Universitas Scholarium — A Community of Scholars Log In
← All Courses
Tutorial Course

Investment and Portfolio Theory

Led by Benjamin Graham Simulacrum

8 modules 8 modules · ~14 hours Accounting & Business Updated yesterday

Eight tutorials on the theory and practice of investment and portfolio construction, drawing on the four foundational voices of twentieth-century investment thinking. Benjamin Graham Simulacrum leads — the father of value investing, on intrinsic value and security analysis. He is joined by Harry Markowitz Simulacrum (Modern Portfolio Theory and the efficient frontier), William Sharpe Simulacrum (CAPM and the Sharpe ratio), and John Bogle Simulacrum (the empirical case for index investing and the cost discipline). Stage 3 of the Accounting & Finance (UK) programme.

Courses are available to holders of a paid pass or membership. See passes & membership →

Value Investing Foun…1Security Analysis at…2Modern Portfolio The…3CAPM and the Sharpe …4The Efficient Market…5The Index Investing …6Bonds, Yield Curves,…7Asset Allocation and…8
  1. Module 1 ○ Open

    Value Investing Foundations · Intrinsic Value, Margin of Safety, Mr Market

    Led by Benjamin Graham Simulacrum

    The question

    An introduction to value investing as Benjamin Graham developed it. Graham Simulacrum covers the three foundational propositions — intrinsic value, margin of safety, and the Mr Market metaphor — and the two investor categories Graham identified (the defensive investor working from quantitative criteria; the enterprising investor pursuing more ambitious strategies). The module covers Graham's defensive-investor screen (size, financial condition, earnings stability, dividend record, moderate multiples), the Graham Number as a back-of-envelope intrinsic-value indicator, and the integration with modern UK markets.

    Outcome

    The student can articulate the three Graham principles (intrinsic value, margin of safety, Mr Market); can apply the defensive-investor quantitative criteria to a list of UK-listed equities; can calculate the Graham Number for a hypothetical security; and can distinguish investment from speculation in Graham's terms. (Value investing foundations)

    Practice scenarios

    Screening the FTSE 100 on Defensive Criteria

    You take Graham's defensive-investor criteria and apply them to a 5-year extract of FTSE 100 fundamentals — size, financial condition, earnings stability, dividend record, moderate multiples — to produce a shortlist of names passing all five tests. The work tests whether you can apply a disciplined quantitative screen and resist a growth-portfolio-manager's challenge to *why have you excluded all the technology names*.

    Your goals

    • Apply the size test (FTSE 100 by definition; all pass).
    • Apply the financial-condition test: current ratio ≥ 2:1; total debt < 2× equity. Hand-pick from a sample of 30 (e.g. Unilever, AstraZeneca, GSK, BP, Shell, Diageo, Tesco, Sainsbury's, Vodafone, BT, Reckitt, Imperial Brands, BAT, Legal & General, Aviva, Persimmon, Taylor Wimpey, Berkeley, Schroders, St James's Place, Barratt, Whitbread, BAE Systems, Rolls-Royce, Pearson, Compass, Bunzl, Smith & Nephew, Croda, Halma).
    • Apply the earnings-stability test: positive earnings every year for past 5 (proxy for 10).
    • Apply the dividend record test: dividend paid every year for past 5 (proxy for 20).
    • Apply the moderate-multiples test: P/E < 15× of past 3-year average earnings; P/B < 1.5×.
    • Produce the shortlist and the Graham Number for each surviving name.
    • Frame as a 700-word memo for a defensive investor's portfolio committee.
  2. Module 2 ○ Open

    Security Analysis at Depth · Discounted Cash Flow, Multiples, Forensic Reading

    Led by Benjamin Graham Simulacrum

    The question

    Security analysis at depth — moving from Graham's screen to a justified estimate of intrinsic value for a specific UK-listed equity. The module covers discounted-cash-flow modelling end-to-end (free-cashflow definition, explicit forecast period, terminal value, WACC), comparable-company analysis with appropriate peer selection, asset-based valuation including Graham's net-net concept, and the forensic reading of accounts for quality-of-earnings concerns. The Beneish M-Score, Altman Z-Score, and Piotroski F-Score are introduced as quantitative screens.

