 65-91. - Carhart, M. M. (1997). On persistence in mutual fund performance. *The Journal of Finance*, 52(1), 57-82. - Fama, E. F., and French, K. R. (2015). A five-factor asset pricing model. *Journal of Financial Economics*, 116(1), 1-22. - CFA Institute. Global Investment Performance Standards (GIPS), 2020 edition, effective 1 January 2020, gipsstandards.org (checked October 2026). - Kenneth R. French Data Library, Tuck School of Business at Dartmouth (named as a data source; checked October 2026). ## Answer key 1. $(110 - 100 + 3) / 100 = 13\%$. 2. $1.07 / 1.025 - 1 = 4.39\%$ (4.3902%); Excel `=1.07/1.025-1`. The shortcut $7\% - 2.5\% = 4.5\%$ slightly overstates it. 3. Arithmetic mean 0%; geometric mean $\sqrt{1.5 \times 0.5} - 1 = -13.40\%$; Excel `=GEOMEAN(1.5,0.5)-1`. The geometric mean tells you what happened to your money: 100 became 75. 4. Sharpe $(9\% - 3\%) / 15\% = 0.40$; Treynor $(9\% - 3\%) / 1.2 = 5.0$ percentage points per unit of beta. 5. $9\% - [3\% + 1.2 \times (8\% - 3\%)] = 0.00\%$: no alpha. At 10.5%, alpha is 1.50%. 6. Weak form (past prices), semi-strong (all public information), strong (all information including private) (Fama 1970). Momentum (Jegadeesh and Titman 1993) challenges the weak form, because past returns predict future returns. 7. Its expected return may be below the owner's requirement; without leverage the owner must move up the frontier towards riskier assets, accepting a lower Sharpe ratio, or change the goal. 8. The CAPM alpha came from a small-cap tilt that the three-factor model prices; it is exposure, not skill beyond the factors. 9. The liability has a fixed date and amount; bonds that mature near the date remove market and interest-rate risk, while the long-term pool could be down by a large amount when the payment falls due. 10. (a) Sharpe ratio (total risk matters). (b) Treynor ratio or Jensen's alpha (only systematic risk matters in a diversified whole). (c) Information ratio (active return per unit of tracking error). ## Revision history | Version | Date | Author | Change summary | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Your name] | First plan for the term | | 0.2 | YYYY-MM-DD | [Your name] | *Example:* Replaced Example sessions with the syllabus | ## Standard and licence note Based on the investment theory in the primary works listed above (Markowitz 1952 to Fama and French 2015) and, for presentation standards, on the publicly described structure of the GIPS standards. The text, mini-case, exhibits, numbers and questions are original; no published case or textbook text is copied or paraphrased. The Tallow Creek Medical Center Foundation, its people and Manager K are fictional, and all capital market assumptions are *Example* values, not forecasts. Session order and grading are typical examples, not any school's syllabus; the template is independent and not affiliated with or endorsed by any business school, CFA Institute, publisher or data provider. Check current official versions and data before you rely on them. Template licence: MIT.