Chapter 6 · Investment Management

The risk-adjusted return on a portfolio must exceed the time value of money (the risk-free rate) PLUS a premium for the risks taken. If it doesn't, you'd be better off in T-bills.

The risk-free rate is typically proxied by short-dated government bonds of the highest-quality issuers (US T-bills, UK gilts). It's the floor for required returns — no rational investor takes risk to earn less than the risk-free rate.

The equity risk premium is the extra return investors demand to hold equities over the risk-free rate. Historically about 4–6% per year for developed markets, though the figure varies hugely depending on the period measured.

• Standard deviation (σ) — total volatility of returns (systematic + specific)
• Beta (β) — sensitivity to MARKET movements. β = 1 moves with market; β > 1 amplifies; β < 1 dampens. Measures only systematic risk.
• Correlation (ρ) — how two assets move relative to each other. Range −1 to +1. Lower correlation = more diversification benefit.

• β = 1.0 — moves with the market on average
• β = 0.5 — moves half as much as the market. Defensive — suitable for cautious investors.
• β = 1.5 — moves 1.5× the market. Aggressive — suitable for risk-tolerant investors.
• β = 2.5 — VERY aggressive. Recommending this for a cautious investor would be a clear suitability breach.
• β < 0 — moves OPPOSITE to the market. Rare, often associated with gold mining stocks or short-funds.

Alpha (α) is the realised return MINUS the return that would have been expected given the portfolio's beta exposure (eg, via CAPM). Positive alpha = outperformance after accounting for risk taken. Negative alpha = underperformance.

Alpha can come from skill (good stock picking, market timing) OR from luck. Distinguishing the two is hard and requires long sample periods.

Combining assets reduces portfolio variance most powerfully when their correlation is LOW or NEGATIVE.

• Correlation +1 → no diversification benefit (both move together)
• Correlation 0 → meaningful benefit (independent movements)
• Correlation −1 → maximum benefit (movements cancel)

Adding international equities, government bonds, gold, or REITs to a domestic equity portfolio typically lowers overall portfolio risk for any given level of expected return.

MPT (Harry Markowitz, 1952 — Nobel Prize 1990) says investors should choose portfolios that maximise expected return for a given level of risk (variance), or minimise risk for a given expected return. The key insights:

• Risk and return should be considered at the portfolio level, not asset by asset
• Adding uncorrelated assets reduces portfolio variance without reducing expected return — "the only free lunch in finance"
• Investors are rewarded only for systematic risk (unsystematic risk can be eliminated by diversification)
• The set of optimal portfolios forms the efficient frontier

Empirical rule from MPT: a reasonably diversified equity portfolio can be achieved with around 15–20 stocks spread across sectors. Beyond that, the marginal diversification benefit is small.

The efficient frontier is the set of all portfolios that offer the highest expected return for each level of risk (or the lowest risk for each level of expected return). Portfolios BELOW the frontier are sub-optimal — there exists another portfolio with higher return at the same risk OR same return at lower risk.

Adding a risk-free asset extends the analysis to the Capital Market Line (CML), which combines the risk-free asset with the market portfolio. Every rational investor should hold some mix of those two.

EMH says asset prices fully reflect available information — so consistently beating the market is hard. Three forms, each stronger than the last:

CAPM gives the required return for an asset as the risk-free rate plus a premium for systematic risk:

Where Rf = risk-free rate, E(Rm) = expected market return, βᵢ = the asset's beta. The term (E(Rm) − Rf) is the equity risk premium.

Key insight: a single factor (the market beta) drives expected return. Higher beta → higher expected return, because the asset carries more non-diversifiable risk.

CAPM assumes:

• Investors are rational, risk-averse, and use mean-variance analysis
• All investors can borrow and lend at the same risk-free rate
• No taxes or transaction costs
• All investors have the same expectations about returns and risk
• Markets are efficient and assets are infinitely divisible

Real-world LIMITATIONS that the exam tests separately:

• Beta is unstable over time
• A single market beta misses other documented risk factors (size, value, momentum, profitability)
• Empirically, low-beta stocks often outperform what CAPM predicts ("low-volatility anomaly")

APT (Ross, 1976) is a multi-factor alternative to CAPM. Expected returns are explained by sensitivities to several systematic factors, not just market beta. Common factors include:

• Inflation rate surprises
• GDP growth surprises
• Interest rate (term spread) changes
• Credit spread changes
• Currency moves

APT is more flexible than CAPM — and arguably more realistic — but harder to use because you have to identify and estimate the factors.