    Outcome

    The student can build a 5-year DCF for a UK-listed company including terminal value and WACC; can perform a comparable-company analysis with a defensible peer group; can read a set of accounts forensically for quality-of-earnings concerns; and can produce a one-page investment thesis with a defensible target price. (Security analysis at depth)

    Practice scenarios

    Equity Research Note on a UK Mid-Cap

    You produce an equity research note on a fictional UK mid-cap industrial firm, Stannary Engineering plc, with declining margins and trading at a P/E of 9× against a sector median of 12×. The work tests whether you can build a 5-year DCF, cross-check with comparable multiples, conduct forensic reading of the accounts for quality-of-earnings concerns, and frame a defensible buy/hold/sell recommendation under sceptical-portfolio-committee challenge.

    Your goals

    • Build a 5-year DCF: revenue trajectory (assume slow recovery in margins from current 8% to 10% by year 5), capex sustaining current asset base, working capital stable, terminal growth 2.5%, WACC 8.5% (illustrative for a mid-cap industrial).
    • Cross-check with comparable multiples: at 11× P/E (modest discount to sector median 12×) and 6.5× EV/EBITDA (modest discount to sector median 7×), what target price emerges?
    • Conduct forensic reading: (a) the goodwill from the acquisition — is it impairment-tested rigorously? what is the recoverable amount headroom? (b) the margin decline — pricing pressure, cost inflation, mix shift? (c) the cash conversion — is operating cash flow keeping pace with reported earnings or diverging? (d) working capital trends — receivables and inventory growth.
    • Identify the investment thesis: undervalued vs sector on multiple grounds (P/E 9× vs 12×; EV/EBITDA 5.5× vs 7×); margin recovery feasible if pricing power restored; goodwill-impairment risk as a downside (sized: if full impairment, equity value reduces by ~15%).
    • Recommend: *Buy* with target price set at the lower of DCF and comparable values; sized risks; key catalysts (interim results showing margin stabilisation; debt reduction); time horizon 18 months.
    • Frame as a 1,500-word equity research note with one-page summary.
  3. Module 3 ○ Open

    Modern Portfolio Theory · Diversification and the Efficient Frontier

    Led by Harry Markowitz Simulacrum, with Benjamin Graham Simulacrum on the limits

    The question

    Modern Portfolio Theory as Markowitz developed it. Markowitz Simulacrum covers the mathematical structure of portfolio risk and return, the role of covariance in driving portfolio variance, the efficient frontier as the locus of optimal portfolios, the minimum-variance portfolio, the tangency portfolio when a risk-free asset is available, and Tobin's separation theorem. The practical limits of mean-variance optimisation (the Markowitz curse, instability of inputs, the Black-Litterman and resampled-frontier responses) close the module.

    Outcome

    The student can calculate portfolio expected return and variance from constituent estimates and a correlation matrix; can identify the efficient frontier conceptually for a small set of candidate securities; and can articulate Tobin's separation theorem and its practical implication for asset allocation. (Modern Portfolio Theory)

    Practice scenarios

    Building an Efficient Frontier for a Three-Asset Portfolio

    You construct an efficient frontier for a three-asset portfolio (UK equity, gilts, corporate bonds) given expected returns, standard deviations, and correlations, and identify the minimum-variance portfolio plus the tangency portfolio at a 3.5% risk-free rate. The work tests whether you can apply mean-variance optimisation in practice and respond to a CIO's reasonable scepticism about input-estimate sensitivity.

