Unit 4: Portfolio theory and derivatives

Harry Markowitz (1952) showed that portfolio risk depends on the covariance between securities, not just their individual risks.

• Efficient frontier: the set of portfolios offering the highest return for each level of risk; rational investors choose a point on it based on their indifference curves.
• Assumptions: investors are risk-averse, decisions based on mean and variance, single-period horizon.

• Adding a risk-free asset gives the Capital Market Line (CML) — a straight line from Rf tangent to the efficient frontier at the market portfolio (M).

• CAPM assumptions: perfect markets, homogeneous expectations, borrowing and lending at Rf, no taxes, single period.

• Assumption: securities move together only because of a common factor — the market index.

• Advantage over Markowitz: needs only 3n + 2 estimates instead of n(n + 3)/2.
• Sharpe's optimal portfolio: rank stocks by excess return to beta (Ri − Rf)/βi and include those above a cut-off rate C*.

• Stephen Ross (1976): expected return depends on several systematic factors, not just the market.

• Factors: inflation, industrial production, interest rate term structure, default risk premium, oil prices, exchange rates.
• Based on no-arbitrage — two portfolios with the same factor exposures must offer the same return.
• Vs CAPM: fewer assumptions, multiple factors, no need for the market portfolio; but factors are not specified by theory.
• Arbitrage portfolio: requires no investment (weights sum to zero), has zero sensitivity to factors, yet earns a positive return — its existence means securities are mispriced; arbitrage trading removes it.

Efficient Market Hypothesis (Eugene Fama, 1970): security prices fully reflect all available information; hence consistently earning above-normal returns is not possible.

• Tests: weak form — serial correlation, runs tests, filter rules; semi-strong — event studies (earnings, splits, bonus); strong form — performance of insiders and fund managers.
• Random Walk Theory (Malkiel): successive price changes are independent and random, so past prices cannot predict future prices — consistent with weak-form efficiency.
• Evidence and anomalies: January effect, small-firm effect, momentum, value premium, bubbles — and behavioural finance explanations (overconfidence, herding).
• Implications: passive investing (index funds), diversification, low-cost strategies.

• Behavioural finance studies how psychological biases cause investors to deviate from rational behaviour and markets to deviate from efficiency.

• Prospect theory (Kahneman and Tversky, 1979): people value gains and losses relative to a reference point, are risk-averse for gains and risk-seeking for losses.
• Anomalies: January effect, momentum, value premium, post-earnings announcement drift.

A derivative is a contract whose value is derived from an underlying asset — shares, indices, currencies, commodities or interest rates.

• Uses: hedging, speculation, arbitrage, price discovery.
• Types: forwards, futures, options and swaps. Equity derivatives in India trade on NSE (Nifty and stock futures and options) and BSE.

• Call option: right, not obligation, to buy at the strike price. Put option: right to sell at the strike price. The buyer pays a premium; the writer (seller) receives it and has the obligation.
• European options are exercised only at expiry (index and stock options in India); American options at any time up to expiry.
• Moneyness: in the money, at the money, out of the money.

• Option value: intrinsic value + time value; determinants — spot price, strike, time to expiry, volatility, interest rate (Black–Scholes model).
• Strategies: protective put, covered call, straddle, strangle, spreads.