Classical finance assumes investors are rational utility-maximisers. Behavioural finance documents that they systematically aren't — they use mental shortcuts (heuristics) and are subject to emotional and cognitive biases that lead to predictable mispricings.

For ICWIM, you need to recognise the labels for common biases and the scenarios that signal them.

Kahneman & Tversky's Prospect Theory shows people:

• Feel losses about 2× more intensely than gains of the same magnitude (loss aversion)
• Take MORE risk to avoid a sure loss than to chase an equivalent sure gain
• Value outcomes relative to a reference point, not in absolute terms

Implication: investors hold losers too long (hoping to break even) and sell winners too quickly (locking in gains). This is the disposition effect.

A hybrid: hold a low-cost passive "core" (often 60–80% of the portfolio, tracking a broad index) plus smaller "satellite" active positions targeting alpha or specific themes.

Benefits: most of the portfolio gets the cost advantages of indexing; the satellites can pursue conviction ideas without endangering the whole portfolio. Common configuration in modern wealth management.

• Value investing — buy companies trading at low multiples (P/E, P/B), often out of favour. Classic exemplars: Buffett, Graham. Bet: the market has temporarily mispriced.
• Growth investing — buy companies with high expected earnings growth, often at high multiples. Bet: rapid growth will justify (or exceed) the valuation.
• GARP (Growth at a Reasonable Price) — combines both: growing companies but with valuation discipline. Often screens by PEG ratio (P/E ÷ growth rate).
• Momentum — buy what's been going up recently. Empirically the most robust factor over short-to-medium horizons.

Strategic asset allocation (SAA) sets the long-term policy mix (eg, "60% equities / 35% bonds / 5% cash") based on the investor's objectives, risk tolerance and time horizon. Reviewed infrequently — once a year or on major life events.

Tactical asset allocation (TAA) tilts AWAY from the SAA over short-to-medium horizons to exploit market opportunities, then reverts. eg, overweight equities when markets look cheap, underweight when expensive.

ESG integration means incorporating material Environmental, Social and Governance factors into investment analysis and decisions, alongside financial factors. Not a value judgement — just acknowledging that climate risk, regulatory risk, labour practices and board governance affect investment outcomes.

LDI is the natural extension of immunisation for pension funds and insurers: match the asset portfolio's behaviour to the LIABILITIES (often long-dated, inflation-linked) rather than to a market benchmark. Heavy use of long bonds and interest-rate / inflation derivatives.

UK LDI famously suffered in late 2022 when sharply rising gilt yields forced LDI funds to post huge margin calls in a hurry, threatening a doom loop until the Bank of England intervened.

Periodic rebalancing means trimming positions that have grown above target and topping up those that have fallen — restoring the strategic mix. Its purposes are:

• Risk control — without rebalancing, the riskier assets gradually dominate (because they have higher expected returns), pushing risk above the client's tolerance
• Built-in sell-high / buy-low discipline

Rebalancing can be CALENDAR-based (eg, annually) or THRESHOLD-based (rebalance when an asset class drifts more than X% from target).

A benchmark is a reference against which portfolio performance is measured. Should match the portfolio's investment universe and style (eg, FTSE All-Share for UK equity income, MSCI World for global equity).

An inappropriate benchmark — say, comparing a UK equity income portfolio to the S&P 500 — produces misleading conclusions.

The most widely-used risk-adjusted performance measure. Excess return per unit of TOTAL volatility:

HIGHER Sharpe = better risk-adjusted return. Useful for comparing portfolios with different risk levels.

Attribution analysis decomposes a portfolio's excess return over benchmark into contributions from different decisions — typically asset allocation, security selection and interaction effects (the Brinson model).

• Allocation effect — value added by over/underweighting sectors (or asset classes) that out/underperformed the benchmark
• Selection effect — value added by stock-picking WITHIN each sector
• Interaction effect — residual capturing combined effects

Tracking error = the standard deviation of (portfolio return − benchmark return). Measures how closely a portfolio's returns follow its benchmark over time.

For a passive (index) fund, low tracking error is desirable — it means the fund is doing its job. For an active fund, tracking error indicates how MUCH the manager is deviating from the benchmark (necessary for alpha, but also indicates risk relative to benchmark).