    Your goals

    • Build the covariance matrix from the SDs and correlations.
    • For each target expected return (5.0%, 5.5%, 6.0%, 6.5%, 7.0%), solve for the weights minimising portfolio variance subject to the return constraint and the constraint Σwi = 1. (Closed-form solution for 3 assets; or use Lagrangian.)
    • Calculate the portfolio variance and SD for each.
    • Identify the minimum-variance portfolio (lowest SD across all return levels).
    • Identify the *tangency portfolio* assuming risk-free rate of 3.5%: maximise (E(Rp) − 3.5%) / SD(Rp).
    • Calculate the Sharpe ratio (Module 4 ahead) for each.
    • Frame as a 1,000-word memo for an asset-allocation committee.
  4. Module 4 ○ Open

    CAPM and the Sharpe Ratio · Pricing Risk

    Led by William Sharpe Simulacrum

    The question

    The Capital Asset Pricing Model and the Sharpe ratio. Sharpe Simulacrum covers the CAPM equation in detail, the calculation and interpretation of beta, the security market line, the difference between systematic and idiosyncratic risk, and the practical use of CAPM for cost-of-equity estimation in DCF and for portfolio performance attribution. The Sharpe ratio, Treynor ratio, Jensen's alpha, and information ratio are introduced; the Fama-French and Carhart factor extensions and their empirical motivation close the module.

    Outcome

    The student can calculate beta from a return regression; can apply CAPM to estimate cost of equity for a UK-listed firm; can calculate Sharpe ratio for a portfolio against a benchmark; and can articulate the Fama-French factor extension and its empirical motivation. (CAPM and Sharpe ratio)

    Practice scenarios

    Cost of Equity for Halberd plc and Performance Evaluation

    You estimate cost of equity for Halberd plc using CAPM with five years of regression data, then evaluate the performance of a fund holding Halberd against the FTSE All-Share including Sharpe ratio comparison and Jensen's alpha calculation. The work tests whether you can link CAPM theory to the practical attribution work that drives institutional fund-allocation decisions.

    Your goals

    • Run the regression of Halberd's monthly excess returns on FTSE All-Share excess returns; obtain beta. (Provide hypothetical numbers — assume β = 1.15, R² = 0.62.)
    • Calculate cost of equity for Halberd: Re = 4.0% + 1.15 × 5.5% = 10.3%.
    • Calculate Halberd's Sharpe ratio (using the fund's 5-year results as the relevant proxy if the fund holds Halberd as a key position): (9.2% − 3.5%) / 14% = 0.41.
    • Calculate the FTSE All-Share Sharpe ratio for the same period: (7.5% − 3.5%) / 13% = 0.31.
    • Calculate Jensen's alpha for the fund: assume fund beta is 1.05; expected return per CAPM = 3.5% + 1.05 × (7.5% − 3.5%) = 7.7%; alpha = 9.2% − 7.7% = +1.5% per year.
    • Recommend on the fund's performance: positive alpha, materially better Sharpe than benchmark, but Sharpe of 0.41 is modest by absolute standards; further attribution analysis required to determine whether the alpha came from stock selection (good) or factor exposure unrelated to skill (less informative).
    • Frame as a 1,000-word performance evaluation memo.
  5. Module 5 ○ Open

    The Efficient Markets Hypothesis · Three Forms and the Active-Passive Debate

    Led by William Sharpe Simulacrum and John Bogle Simulacrum jointly, with Benjamin Graham Simulacrum on the dissent

    The question

    The Efficient Markets Hypothesis and the active-vs-passive debate. Sharpe Simulacrum and Bogle Simulacrum cover the three forms of market efficiency (weak, semi-strong, strong) and the empirical evidence for each, the major documented anomalies (value, small-cap, momentum, low-volatility, post-earnings-announcement drift), the Grossman-Stiglitz paradox of perfect efficiency, and Bogle's cost-arithmetic case for passive investing. The SPIVA evidence and the practical implications for institutional and retail investors close the module.

    Outcome

    The student can articulate the three forms of EMH and the empirical evidence for each; can identify the major documented anomalies and their persistence; and can structure a coherent position in the active-vs-passive debate appropriate to a specific investment context. (Efficient markets hypothesis)

    Practice scenarios

    Briefing a Pension Trustee Board on Active vs Passive

    You brief the trustee board of a £2bn UK DB pension fund considering a shift from active to passive UK equity, given a 10-year underperformance of 1.2% per year against the index. The work tests whether you can structure the SPIVA evidence into a defensible recommendation and navigate the resistance of a board chair who has championed active management for 15 years.

    Your goals

    • Frame the data: active equity has underperformed passive equity by 120 bps annually; consistent with SPIVA findings; the underperformance is roughly equal to the fee differential.
    • Recommend: shift the UK equity from active to passive (or core-satellite — 80% passive, 20% high-conviction active); save ~55 bps annually = ~£5.5m on the £1bn UK equity allocation.
    • Address the bond allocation: the case for active fixed-income management is stronger; recommend keeping bonds active but with closer benchmarking and active-share scrutiny.
    • Address the global equity allocation: passive is appropriate for developed markets; consider adding small-cap or emerging-markets active satellites (the markets where active management has stronger empirical case).
    • Present the cost-saving as net-of-tracking-risk: passive accepts benchmark return; active brings tracking error in either direction; given the 10-year underperformance, the asymmetry favours passive.
    • Frame as a 1,500-word trustee paper structured for a 90-minute board discussion.
  6. Module 6 ○ Open

    The Index Investing Case · Vanguard, Costs, and the Long Arithmetic

    Led by John Bogle Simulacrum

    The question

    John Bogle's case for index investing — the empirical, mathematical, and structural argument that has reshaped global investment practice. Bogle Simulacrum covers the cost-arithmetic of fee differentials over multi-decade horizons (a 1.5% fee differential compounds to ~30% of terminal wealth over 30 years), survivorship bias, the behaviour gap between investor and fund returns, Vanguard's mutual-ownership innovation, and the design of a core-and-satellite portfolio that operationalises the index investing case while leaving room for active management in defensible niches.

    Outcome

    The student can perform the cost-arithmetic of fee differentials over multi-decade horizons; can identify the Bogle structural arguments (cost compounding, survivorship bias, behaviour gap); and can construct a core-and-satellite portfolio that operationalises the index investing case while leaving room for selective active management in defensible niches. (The index investing case)

    Practice scenarios

    Designing a £100k 30-Year Retirement Portfolio

    You design a £100k 30-year retirement portfolio for a 35-year-old UK professional, minimising lifetime cost while delivering an appropriate risk-return profile. The work tests whether you can apply Bogle's principles in practice — asset allocation, vehicle selection, weighted-average expense ratio, rebalancing protocol — and defend the recommendation against an active-fund-advisor brother-in-law's predictable challenge.

    Your goals

    • Recommend asset allocation: 75% global equity, 20% bonds, 5% cash; rebalanced annually.
    • Within global equity: split 65% global developed (passive index ETF, expense ratio ~0.15%); 10% emerging markets (passive ETF, ~0.20%); avoid active funds in developed markets given the cost differential.
    • Within bonds: 60% UK gilts ladder or gilt index (passive, ~0.10%); 40% global investment-grade credit (passive, ~0.15%).
    • Calculate weighted-average expense ratio: ~0.14% all-in.
    • Calculate terminal value at 6% nominal pre-fee return over 30 years: £574k vs alternative active-fund portfolio at 1.0% expense: £461k. Cost saving: £113k or 25% of terminal.
    • Recommend the rebalancing protocol: annually, threshold-based (rebalance only if allocation drifts >5% from target).
    • Frame as a 1,000-word client-facing investment plan.
  7. Module 7 ○ Open

    Bonds, Yield Curves, and Fixed-Income Strategy

    Led by Benjamin Graham Simulacrum

    The question

    Bonds and fixed-income strategy — the larger half of capital markets and the dominant institutional asset class. The module covers bond pricing and yield-to-maturity, duration and convexity as sensitivity measures, the yield curve and what its shape signals about economic expectations, credit spreads and credit ratings, the major bond types (gilts, corporate IG, high-yield, EM, index-linked, FRNs), portfolio strategies (bullet, barbell, ladder, immunisation), and liability-driven investment for UK DB pension funds. The September 2022 UK gilt crisis runs as a case study in LDI structural risk.

    Outcome

    The student can price a vanilla coupon bond given a target yield, calculate duration and modified duration, interpret a yield-curve shape, and design a bond portfolio appropriate to a stated objective (income, immunisation, total return). (Fixed income)

    Practice scenarios

    Designing the Bond Allocation for a UK DB Pension Fund

    You design the bond allocation for a £1bn UK DB pension fund seeking to immunise £30m/year of inflation-indexed liabilities for 30 years, including consideration of LDI leverage and collateral structure. The work tests whether you can construct a duration-matched portfolio, design a credible LDI structure that survives a 2022-style gilt crisis, and brief a sceptical trustee through the design.

    Your goals

    • Calculate the present value of the liabilities at a representative discount rate (e.g. 4% real, 6% nominal): inflation-adjusted £30m × 30 years; PV approximately £680m at 4% real.
    • Recommend the asset structure: 60% index-linked gilts (matching the inflation linkage of the liabilities); 30% nominal gilts (for residual fixed payments); 10% investment-grade credit (modest credit spread for return enhancement, with attention to liquidity).
    • Within index-linked gilts: ladder across maturities to match the liability duration profile (average liability duration ~12 years; bond ladder spanning 1y to 30y).
    • Address the LDI question: the fund could amplify the duration match using gilt repo or interest-rate swaps (typical pre-2022 LDI structure); but the September 2022 crisis demonstrated the leverage-and-collateral risks; recommend an unlevered or modestly levered LDI structure with explicit collateral buffer.
    • Calculate the headroom against funding stress: in a 100bp rate shock, the duration-matched portfolio should hold its funding ratio approximately constant; in a credit-spread widening, a small loss; in a 2022-style gilt crisis, a substantial collateral call if levered.
    • Frame as a 1,500-word trustee paper for a 2-hour board discussion.
  8. Module 8 ○ Open

    Asset Allocation and Portfolio Construction

    Led by Benjamin Graham Simulacrum, with all four host simulacra contributing

    The question

    Asset allocation and portfolio construction — the highest-level investment decision, empirically explaining ~90% of return variability. The closing module integrates the previous seven into the practical work of building portfolios for three reference investor profiles (the young accumulator, the pre-retirement individual, the institutional endowment). All four host simulacra contribute: Markowitz on the framework, Sharpe on the factor structure, Bogle on the cost discipline, Graham on the bottom-up. Strategic vs tactical allocation, rebalancing protocols, and tax-aware asset location close the course.

    Outcome

    The student can design a strategic asset allocation appropriate to a stated investor profile (age, horizon, objective, risk tolerance); can select appropriate vehicles (active or passive) within each allocation bucket; can specify a rebalancing protocol; and can articulate the integration of value-investing security analysis, MPT diversification, CAPM cost of capital, and indexing cost discipline. (Asset allocation and portfolio construction)

    Practice scenarios

    Three Investor Profiles

    You design strategic asset allocations for three reference investor profiles — a 32-year-old professional, a 58-year-old pre-retirement couple, and a £1.5bn perpetual endowment — and frame each as an investment policy statement. The work tests whether you can integrate value-investing, MPT, CAPM, and indexing principles into coherent portfolios appropriate to materially different objectives, horizons, and risk tolerances.

    Your goals

    • Profile A allocation: 85% global equity (60% global developed passive index, 15% emerging markets passive, 10% UK active value/quality satellite for Graham-style upside); 10% bonds (UK gilts + global aggregate index); 5% cash. WAER ~0.20%. Annual rebalancing. Continue full equity-weighting until age 45, begin de-risking trajectory.
    • Profile B allocation: 60% equity (45% global developed passive, 10% UK passive, 5% emerging markets passive); 35% bonds (mix of gilts ladder, index-linked gilts for inflation protection, investment-grade credit); 5% cash. WAER ~0.18%. Annual rebalancing. Set explicit de-risking glide path: 5% equity-to-bond shift every 3 years to age 65, then maintain.
    • Profile C allocation (endowment): 60% public equity (35% global developed, 10% UK, 10% emerging, 5% small-cap); 15% private markets (private equity + infrastructure); 10% absolute return / hedge funds; 10% real assets (real estate, natural resources); 5% fixed income (treasury / cash for liquidity). The Yale-influenced model with disciplined illiquid-asset allocation; explicit recognition of liquidity constraint (≤25% in illiquids); spending rule (e.g. 4% smoothed); rebalancing toward strategic targets annually.
    • Frame each as a 1,500-word investment policy statement.